1
Unit 1: Geometry & Spatial Understanding • Class 4 Mathematics (New NEP 2020)
Chapter 1: Shapes Around Us
Exploring 2D & 3D Shapes, Faces, Edges, Vertices, Tangrams & Tessellations
Chapter Highlights, Mathematical Ideas & Key Properties
- Distinction between 2D flat shapes (squares, rectangles, circles, triangles) and 3D solid shapes (cubes, cuboids, cylinders, cones, spheres).
- Counting flat faces, curved faces, straight edges, curved edges, and vertices on everyday objects.
- Understanding rolling vs. sliding properties based on curved and flat surfaces.
- Creating pictures and figures using the 7-piece Tangram puzzle.
- Tessellation: Tiling patterns that cover a plane completely without any gaps or overlaps.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Look around your classroom and home. Name two objects each that: (a) Only roll, (b) Only slide, (c) Both roll and slide. Explain the geometric reason for each behavior.
Textbook Exercise • 3D Properties
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Objects that only roll:
• Examples: A cricket ball, a marble, an orange.
• Reason: These objects have only a continuous curved surface and no flat faces or straight edges, so they rotate smoothly over surfaces.
(b) Objects that only slide:
• Examples: A textbook, a rectangular pencil box, an eraser.
• Reason: These objects have only flat planar faces and straight edges. When pushed, a flat face stays in contact with the table and slides without rolling.
(c) Objects that both roll and slide:
• Examples: A one-rupee coin, a water bottle, a round cylindrical marker pen.
• Reason: These objects possess both flat faces and a curved surface. When placed on their flat circular base, they slide; when placed on their curved lateral side, they roll.
• Examples: A cricket ball, a marble, an orange.
• Reason: These objects have only a continuous curved surface and no flat faces or straight edges, so they rotate smoothly over surfaces.
(b) Objects that only slide:
• Examples: A textbook, a rectangular pencil box, an eraser.
• Reason: These objects have only flat planar faces and straight edges. When pushed, a flat face stays in contact with the table and slides without rolling.
(c) Objects that both roll and slide:
• Examples: A one-rupee coin, a water bottle, a round cylindrical marker pen.
• Reason: These objects possess both flat faces and a curved surface. When placed on their flat circular base, they slide; when placed on their curved lateral side, they roll.
CBSE Step-by-Step Marking Scheme
Correct examples for all 3 categories
1.5 M
Scientific explanation relating flat/curved faces to rolling/sliding
1.5 M
Q2
Complete the table by counting the number of faces, edges, and corners (vertices) for: (1) A chalk box (Cube), (2) A matchbox (Cuboid), (3) A new unsharpened pencil (Hexagonal Prism / Cylinder), (4) A football (Sphere).
Textbook Exercise • Geometric Attributes
4 Marks
✅ Step-by-Step Model Answer & Solution:
| Shape / Object | Flat Faces | Curved Faces | Total Edges | Corners (Vertices) |
|---|---|---|---|---|
| 1. Chalk box (Cube) | 6 square faces | 0 | 12 straight edges | 8 corners |
| 2. Matchbox (Cuboid) | 6 rectangular faces | 0 | 12 straight edges | 8 corners |
| 3. Cylinder (Can/Pencil) | 2 circular faces | 1 curved face | 2 curved edges | 0 corners |
| 4. Football (Sphere) | 0 | 1 curved face | 0 edges | 0 corners |
CBSE Step-by-Step Marking Scheme
Correct counts for Cube & Cuboid
2.0 M
Correct counts for Cylinder & Sphere
2.0 M
Q3
What is a Tangram? How many pieces does a standard Chinese tangram have, and which geometric shapes are present in it? Can a circle tessellate on a floor? Why or why not?
Tangram & Tessellation Investigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
1. Tangram Definition & Composition:
A Tangram is a traditional geometric dissection puzzle consisting of a square cut into 7 flat pieces called 'tans':
• 5 Triangles: 2 large right-angled isosceles triangles, 1 medium right-angled triangle, and 2 small right-angled triangles.
• 1 Square: Formed using 2 small triangles.
• 1 Parallelogram: Formed with opposite sides equal and parallel.
2. Can Circles Tessellate?
• Answer: No, circles cannot tessellate.
• Mathematical Reason: Tessellation requires shapes to fit together leaving zero gaps and zero overlaps. When round circular coins or tiles are placed side by side, empty curved spaces (interstices) are always left between them. Therefore, circles cannot tile a flat surface completely.
A Tangram is a traditional geometric dissection puzzle consisting of a square cut into 7 flat pieces called 'tans':
• 5 Triangles: 2 large right-angled isosceles triangles, 1 medium right-angled triangle, and 2 small right-angled triangles.
• 1 Square: Formed using 2 small triangles.
• 1 Parallelogram: Formed with opposite sides equal and parallel.
2. Can Circles Tessellate?
• Answer: No, circles cannot tessellate.
• Mathematical Reason: Tessellation requires shapes to fit together leaving zero gaps and zero overlaps. When round circular coins or tiles are placed side by side, empty curved spaces (interstices) are always left between them. Therefore, circles cannot tile a flat surface completely.
CBSE Step-by-Step Marking Scheme
Correct description of 7 tangram pieces
1.5 M
Logical reason why circles leave gaps and cannot tessellate
1.5 M
Q4
How many faces, edges, and vertices does a cuboid have? Draw or describe the net of an open rectangular box.
3D Shapes • Nets & Vertices
3 Marks
✅ Step-by-Step Model Answer & Solution:
1. Properties of a Cuboid:
• Faces: 6 flat rectangular faces (opposite faces are identical in size).
• Edges: 12 straight edges where two faces meet.
• Vertices (Corners): 8 vertices where three edges meet.
2. Net of an Open Box (without lid):
An open box has 5 faces (1 base + 4 side walls). Its net consists of a central rectangular base surrounded by four rectangular flaps attached to its four sides, forming a cross shape (+). When the four flaps are folded upward at 90°, they form the four walls of the open box.
• Faces: 6 flat rectangular faces (opposite faces are identical in size).
• Edges: 12 straight edges where two faces meet.
• Vertices (Corners): 8 vertices where three edges meet.
2. Net of an Open Box (without lid):
An open box has 5 faces (1 base + 4 side walls). Its net consists of a central rectangular base surrounded by four rectangular flaps attached to its four sides, forming a cross shape (+). When the four flaps are folded upward at 90°, they form the four walls of the open box.
CBSE Step-by-Step Marking Scheme
Correct counts: 6 faces, 12 edges, 8 vertices
1.5 M
Accurate structural description of 5-face cross net
1.5 M
Q5
In Chapter 1 ('Shapes Around Us'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Floor Tiling Design for the School Assembly Hall
Real-World Math Context: The school headmaster wants to tile the newly renovated assembly floor. The mason proposes two tile options: Hexagonal tiles and Pentagonal tiles. Rahul observes that honeycombs in nature use hexagons without any gaps.
Analytical Task: Which of the two shapes (regular hexagon or regular pentagon) will successfully tile the floor without leaving empty gaps? State the geometric reason.
Selected Shape: Regular Hexagon.
Reason: The interior angle of a regular hexagon is 120°. When three hexagons meet at a single vertex point, their angles sum to exactly 120° + 120° + 120° = 360°, which forms a complete flat turn leaving zero gaps. In contrast, regular pentagons have interior angles of 108°; three pentagons sum to 324° (leaving a 36° gap) and four pentagons sum to 432° (overlapping). Hence, between the two proposed options, only the regular hexagon can tile the floor. (Note: In plane geometry, the only regular polygons that can tile a flat surface without gaps are equilateral triangles, squares, and regular hexagons; regular pentagons cannot).
Reason: The interior angle of a regular hexagon is 120°. When three hexagons meet at a single vertex point, their angles sum to exactly 120° + 120° + 120° = 360°, which forms a complete flat turn leaving zero gaps. In contrast, regular pentagons have interior angles of 108°; three pentagons sum to 324° (leaving a 36° gap) and four pentagons sum to 432° (overlapping). Hence, between the two proposed options, only the regular hexagon can tile the floor. (Note: In plane geometry, the only regular polygons that can tile a flat surface without gaps are equilateral triangles, squares, and regular hexagons; regular pentagons cannot).
CBSE Assessment Rubric: 1 Mark for choosing hexagon; 1 Mark for explaining angle sum of 360° at vertex.
2
Unit 1: Spatial Perspectives & Mapping • Class 4 Mathematics (New NEP 2020)
Chapter 2: Hide and Seek
Top View, Front View, Side View, Grid Directions & Spatial Mapping
Chapter Highlights, Mathematical Ideas & Key Properties
- Understanding that 3D objects look different when viewed from different angles: Top View (Plan), Front View (Elevation), and Side View.
- Connecting 2D perspective drawings with actual 3D objects like tables, cars, houses, and shoe boxes.
- Navigating simple grid maps using cardinal directions: North, South, East, West, Left, and Right.
- Solving bird's-eye view problems and matching aerial views with ground elevations.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Draw or describe what the following objects look like from the TOP and from the SIDE: (a) A tea cup, (b) A railway track, (c) A pressure cooker, (d) A staircase.
Perspective Identification
4 Marks
✅ Step-by-Step Model Answer & Solution:
(a) A Tea Cup:
• Top View: A circular rim with a smaller concentric circle inside (the base), and the handle sticking out on one side like a small loop.
• Side View: A curved cylindrical or tapered profile with the full vertical handle visible.
(b) A Railway Track:
• Top View: Two parallel straight lines connected by equidistant perpendicular wooden or concrete rectangular sleepers.
• Side View / Front Perspective: The two tracks appear wide near your feet and converge toward a point in the distance.
(c) A Pressure Cooker:
• Top View: A round circle with a long black handle extending outwards and a central weight (whistle).
• Side View: The body height, curved metal base, safety valve, and side handle profile.
(d) A Staircase:
• Top View: A series of adjacent rectangles of identical width.
• Side View: A zig-zag step pattern (up and across) resembling a stepped right-angled triangle.
• Top View: A circular rim with a smaller concentric circle inside (the base), and the handle sticking out on one side like a small loop.
• Side View: A curved cylindrical or tapered profile with the full vertical handle visible.
(b) A Railway Track:
• Top View: Two parallel straight lines connected by equidistant perpendicular wooden or concrete rectangular sleepers.
• Side View / Front Perspective: The two tracks appear wide near your feet and converge toward a point in the distance.
(c) A Pressure Cooker:
• Top View: A round circle with a long black handle extending outwards and a central weight (whistle).
• Side View: The body height, curved metal base, safety valve, and side handle profile.
(d) A Staircase:
• Top View: A series of adjacent rectangles of identical width.
• Side View: A zig-zag step pattern (up and across) resembling a stepped right-angled triangle.
CBSE Step-by-Step Marking Scheme
Accurate description of top views for all 4 items
2.0 M
Accurate description of side views for all 4 items
2.0 M
Q2
Meera is standing at position (2, 1) on a square grid. She walks 3 steps North and then 4 steps East. (a) What are her new grid coordinates? (b) What is the shortest direct path in total steps along the grid lines back to her starting point?
Grid Map & Navigation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step 1: Finding New Coordinates:
• Starting position: (X = 2, Y = 1).
• Walking 3 steps North increases the Y-coordinate by 3: New Y = 1 + 3 = 4.
• Walking 4 steps East increases the X-coordinate by 4: New X = 2 + 4 = 6.
• Final Coordinates: (6, 4).
Step 2: Shortest path along grid lines back to starting point:
• To return to (2, 1) from (6, 4):
- She must walk 4 steps West (6 - 2 = 4 steps).
- She must walk 3 steps South (4 - 1 = 3 steps).
• Total steps along grid lines = 4 + 3 = 7 steps.
• Starting position: (X = 2, Y = 1).
• Walking 3 steps North increases the Y-coordinate by 3: New Y = 1 + 3 = 4.
• Walking 4 steps East increases the X-coordinate by 4: New X = 2 + 4 = 6.
• Final Coordinates: (6, 4).
Step 2: Shortest path along grid lines back to starting point:
• To return to (2, 1) from (6, 4):
- She must walk 4 steps West (6 - 2 = 4 steps).
- She must walk 3 steps South (4 - 1 = 3 steps).
• Total steps along grid lines = 4 + 3 = 7 steps.
CBSE Step-by-Step Marking Scheme
Correct final coordinate (6, 4) with working
1.5 M
Correct calculation of return steps (7 steps)
1.5 M
Q3
A boy builds a tower using 8 identical unit cubes. If viewed from the front, it looks 4 cubes high and 2 cubes wide. How does the view change when observed from directly above (top view)?
Spatial Perspectives • 3D Block Towers
2 Marks
✅ Step-by-Step Model Answer & Solution:
Top View Analysis:
The top view shows only the arrangement of cubes on the floor grid (the footprint), regardless of their height. If the tower is 2 cubes wide and built against a straight base, the top view shows 2 square faces side by side (a 2 × 1 rectangle). Looking from directly above, the height of 4 cubes cannot be seen; only the roof surface is visible.
The top view shows only the arrangement of cubes on the floor grid (the footprint), regardless of their height. If the tower is 2 cubes wide and built against a straight base, the top view shows 2 square faces side by side (a 2 × 1 rectangle). Looking from directly above, the height of 4 cubes cannot be seen; only the roof surface is visible.
CBSE Step-by-Step Marking Scheme
Top view shows footprint independent of vertical height
1.0 M
Correct geometric representation (2 side-by-side squares)
1.0 M
Q4
On a map grid, a school is at (2, 3) and a playground is at (6, 7). How many units East and how many units North must a child walk to reach the playground from the school?
Coordinate Grids • Route Mapping
2 Marks
✅ Step-by-Step Model Answer & Solution:
Grid Movement Calculation:
• Initial Position (School): X = 2, Y = 3
• Destination (Playground): X = 6, Y = 7
1. Movement East (along X-axis):
6 - 2 = 4 units East.
2. Movement North (along Y-axis):
7 - 3 = 4 units North.
Total distance walked along grid lines = 4 + 4 = 8 units.
• Initial Position (School): X = 2, Y = 3
• Destination (Playground): X = 6, Y = 7
1. Movement East (along X-axis):
6 - 2 = 4 units East.
2. Movement North (along Y-axis):
7 - 3 = 4 units North.
Total distance walked along grid lines = 4 + 4 = 8 units.
CBSE Step-by-Step Marking Scheme
Horizontal calculation (4 units East)
1.0 M
Vertical calculation (4 units North)
1.0 M
Q5
In Chapter 2 ('Hide and Seek'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Drone Photography of the School Sports Ground
Real-World Math Context: A drone flies directly above the sports field and takes an aerial snapshot. The football goalpost, which looks like a tall upside-down U-shaped white frame from the ground, looks like a single thin white horizontal line from the sky.
Analytical Task: Why does the goalpost look like a single thin straight line from above? What happens to the two vertical posts?
Explanation: From directly above (bird's-eye view), the vertical posts align straight downward beneath the crossbar along the camera's line of sight. Therefore, the upright posts appear as tiny dots, while the horizontal crossbar spans across the top, making the entire goalpost look like a single straight line from the air.
CBSE Assessment Rubric: 1 Mark for explaining line of sight; 1 Mark for vertical post alignment.
3
Unit 2: Patterns, Symmetry & Number Rules • Class 4 Mathematics (New NEP 2020)
Chapter 3: Patterns Around Us
Growing Patterns, Repeating Patterns, Rotational Turns & Symmetrical Borders
Chapter Highlights, Mathematical Ideas & Key Properties
- Identifying repeating units (motifs) and generating geometric patterns.
- Understanding rotational turns: Half Turn (180°), Quarter Turn (90°), and Three-Quarter Turn (270°).
- Analyzing growing number sequences involving addition, multiplication, and geometric growth.
- Recognizing patterns in border designs, rangolis, and fabrics.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Find the rule and write the next three terms for each pattern: (a) 7, 14, 21, 28, __, __, __; (b) 2, 4, 8, 16, __, __, __; (c) 1, 4, 9, 16, 25, __, __, __; (d) 100, 92, 84, 76, __, __, __.
Number Sequence Pattern Rules
4 Marks
✅ Step-by-Step Model Answer & Solution:
(a) 7, 14, 21, 28, ...
• Rule: Add 7 to each term (Multiples of 7).
• Next three terms: 28 + 7 = 35, 35 + 7 = 42, 42 + 7 = 49.
(b) 2, 4, 8, 16, ...
• Rule: Multiply each term by 2 (Doubling rule).
• Next three terms: 16 × 2 = 32, 32 × 2 = 64, 64 × 2 = 128.
(c) 1, 4, 9, 16, 25, ...
• Rule: Square numbers (1×1, 2×2, 3×3, 4×4, 5×5) or consecutive odd addition (+3, +5, +7, +9, +11...).
• Next three terms: 6×6 = 36, 7×7 = 49, 8×8 = 64.
(d) 100, 92, 84, 76, ...
• Rule: Subtract 8 from each term.
• Next three terms: 76 - 8 = 68, 68 - 8 = 60, 60 - 8 = 52.
• Rule: Add 7 to each term (Multiples of 7).
• Next three terms: 28 + 7 = 35, 35 + 7 = 42, 42 + 7 = 49.
(b) 2, 4, 8, 16, ...
• Rule: Multiply each term by 2 (Doubling rule).
• Next three terms: 16 × 2 = 32, 32 × 2 = 64, 64 × 2 = 128.
(c) 1, 4, 9, 16, 25, ...
• Rule: Square numbers (1×1, 2×2, 3×3, 4×4, 5×5) or consecutive odd addition (+3, +5, +7, +9, +11...).
• Next three terms: 6×6 = 36, 7×7 = 49, 8×8 = 64.
(d) 100, 92, 84, 76, ...
• Rule: Subtract 8 from each term.
• Next three terms: 76 - 8 = 68, 68 - 8 = 60, 60 - 8 = 52.
CBSE Step-by-Step Marking Scheme
Correct rule and terms for (a) & (b)
2.0 M
Correct rule and terms for (c) & (d)
2.0 M
Q2
Which English capital letters look exactly the same after a HALF TURN (180° rotation)? Test the letters: A, H, I, M, N, O, S, X, Z.
Rotational Symmetry & Letter Turns
3 Marks
✅ Step-by-Step Model Answer & Solution:
Let us test each letter by rotating it upside down by 180°:
• H: Rotates to H (Same) ✅
• I: Rotates to I (Same) ✅
• N: Rotates to N (Same) ✅
• O: Rotates to O (Same) ✅
• S: Rotates to S (Same) ✅
• X: Rotates to X (Same) ✅
• Z: Rotates to Z (Same) ✅
Letters that change:
• A becomes upside down (∀) ❌
• M rotates to W ❌
Conclusion: The letters that look identical after a half turn are H, I, N, O, S, X, and Z.
• H: Rotates to H (Same) ✅
• I: Rotates to I (Same) ✅
• N: Rotates to N (Same) ✅
• O: Rotates to O (Same) ✅
• S: Rotates to S (Same) ✅
• X: Rotates to X (Same) ✅
• Z: Rotates to Z (Same) ✅
Letters that change:
• A becomes upside down (∀) ❌
• M rotates to W ❌
Conclusion: The letters that look identical after a half turn are H, I, N, O, S, X, and Z.
CBSE Step-by-Step Marking Scheme
Correctly identifies all 7 valid letters
2.0 M
Explains why A and M fail
1.0 M
Q3
Observe the pattern of dot arrays: 1, 4, 9, 16... What are the next two numbers in this sequence? Explain the rule.
Number Patterns • Square Numbers
3 Marks
✅ Step-by-Step Model Answer & Solution:
Rule and Next Terms:
1. Rule: These are Square Numbers, formed by multiplying a whole number by itself (or by arranging dots in perfect squares):
• 1 × 1 = 1
• 2 × 2 = 4 (difference +3)
• 3 × 3 = 9 (difference +5)
• 4 × 4 = 16 (difference +7)
2. Next Two Numbers:
• 5 × 5 = 25 (16 + 9)
• 6 × 6 = 36 (25 + 11)
The next two numbers in the sequence are 25 and 36.
1. Rule: These are Square Numbers, formed by multiplying a whole number by itself (or by arranging dots in perfect squares):
• 1 × 1 = 1
• 2 × 2 = 4 (difference +3)
• 3 × 3 = 9 (difference +5)
• 4 × 4 = 16 (difference +7)
2. Next Two Numbers:
• 5 × 5 = 25 (16 + 9)
• 6 × 6 = 36 (25 + 11)
The next two numbers in the sequence are 25 and 36.
CBSE Step-by-Step Marking Scheme
Stating the multiplication rule or consecutive odd additions
1.5 M
Correctly identifying 25 and 36
1.5 M
Q4
If the word 'MATH' is coded as 'N B U I' by shifting each letter forward by one alphabet (A→B, B→C), what is the secret word coded as 'C B M M'?
Secret Codes • Decoding Patterns
2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding the Message:
The encoding rule adds +1 letter. To decode, we reverse the rule by shifting each letter backward by one alphabet (-1):
• C - 1 = B
• B - 1 = A
• M - 1 = L
• M - 1 = L
The original secret word is BALL.
The encoding rule adds +1 letter. To decode, we reverse the rule by shifting each letter backward by one alphabet (-1):
• C - 1 = B
• B - 1 = A
• M - 1 = L
• M - 1 = L
The original secret word is BALL.
CBSE Step-by-Step Marking Scheme
Reversing the +1 rule to -1 letter shift
1.0 M
Accurately decoding to 'BALL'
1.0 M
Q5
In Chapter 3 ('Patterns Around Us'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Secret Spy Code Pattern
Real-World Math Context: Rohan receives an encrypted message: 'GDKKN VNQKC'. The encryption rule shifts every English letter 1 position backward in the alphabet (e.g., B becomes A, C becomes B).
Analytical Task: Decrypt Rohan's secret message using the reverse pattern rule.
Decrypted Message: 'HELLO WORLD'.
Working: To reverse the encryption, we shift each letter 1 step forward in the alphabet:
• G ➔ H, D ➔ E, K ➔ L, K ➔ L, N ➔ O (HELLO)
• V ➔ W, N ➔ O, Q ➔ R, K ➔ L, C ➔ D (WORLD).
Working: To reverse the encryption, we shift each letter 1 step forward in the alphabet:
• G ➔ H, D ➔ E, K ➔ L, K ➔ L, N ➔ O (HELLO)
• V ➔ W, N ➔ O, Q ➔ R, K ➔ L, C ➔ D (WORLD).
CBSE Assessment Rubric: 1 Mark for reverse shift rule; 1 Mark for correct decrypted phrase.
4
Unit 2: Numbers up to 10,000 • Class 4 Mathematics (New NEP 2020)
Chapter 4: Thousands Around Us
Place Value, Face Value, Expanded Form, Number Names & Abacus
Chapter Highlights, Mathematical Ideas & Key Properties
- Extending 3-digit place value to 4-digit numbers: Thousands (Th), Hundreds (H), Tens (T), Ones (O).
- Smallest 4-digit number is 1,000; largest 4-digit number is 9,999.
- Place Value vs. Face Value of digits in a 4-digit number.
- Writing numbers in expanded form and standard form.
- Ordering 4-digit numbers on a number line and comparing using >, <, and =.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
In the numeral 6,835: (a) What is the place value and face value of 8? (b) What is the place value and face value of 6? (c) Write 6,835 in expanded notation and word form.
Place Value vs. Face Value
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) For digit 8:
• Face Value = 8 (the digit itself).
• Place Value = 8 × 100 = 800 (Eight Hundred).
(b) For digit 6:
• Face Value = 6.
• Place Value = 6 × 1,000 = 6,000 (Six Thousand).
(c) Expanded Notation & Word Form:
• Expanded Form: 6,000 + 800 + 30 + 5
• Number Name: Six thousand eight hundred thirty-five.
• Face Value = 8 (the digit itself).
• Place Value = 8 × 100 = 800 (Eight Hundred).
(b) For digit 6:
• Face Value = 6.
• Place Value = 6 × 1,000 = 6,000 (Six Thousand).
(c) Expanded Notation & Word Form:
• Expanded Form: 6,000 + 800 + 30 + 5
• Number Name: Six thousand eight hundred thirty-five.
CBSE Step-by-Step Marking Scheme
Correct place and face value for 8 & 6
1.5 M
Correct expanded form and word name
1.5 M
Q2
Using the digits 3, 0, 7, and 9 only once: (a) Form the largest possible 4-digit number. (b) Form the smallest possible 4-digit number. (c) Find the difference between them.
Number Formation & Comparison
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Largest 4-digit number:
To make the largest number, arrange digits in descending order: 9,730.
(b) Smallest 4-digit number:
We cannot put 0 at the thousands place (or it becomes a 3-digit number). So choose the smallest non-zero digit first (3), followed by 0, then remaining digits in ascending order: 3,079.
(c) Difference:
9,730
- 3,079
--------
6,651
Check: 3,079 + 6,651 = 9,730. Correct!
To make the largest number, arrange digits in descending order: 9,730.
(b) Smallest 4-digit number:
We cannot put 0 at the thousands place (or it becomes a 3-digit number). So choose the smallest non-zero digit first (3), followed by 0, then remaining digits in ascending order: 3,079.
(c) Difference:
9,730
- 3,079
--------
6,651
Check: 3,079 + 6,651 = 9,730. Correct!
CBSE Step-by-Step Marking Scheme
Correct largest number 9,730
1.0 M
Correct smallest number 3,079 (justifying 0 placement)
1.0 M
Accurate subtraction working 6,651
1.0 M
Q3
In the number 7,408: (a) Write its expanded form, (b) Find the difference between the place value and face value of the digit 4.
Place Value & Expanded Form • 4-Digit Numbers
3 Marks
✅ Step-by-Step Model Answer & Solution:
1. Expanded Form:
7,408 = 7,000 + 400 + 0 + 8 (or 7 Thousands + 4 Hundreds + 0 Tens + 8 Ones).
2. Place Value vs. Face Value of 4:
• Place Value of 4: Since 4 is in the hundreds place = 4 × 100 = 400.
• Face Value of 4: The digit itself = 4.
• Difference: 400 - 4 = 396.
7,408 = 7,000 + 400 + 0 + 8 (or 7 Thousands + 4 Hundreds + 0 Tens + 8 Ones).
2. Place Value vs. Face Value of 4:
• Place Value of 4: Since 4 is in the hundreds place = 4 × 100 = 400.
• Face Value of 4: The digit itself = 4.
• Difference: 400 - 4 = 396.
CBSE Step-by-Step Marking Scheme
Correct expanded form
1.5 M
Place value (400), face value (4), difference (396)
1.5 M
Q4
A cricket stadium sold 6,874 tickets on Saturday. Round this attendance to: (a) the nearest 10, (b) the nearest 100, (c) the nearest 1,000.
Estimation • Rounding Numbers
3 Marks
✅ Step-by-Step Model Answer & Solution:
Rounding 6,874:
• (a) Nearest 10: The ones digit is 4 (< 5), so round down to 6,870.
• (b) Nearest 100: The tens digit is 7 (≥ 5), so round up to 6,900.
• (c) Nearest 1,000: The hundreds digit is 8 (≥ 5), so round up to 7,000.
• (a) Nearest 10: The ones digit is 4 (< 5), so round down to 6,870.
• (b) Nearest 100: The tens digit is 7 (≥ 5), so round up to 6,900.
• (c) Nearest 1,000: The hundreds digit is 8 (≥ 5), so round up to 7,000.
CBSE Step-by-Step Marking Scheme
Nearest 10: 6,870
1.0 M
Nearest 100: 6,900
1.0 M
Nearest 1,000: 7,000
1.0 M
Q5
In Chapter 4 ('Thousands Around Us'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Bank Token Display Counter
Real-World Math Context: At a rural bank branch, token numbers run from 1,001 to 2,000. Customer Aman holds token 1,489. Customer Priya holds token 1,512.
Analytical Task: How many tokens are there strictly between Aman's token and Priya's token? Who will be served first?
Aman will be served first because 1,489 < 1,512.
Tokens between them:
1,512 - 1,489 - 1 = 22 tokens strictly between them (from 1,490 to 1,511).
Tokens between them:
1,512 - 1,489 - 1 = 22 tokens strictly between them (from 1,490 to 1,511).
CBSE Assessment Rubric: 1 Mark for identifying Aman served first; 1 Mark for calculating 22 tokens.
5
Unit 3: Operations & Arithmetic Problem Solving • Class 4 Mathematics (New NEP 2020)
Chapter 5: Sharing and Measuring
Equal Sharing, Division Concepts, Quotients, Remainders & Real-Life Grouping
Chapter Highlights, Mathematical Ideas & Key Properties
- Division as equal sharing and repeated subtraction.
- Terms of division: Dividend ÷ Divisor = Quotient with Remainder.
- The division check rule: Dividend = (Divisor × Quotient) + Remainder, where Remainder < Divisor.
- Solving real-world word problems involving distribution of seeds, sweets, and books.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
A farmer packs 148 oranges equally into boxes that hold 6 oranges each. (a) How many full boxes can he pack? (b) How many oranges are left over? (c) Verify your answer using the division verification rule.
Division with Remainder & Verification
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step 1: Perform the division:
We need to calculate 148 ÷ 6.
• Divide 14 by 6: 6 × 2 = 12. Remainder = 14 - 12 = 2.
• Bring down 8 to make 28.
• Divide 28 by 6: 6 × 4 = 24. Remainder = 28 - 24 = 4.
• Quotient = 24, Remainder = 4.
(a) The farmer can pack 24 full boxes.
(b) 4 oranges are left over.
(c) Verification:
• Formula: Dividend = (Divisor × Quotient) + Remainder
• RHS = (6 × 24) + 4 = 144 + 4 = 148.
• LHS = Dividend = 148. Verified successfully!
We need to calculate 148 ÷ 6.
• Divide 14 by 6: 6 × 2 = 12. Remainder = 14 - 12 = 2.
• Bring down 8 to make 28.
• Divide 28 by 6: 6 × 4 = 24. Remainder = 28 - 24 = 4.
• Quotient = 24, Remainder = 4.
(a) The farmer can pack 24 full boxes.
(b) 4 oranges are left over.
(c) Verification:
• Formula: Dividend = (Divisor × Quotient) + Remainder
• RHS = (6 × 24) + 4 = 144 + 4 = 148.
• LHS = Dividend = 148. Verified successfully!
CBSE Step-by-Step Marking Scheme
Correct division steps showing Quotient 24 & Remainder 4
1.5 M
Accurate verification formula and arithmetic proof
1.5 M
Q2
In a school library, there are 215 storybooks. The librarian wants to place an equal number of books on 7 empty shelves. How many books will be placed on each shelf, and how many additional books are needed to fill the last shelf completely?
Real-Life Grouping Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step 1: Divide books equally:
Calculate 215 ÷ 7.
• 7 × 30 = 210.
• 215 - 210 = 5 remainder.
• So, each shelf gets 30 books.
• 5 books remain on the last shelf.
Step 2: Additional books needed for full shelf:
• Each shelf needs 31 books if all shelves are equally full.
• Currently, 5 books are left.
• Additional books needed = 7 - 5 = 2 books.
Calculate 215 ÷ 7.
• 7 × 30 = 210.
• 215 - 210 = 5 remainder.
• So, each shelf gets 30 books.
• 5 books remain on the last shelf.
Step 2: Additional books needed for full shelf:
• Each shelf needs 31 books if all shelves are equally full.
• Currently, 5 books are left.
• Additional books needed = 7 - 5 = 2 books.
CBSE Step-by-Step Marking Scheme
Correct quotient 30 books per shelf
1.5 M
Correct calculation of 2 additional books needed
1.5 M
Q3
A fruit vendor has a basket of 36 mangoes. He sells 1/4 of them in the morning and 1/2 of them in the afternoon. (a) How many mangoes did he sell in total? (b) How many mangoes are left?
Fraction of a Collection • Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
Total mangoes = 36
1. Morning Sales:
1/4 of 36 = 36 ÷ 4 = 9 mangoes.
2. Afternoon Sales:
1/2 of 36 = 36 ÷ 2 = 18 mangoes.
3. Total Sold:
9 + 18 = 27 mangoes.
4. Mangoes Left:
36 - 27 = 9 mangoes (which is 1/4 of the basket).
Total mangoes = 36
1. Morning Sales:
1/4 of 36 = 36 ÷ 4 = 9 mangoes.
2. Afternoon Sales:
1/2 of 36 = 36 ÷ 2 = 18 mangoes.
3. Total Sold:
9 + 18 = 27 mangoes.
4. Mangoes Left:
36 - 27 = 9 mangoes (which is 1/4 of the basket).
CBSE Step-by-Step Marking Scheme
Morning calculation (9) and afternoon (18)
1.5 M
Total sold (27) and remaining mangoes (9)
1.5 M
Q4
Show that 2/4 and 4/8 are equivalent to 1/2 using a rectangular strip model.
Equivalent Fractions • Shading Models
2 Marks
✅ Step-by-Step Model Answer & Solution:
Demonstration of Equivalent Fractions:
Take three identical strips of paper of length 12 cm:
1. Strip 1 (1/2): Divide into 2 equal parts of 6 cm each. Shade 1 part. Shaded length = 6 cm.
2. Strip 2 (2/4): Divide into 4 equal parts of 3 cm each. Shade 2 parts. Shaded length = 2 × 3 cm = 6 cm.
3. Strip 3 (4/8): Divide into 8 equal parts of 1.5 cm each. Shade 4 parts. Shaded length = 4 × 1.5 cm = 6 cm.
Since all three shaded portions cover the exact same physical length of 6 cm, 1/2 = 2/4 = 4/8. They represent the exact same fraction of the whole.
Take three identical strips of paper of length 12 cm:
1. Strip 1 (1/2): Divide into 2 equal parts of 6 cm each. Shade 1 part. Shaded length = 6 cm.
2. Strip 2 (2/4): Divide into 4 equal parts of 3 cm each. Shade 2 parts. Shaded length = 2 × 3 cm = 6 cm.
3. Strip 3 (4/8): Divide into 8 equal parts of 1.5 cm each. Shade 4 parts. Shaded length = 4 × 1.5 cm = 6 cm.
Since all three shaded portions cover the exact same physical length of 6 cm, 1/2 = 2/4 = 4/8. They represent the exact same fraction of the whole.
CBSE Step-by-Step Marking Scheme
Equal partition measurement of strips
1.0 M
Equal shaded length proving equivalence
1.0 M
Q5
In Chapter 5 ('Sharing and Measuring'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
School Van Seating Arrangement
Real-World Math Context: A school organizes an excursion for 58 students. Each school cab can carry a maximum of 8 students safely.
Analytical Task: How many cabs must be booked so that EVERY student gets a seat?
Answer: 8 cabs must be booked.
Explanation: 58 ÷ 8 = 7 with a remainder of 2 students.
7 cabs can only seat 7 × 8 = 56 students. The remaining 2 students cannot be left behind, so 1 more cab must be hired.
Total cabs required = 7 + 1 = 8 cabs.
Explanation: 58 ÷ 8 = 7 with a remainder of 2 students.
7 cabs can only seat 7 × 8 = 56 students. The remaining 2 students cannot be left behind, so 1 more cab must be hired.
Total cabs required = 7 + 1 = 8 cabs.
CBSE Assessment Rubric: 1 Mark for division quotient 7 with remainder 2; 1 Mark for practical round-up to 8 cabs.
6
Unit 3: Measurement & Metric Conversions • Class 4 Mathematics (New NEP 2020)
Chapter 6: Measuring Length
Centimetres, Metres, Kilometres, Conversions & Perimeter of Shapes
Chapter Highlights, Mathematical Ideas & Key Properties
- Metric units of length: millimetre (mm), centimetre (cm), metre (m), and kilometre (km).
- Key conversion relationships: 1 m = 100 cm; 1 km = 1,000 m; 1 cm = 10 mm.
- Measuring curved paths using a string and ruler.
- Calculating perimeter (total boundary length) by summing the lengths of all outer sides.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Convert the following: (a) 4 metres 65 centimetres into cm; (b) 7,500 metres into kilometres and metres; (c) 8 kilometres 40 metres into metres.
Metric Unit Conversions
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) 4 m 65 cm into cm:
• Since 1 m = 100 cm, 4 m = 4 × 100 = 400 cm.
• Total = 400 cm + 65 cm = 465 cm.
(b) 7,500 m into km and m:
• Since 1,000 m = 1 km, divide 7,500 by 1,000.
• 7,500 m = 7,000 m + 500 m = 7 km 500 m.
(c) 8 km 40 m into m:
• Since 1 km = 1,000 m, 8 km = 8 × 1,000 = 8,000 m.
• Total = 8,000 m + 40 m = 8,040 m (be careful not to write 8,400 m!).
• Since 1 m = 100 cm, 4 m = 4 × 100 = 400 cm.
• Total = 400 cm + 65 cm = 465 cm.
(b) 7,500 m into km and m:
• Since 1,000 m = 1 km, divide 7,500 by 1,000.
• 7,500 m = 7,000 m + 500 m = 7 km 500 m.
(c) 8 km 40 m into m:
• Since 1 km = 1,000 m, 8 km = 8 × 1,000 = 8,000 m.
• Total = 8,000 m + 40 m = 8,040 m (be careful not to write 8,400 m!).
CBSE Step-by-Step Marking Scheme
Correct conversion for (a)
1.0 M
Correct conversion for (b)
1.0 M
Correct conversion for (c) with zero placeholder
1.0 M
Q2
A rectangular playground is 35 metres long and 20 metres wide. An athlete runs around the boundary 4 times every morning. What is the total distance run by the athlete in metres and kilometres?
Perimeter Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step 1: Calculate the perimeter of the playground:
• Formula: Perimeter = 2 × (Length + Width)
• Perimeter = 2 × (35 m + 20 m) = 2 × 55 m = 110 metres.
(One full round = 110 m).
Step 2: Calculate distance for 4 rounds:
• Total distance = 4 × 110 m = 440 metres.
Step 3: Convert into kilometres:
• 440 m = 440 ÷ 1,000 = 0.44 km.
• Formula: Perimeter = 2 × (Length + Width)
• Perimeter = 2 × (35 m + 20 m) = 2 × 55 m = 110 metres.
(One full round = 110 m).
Step 2: Calculate distance for 4 rounds:
• Total distance = 4 × 110 m = 440 metres.
Step 3: Convert into kilometres:
• 440 m = 440 ÷ 1,000 = 0.44 km.
CBSE Step-by-Step Marking Scheme
Perimeter calculation of 110 m
1.5 M
Total 4 rounds distance 440 m and km conversion
1.5 M
Q3
A rectangular school playground is 45 metres long and 30 metres wide. (a) What is its perimeter? (b) If an athlete runs 3 complete rounds around it, what total distance does she run?
Geometry • Perimeter Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Calculation:
Length (l) = 45 m, Breadth (b) = 30 m
1. Perimeter of the Playground:
Perimeter = 2 × (Length + Breadth)
= 2 × (45 m + 30 m) = 2 × 75 m = 150 metres.
2. Total Distance for 3 Rounds:
Distance = 3 × Perimeter = 3 × 150 m = 450 metres.
Length (l) = 45 m, Breadth (b) = 30 m
1. Perimeter of the Playground:
Perimeter = 2 × (Length + Breadth)
= 2 × (45 m + 30 m) = 2 × 75 m = 150 metres.
2. Total Distance for 3 Rounds:
Distance = 3 × Perimeter = 3 × 150 m = 450 metres.
CBSE Step-by-Step Marking Scheme
Perimeter formula and correct answer (150 m)
1.5 M
Multiplication by 3 rounds (450 m)
1.5 M
Q4
Convert: (a) 4,250 metres into kilometres and metres, (b) 7 kilometres 85 metres into metres.
Unit Conversions • Metres & Kilometres
2 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions (1 km = 1,000 m):
• (a) 4,250 m:
4,250 ÷ 1,000 = 4 km and 250 m.
• (b) 7 km 85 m:
(7 × 1,000 m) + 85 m = 7,000 m + 85 m = 7,085 m.
• (a) 4,250 m:
4,250 ÷ 1,000 = 4 km and 250 m.
• (b) 7 km 85 m:
(7 × 1,000 m) + 85 m = 7,000 m + 85 m = 7,085 m.
CBSE Step-by-Step Marking Scheme
Part (a): 4 km 250 m
1.0 M
Part (b): 7,085 m
1.0 M
Q5
In Chapter 6 ('Measuring Length'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
School Boundary Fencing Budget
Real-World Math Context: The school management needs to put a wire fence around a square herb garden measuring 15 metres on each side. The fencing contractor charges ₹40 per metre of wire.
Analytical Task: Calculate: (a) The total length of wire needed for 1 round of fence, (b) The total cost of fencing.
(a) Length of wire:
Perimeter of square garden = 4 × side = 4 × 15 m = 60 metres.
(b) Total Cost:
Cost = 60 m × ₹40/m = ₹2,400.
Perimeter of square garden = 4 × side = 4 × 15 m = 60 metres.
(b) Total Cost:
Cost = 60 m × ₹40/m = ₹2,400.
CBSE Assessment Rubric: 1 Mark for perimeter 60 m; 1 Mark for multiplying rate to get ₹2,400.
7
Unit 3: Community Projects & Applied Arithmetic • Class 4 Mathematics (New NEP 2020)
Chapter 7: The Cleanest Village
Data Organization, Tally Marks, Environmental Cleanliness Drives & Applied Math
Chapter Highlights, Mathematical Ideas & Key Properties
- Using tally marks (groups of 5: ||||) to record counts efficiently.
- Solving multi-step addition and subtraction problems based on community waste collection.
- Calculating recyclable waste weights and earnings from community recycling.
- Promoting civic responsibility through mathematical measurement.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
During a clean-up campaign, children recorded dry leaves baskets using tally marks: Team Red gathered '卌 卌 卌 卌 |', Team Blue gathered '卌 卌 卌 |||', and Team Green gathered '卌 卌 卌 卌 卌'. (a) How many baskets did each team gather? (b) Which team collected the most? (c) What is the total count of baskets?
Tally Chart Interpretation
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Basket counts from tally marks:
• Team Red: 4 bundles of 5 + 1 = (4 × 5) + 1 = 21 baskets.
• Team Blue: 3 bundles of 5 + 3 = (3 × 5) + 3 = 18 baskets.
• Team Green: 5 bundles of 5 = (5 × 5) = 25 baskets.
(b) Maximum collection:
Team Green collected the most with 25 baskets.
(c) Total baskets collected:
Total = 21 + 18 + 25 = 64 baskets.
• Team Red: 4 bundles of 5 + 1 = (4 × 5) + 1 = 21 baskets.
• Team Blue: 3 bundles of 5 + 3 = (3 × 5) + 3 = 18 baskets.
• Team Green: 5 bundles of 5 = (5 × 5) = 25 baskets.
(b) Maximum collection:
Team Green collected the most with 25 baskets.
(c) Total baskets collected:
Total = 21 + 18 + 25 = 64 baskets.
CBSE Step-by-Step Marking Scheme
Correct counts for all three teams
1.5 M
Correct identification of winner and total sum 64
1.5 M
Q2
In a village cleanliness drive, four teams collected wet waste: Team A collected 42 kg 500 g, Team B collected 38 kg 250 g, Team C collected 51 kg 750 g, and Team D collected 47 kg. What was the total weight of wet waste collected?
Weight & Community Cleanliness • Tally Arithmetic
3 Marks
✅ Step-by-Step Model Answer & Solution:
Column Addition of Weight:
kg g
42 500
+ 38 250
+ 51 750
+ 47 000
-------------------
Sum of grams = 500 + 250 + 750 + 0 = 1,500 g = 1 kg 500 g.
Sum of kg = 42 + 38 + 51 + 47 + 1 (carry) = 179 kg.
Total wet waste collected = 179 kg 500 g.
kg g
42 500
+ 38 250
+ 51 750
+ 47 000
-------------------
Sum of grams = 500 + 250 + 750 + 0 = 1,500 g = 1 kg 500 g.
Sum of kg = 42 + 38 + 51 + 47 + 1 (carry) = 179 kg.
Total wet waste collected = 179 kg 500 g.
CBSE Step-by-Step Marking Scheme
Correct column alignment of kg and g
1.0 M
Gram sum carry-over (1,500 g = 1 kg 500 g)
1.0 M
Final sum: 179 kg 500 g
1.0 M
Q3
A leaky public tap wastes 150 mL of clean drinking water every minute. How many litres of water are wasted if the tap is left leaking for 2 hours?
Capacity & Conservation • Water Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Calculation:
1. Wastage in 1 hour (60 minutes):
150 mL × 60 = 9,000 mL.
2. Wastage in 2 hours:
9,000 mL × 2 = 18,000 mL.
3. Convert to Litres (1 L = 1,000 mL):
18,000 ÷ 1,000 = 18 Litres.
In 2 hours, 18 litres of precious drinking water are wasted.
1. Wastage in 1 hour (60 minutes):
150 mL × 60 = 9,000 mL.
2. Wastage in 2 hours:
9,000 mL × 2 = 18,000 mL.
3. Convert to Litres (1 L = 1,000 mL):
18,000 ÷ 1,000 = 18 Litres.
In 2 hours, 18 litres of precious drinking water are wasted.
CBSE Step-by-Step Marking Scheme
Calculating minutes in 2 hours (120 mins)
1.0 M
Total mL calculation (18,000 mL)
1.0 M
Conversion to litres (18 L)
1.0 M
Q4
A school canteen produced 65 kg of garbage in a week. If 3/5 of it was biodegradable food waste and the rest was recyclable plastic and paper, find the weight of recyclable waste.
Practical Arithmetic • Garbage Sorting
2 Marks
✅ Step-by-Step Model Answer & Solution:
Fraction & Weight Solution:
Total garbage = 65 kg
1. Weight of Biodegradable Food Waste:
3/5 of 65 kg = (65 ÷ 5) × 3 = 13 × 3 = 39 kg.
2. Weight of Recyclable Waste:
65 kg - 39 kg = 26 kg.
(Alternatively, 1 - 3/5 = 2/5; 2/5 of 65 = 26 kg).
Total garbage = 65 kg
1. Weight of Biodegradable Food Waste:
3/5 of 65 kg = (65 ÷ 5) × 3 = 13 × 3 = 39 kg.
2. Weight of Recyclable Waste:
65 kg - 39 kg = 26 kg.
(Alternatively, 1 - 3/5 = 2/5; 2/5 of 65 = 26 kg).
CBSE Step-by-Step Marking Scheme
Calculating food waste fraction (39 kg)
1.0 M
Deducting to find recyclable waste (26 kg)
1.0 M
Q5
In Chapter 7 ('The Cleanest Village'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Recycling Waste Funds for Village Library
Real-World Math Context: The village panchayat collected 120 kg of old newspapers and 45 kg of cardboard boxes. The scrap dealer buys newspapers at ₹14 per kg and cardboard at ₹10 per kg.
Analytical Task: How much total money did the village raise for their new reading room?
Working:
• Money from newspapers = 120 kg × ₹14 = ₹1,680.
• Money from cardboard = 45 kg × ₹10 = ₹450.
• Total funds raised = ₹1,680 + ₹450 = ₹2,130.
• Money from newspapers = 120 kg × ₹14 = ₹1,680.
• Money from cardboard = 45 kg × ₹10 = ₹450.
• Total funds raised = ₹1,680 + ₹450 = ₹2,130.
CBSE Assessment Rubric: 1 Mark for individual product calculations; 1 Mark for total ₹2,130.
8
Unit 3: Weight and Capacity Measurement • Class 4 Mathematics (New NEP 2020)
Chapter 8: Weigh it, Pour it
Grams, Kilograms, Millilitres, Litres, Balance Scales & Liquid Capacities
Chapter Highlights, Mathematical Ideas & Key Properties
- Standard units of mass: Gram (g) and Kilogram (kg); 1 kg = 1,000 g.
- Standard units of capacity: Millilitre (ml) and Litre (l); 1 l = 1,000 ml.
- Balancing pans: Understanding equilibrium on a two-pan balance beam.
- Comparing light and heavy objects; estimating volume in daily household containers.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Solve: (a) A grocer has a 5 kg bag of sugar. He sells 1 kg 750 g. How much sugar remains? (b) A jug holds 2 litres of mango juice. If each glass holds 250 ml, how many glasses can be filled?
Mass & Capacity Metric Arithmetic
4 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Remaining Sugar:
• Convert 5 kg to grams: 5 kg = 5,000 g.
• Convert 1 kg 750 g to grams: 1,000 g + 750 g = 1,750 g.
• Subtraction: 5,000 g - 1,750 g = 3,250 g.
• Converting back to kg and g: 3 kg 250 g of sugar remains.
(b) Number of glasses of mango juice:
• 1 litre = 1,000 ml, so 2 litres = 2 × 1,000 = 2,000 ml.
• Capacity of 1 glass = 250 ml.
• Number of glasses = 2,000 ÷ 250 = 8 glasses.
Check: 8 × 250 ml = 2,000 ml = 2 l.
• Convert 5 kg to grams: 5 kg = 5,000 g.
• Convert 1 kg 750 g to grams: 1,000 g + 750 g = 1,750 g.
• Subtraction: 5,000 g - 1,750 g = 3,250 g.
• Converting back to kg and g: 3 kg 250 g of sugar remains.
(b) Number of glasses of mango juice:
• 1 litre = 1,000 ml, so 2 litres = 2 × 1,000 = 2,000 ml.
• Capacity of 1 glass = 250 ml.
• Number of glasses = 2,000 ÷ 250 = 8 glasses.
Check: 8 × 250 ml = 2,000 ml = 2 l.
CBSE Step-by-Step Marking Scheme
Correct subtraction for sugar (3 kg 250 g)
2.0 M
Correct division for juice glasses (8 glasses)
2.0 M
Q2
A doctor prescribes 5 mL of cough syrup three times a day to a patient for 6 days. (a) How much syrup does the patient consume in one day? (b) Will a 100 mL bottle be sufficient for the full course?
Measurement of Capacity • Mixing Solutions
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
Dosage per intake = 5 mL
1. Daily Consumption:
3 doses × 5 mL = 15 mL per day.
2. Total Consumption in 6 Days:
15 mL × 6 = 90 mL.
3. Sufficiency of Bottle:
The bottle contains 100 mL, and the patient requires 90 mL.
Since 100 mL > 90 mL, yes, the 100 mL bottle will be sufficient (with 10 mL left over).
Dosage per intake = 5 mL
1. Daily Consumption:
3 doses × 5 mL = 15 mL per day.
2. Total Consumption in 6 Days:
15 mL × 6 = 90 mL.
3. Sufficiency of Bottle:
The bottle contains 100 mL, and the patient requires 90 mL.
Since 100 mL > 90 mL, yes, the 100 mL bottle will be sufficient (with 10 mL left over).
CBSE Step-by-Step Marking Scheme
Daily dosage calculation (15 mL)
1.0 M
Total 6-day requirement (90 mL)
1.0 M
Comparison and positive conclusion (100 > 90)
1.0 M
Q3
You have only three standard weights: 100 g, 250 g, and 500 g. How will you measure exactly 350 g of flour on a two-pan balance in one step?
Weight Balancing • Pan Scales
2 Marks
✅ Step-by-Step Model Answer & Solution:
Pan Balance Arrangement:
To measure 350 g:
• Place the 100 g and 250 g weights together in the left pan.
• Total weight in left pan = 100 g + 250 g = 350 g.
• Pour flour into the right pan until both pans balance horizontally.
The weighed flour will be exactly 350 g.
To measure 350 g:
• Place the 100 g and 250 g weights together in the left pan.
• Total weight in left pan = 100 g + 250 g = 350 g.
• Pour flour into the right pan until both pans balance horizontally.
The weighed flour will be exactly 350 g.
CBSE Step-by-Step Marking Scheme
Identifying 100 g + 250 g combination
1.0 M
Explaining balance equilibrium
1.0 M
Q4
A milkman has a 20-litre milk can. In the morning, he sells 4 L 750 mL to House A and 6 L 500 mL to House B. How much milk is still left in his can?
Capacity Arithmetic • Milk Delivery
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Calculation:
1. Total Milk Sold:
4 L 750 mL + 6 L 500 mL = 10 L 1,250 mL = 11 L 250 mL.
2. Milk Left in the 20 L Can:
20 L 000 mL - 11 L 250 mL
= 19 L 1,000 mL - 11 L 250 mL = 8 L 750 mL.
The milkman has 8 litres 750 millilitres of milk left.
1. Total Milk Sold:
4 L 750 mL + 6 L 500 mL = 10 L 1,250 mL = 11 L 250 mL.
2. Milk Left in the 20 L Can:
20 L 000 mL - 11 L 250 mL
= 19 L 1,000 mL - 11 L 250 mL = 8 L 750 mL.
The milkman has 8 litres 750 millilitres of milk left.
CBSE Step-by-Step Marking Scheme
Adding milk sold (11 L 250 mL)
1.5 M
Borrowing and subtracting from 20 L (8 L 750 mL)
1.5 M
Q5
In Chapter 8 ('Weigh it, Pour it'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Measuring Cough Syrup Doses
Real-World Math Context: Doctor advises a patient to take 5 ml of cough syrup three times a day for 7 days. The chemist gives a bottle containing 100 ml of syrup.
Analytical Task: Is the 100 ml bottle sufficient for the complete course? How much syrup is used, and how much is left over?
Working:
• Daily dosage = 5 ml × 3 times = 15 ml per day.
• Dosage for 7 days = 15 ml × 7 = 105 ml.
Conclusion:
No, the 100 ml bottle is NOT sufficient because the patient needs 105 ml (short by 5 ml).
• Daily dosage = 5 ml × 3 times = 15 ml per day.
• Dosage for 7 days = 15 ml × 7 = 105 ml.
Conclusion:
No, the 100 ml bottle is NOT sufficient because the patient needs 105 ml (short by 5 ml).
CBSE Assessment Rubric: 1 Mark for calculating 105 ml total required; 1 Mark for concluding 100 ml is not sufficient.
9
Unit 3: Multiplication Strategies & Tables • Class 4 Mathematics (New NEP 2020)
Chapter 9: Equal Groups
Multiplication as Arrays, Distributive Break-up, Box Method & Tables up to 15
Chapter Highlights, Mathematical Ideas & Key Properties
- Multiplication concepts: multiplicand × multiplier = product.
- Building multiplication tables using known facts (e.g., table of 7 = table of 5 + table of 2).
- Using the box / grid multiplication method for 2-digit by 1-digit and 2-digit numbers.
- Solving multi-step real-world problems involving rows and columns of objects.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Show how to construct the multiplication table of 8 using the tables of 5 and 3. Write out the values for 8 × 1 up to 8 × 6.
Multiplication Strategy & Break-up
3 Marks
✅ Step-by-Step Model Answer & Solution:
By the distributive property of multiplication:
8 × n = (5 + 3) × n = (5 × n) + (3 × n).
• 8 × 1 = (5 × 1) + (3 × 1) = 5 + 3 = 8
• 8 × 2 = (5 × 2) + (3 × 2) = 10 + 6 = 16
• 8 × 3 = (5 × 3) + (3 × 3) = 15 + 9 = 24
• 8 × 4 = (5 × 4) + (3 × 4) = 20 + 12 = 32
• 8 × 5 = (5 × 5) + (3 × 5) = 25 + 15 = 40
• 8 × 6 = (5 × 6) + (3 × 6) = 30 + 18 = 48
8 × n = (5 + 3) × n = (5 × n) + (3 × n).
• 8 × 1 = (5 × 1) + (3 × 1) = 5 + 3 = 8
• 8 × 2 = (5 × 2) + (3 × 2) = 10 + 6 = 16
• 8 × 3 = (5 × 3) + (3 × 3) = 15 + 9 = 24
• 8 × 4 = (5 × 4) + (3 × 4) = 20 + 12 = 32
• 8 × 5 = (5 × 5) + (3 × 5) = 25 + 15 = 40
• 8 × 6 = (5 × 6) + (3 × 6) = 30 + 18 = 48
CBSE Step-by-Step Marking Scheme
Explains distributive break-up (5 + 3)
1.0 M
Correct step-by-step table construction
2.0 M
Q2
A cinema hall has 28 rows of seats, and each row has 15 seats. During a premiere show, all seats are occupied except 12 seats. How many people are watching the movie?
Two-Digit Multiplication Word Problem
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step 1: Calculate total seating capacity:
Total seats = 28 rows × 15 seats/row.
• Using break-up: 28 × 15 = 28 × (10 + 5) = (28 × 10) + (28 × 5)
• 28 × 10 = 280
• 28 × 5 = 140
• Total seats = 280 + 140 = 420 seats.
Step 2: Subtract empty seats:
• Empty seats = 12
• People watching = 420 - 12 = 408 people.
Total seats = 28 rows × 15 seats/row.
• Using break-up: 28 × 15 = 28 × (10 + 5) = (28 × 10) + (28 × 5)
• 28 × 10 = 280
• 28 × 5 = 140
• Total seats = 280 + 140 = 420 seats.
Step 2: Subtract empty seats:
• Empty seats = 12
• People watching = 420 - 12 = 408 people.
CBSE Step-by-Step Marking Scheme
Accurate multiplication 28 × 15 = 420
2.0 M
Correct subtraction giving 408 people
1.0 M
Q3
A school library buys 24 copies of an encyclopedia. If each encyclopedia costs ₹345, calculate the total bill amount using the standard multiplication method.
Multiplication Algorithm • 3-Digit by 2-Digit
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Multiplication:
3 4 5
× 2 4
-----------
1 3 8 0 (345 × 4)
+ 6 9 0 0 (345 × 20)
-----------
8 2 8 0
The total bill amount is ₹8,280.
3 4 5
× 2 4
-----------
1 3 8 0 (345 × 4)
+ 6 9 0 0 (345 × 20)
-----------
8 2 8 0
The total bill amount is ₹8,280.
CBSE Step-by-Step Marking Scheme
Partial product 1 (345 × 4 = 1380)
1.0 M
Partial product 2 (345 × 20 = 6900)
1.0 M
Final total: ₹8,280
1.0 M
Q4
Calculate mentally using place value patterns:
(a) 70 × 60
(b) 125 × 40
(c) 48 × 25 Mental Math • Multiples of 10 and 100 3 Marks
(a) 70 × 60
(b) 125 × 40
(c) 48 × 25 Mental Math • Multiples of 10 and 100 3 Marks
✅ Step-by-Step Model Answer & Solution:
Mental Calculation Strategies:
• (a) 70 × 60:
Multiply the non-zero digits: 7 × 6 = 42, then attach two zeroes: 4,200.
• (b) 125 × 40:
Think of (125 × 4) × 10 = 500 × 10 = 5,000.
• (c) 48 × 25:
Since 25 = 100 ÷ 4, we divide 48 by 4 and multiply by 100: (48 ÷ 4) × 100 = 12 × 100 = 1,200.
• (a) 70 × 60:
Multiply the non-zero digits: 7 × 6 = 42, then attach two zeroes: 4,200.
• (b) 125 × 40:
Think of (125 × 4) × 10 = 500 × 10 = 5,000.
• (c) 48 × 25:
Since 25 = 100 ÷ 4, we divide 48 by 4 and multiply by 100: (48 ÷ 4) × 100 = 12 × 100 = 1,200.
CBSE Step-by-Step Marking Scheme
(a) 4,200
1.0 M
(b) 5,000
1.0 M
(c) 1,200
1.0 M
Q5
In Chapter 9 ('Equal Groups'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Tree Plantation Drive Rows
Real-World Math Context: The Forest Department plants 36 saplings in each row across 25 parallel strips. The cost of protecting each sapling with a bamboo guard is ₹50.
Analytical Task: How many total saplings are planted, and what is the total cost of bamboo guards for all saplings?
Step 1: Total saplings:
36 × 25 = 36 × (100 ÷ 4) = 3,600 ÷ 4 = 900 saplings.
Step 2: Total cost:
900 × ₹50 = ₹45,000.
36 × 25 = 36 × (100 ÷ 4) = 3,600 ÷ 4 = 900 saplings.
Step 2: Total cost:
900 × ₹50 = ₹45,000.
CBSE Assessment Rubric: 1 Mark for 900 saplings; 1 Mark for ₹45,000.
10
Unit 4: Wildlife Conservation & Multi-Digit Operations • Class 4 Mathematics (New NEP 2020)
Chapter 10: Elephants, Tigers, and Leopards
Wildlife Census Data, Addition & Subtraction with Regrouping & Comparison
Chapter Highlights, Mathematical Ideas & Key Properties
- Real-world data handling from wildlife census across Indian National Parks.
- Multi-digit addition and subtraction involving regrouping (carrying and borrowing) across thousands.
- Estimating sums and differences to the nearest ten and nearest hundred.
- Developing environmental appreciation through numerical analysis.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
In Corbett National Park, the wildlife census recorded 1,245 elephants, 680 leopards, and 315 tigers. (a) What is the total population of these three animals? (b) How many more elephants are there than tigers and leopards combined?
Multi-Digit Addition & Subtraction
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Total Population:
1,245
+ 680
+ 315
-------
2,240 total animals.
(b) Comparison with combined tigers and leopards:
• Tigers + Leopards = 315 + 680 = 995 animals.
• Difference from elephants = 1,245 - 995 = 250.
• There are 250 more elephants than tigers and leopards combined.
1,245
+ 680
+ 315
-------
2,240 total animals.
(b) Comparison with combined tigers and leopards:
• Tigers + Leopards = 315 + 680 = 995 animals.
• Difference from elephants = 1,245 - 995 = 250.
• There are 250 more elephants than tigers and leopards combined.
CBSE Step-by-Step Marking Scheme
Correct addition of 2,240 with regrouping
1.5 M
Correct subtraction giving 250 difference
1.5 M
Q2
Divide 487 by 6. Show the dividend, divisor, quotient, and remainder. Verify your answer using the division verification formula.
Long Division • Quotient and Remainder
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Long Division:
487 ÷ 6
• 48 ÷ 6 = 8 (6 × 8 = 48), remainder 0.
• Bring down 7.
• 7 ÷ 6 = 1 (6 × 1 = 6), remainder 1.
Components:
• Dividend: 487
• Divisor: 6
• Quotient: 81
• Remainder: 1
Verification Formula:
Dividend = (Divisor × Quotient) + Remainder
= (6 × 81) + 1 = 486 + 1 = 487 (Verified).
487 ÷ 6
• 48 ÷ 6 = 8 (6 × 8 = 48), remainder 0.
• Bring down 7.
• 7 ÷ 6 = 1 (6 × 1 = 6), remainder 1.
Components:
• Dividend: 487
• Divisor: 6
• Quotient: 81
• Remainder: 1
Verification Formula:
Dividend = (Divisor × Quotient) + Remainder
= (6 × 81) + 1 = 486 + 1 = 487 (Verified).
CBSE Step-by-Step Marking Scheme
Correct division step yielding Q = 81, R = 1
1.5 M
Identification of components and successful verification
1.5 M
Q3
A national park has 125 tourists waiting for a tiger safari. Each safari jeep can seat a maximum of 6 tourists. (a) How many jeeps will be completely full? (b) How many total jeeps are needed so that no tourist is left behind?
Real-Life Division • Safari Jeeps
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Word Problem:
Total tourists = 125, Capacity per jeep = 6
1. Division:
125 ÷ 6 = 20 with a remainder of 5.
2. Answers:
• (a) Completely Full Jeeps: Exactly 20 jeeps will be completely full (20 × 6 = 120 tourists).
• (b) Total Jeeps Needed: The remaining 5 tourists also need to go on the safari. Therefore, 1 additional jeep is required.
Total jeeps needed = 20 + 1 = 21 jeeps.
Total tourists = 125, Capacity per jeep = 6
1. Division:
125 ÷ 6 = 20 with a remainder of 5.
2. Answers:
• (a) Completely Full Jeeps: Exactly 20 jeeps will be completely full (20 × 6 = 120 tourists).
• (b) Total Jeeps Needed: The remaining 5 tourists also need to go on the safari. Therefore, 1 additional jeep is required.
Total jeeps needed = 20 + 1 = 21 jeeps.
CBSE Step-by-Step Marking Scheme
Division 125 ÷ 6 = 20 R 5
1.5 M
Interpreting remainder: 20 full jeeps and 21 total jeeps needed
1.5 M
Q4
7 children share 91 marbles equally among themselves. How many marbles does each child get?
Mental Arithmetic • Equal Sharing
2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
91 ÷ 7
• 70 ÷ 7 = 10
• 21 ÷ 7 = 3
• 10 + 3 = 13
Each child gets exactly 13 marbles.
91 ÷ 7
• 70 ÷ 7 = 10
• 21 ÷ 7 = 3
• 10 + 3 = 13
Each child gets exactly 13 marbles.
CBSE Step-by-Step Marking Scheme
Correct division yielding 13 marbles
2.0 M
Q5
In Chapter 10 ('Elephants, Tigers, and Leopards'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Wildlife Habitat Expansion Project
Real-World Math Context: The state sanctuary recorded 2,870 deer in 2024. In 2026, 420 fawns were born, while 185 deer were relocated to another forest.
Analytical Task: Calculate the current deer population in the sanctuary.
Current Population:
2,870 + 420 - 185 = 3,290 - 185 = 3,105 deer.
2,870 + 420 - 185 = 3,290 - 185 = 3,105 deer.
CBSE Assessment Rubric: 1 Mark for addition (3,290); 1 Mark for subtraction (3,105).
11
Unit 4: Symmetry, Reflection & Mirror Images • Class 4 Mathematics (New NEP 2020)
Chapter 11: Fun with Symmetry
Lines of Symmetry, Mirror Reflections, Folding Paper & Symmetrical Shapes
Chapter Highlights, Mathematical Ideas & Key Properties
- A line of symmetry divides a figure into two identical halves that overlap exactly when folded.
- Vertical, horizontal, and diagonal lines of symmetry.
- Recognizing symmetry in nature (butterflies, leaves), architecture (Taj Mahal), and geometrical shapes.
- Completing symmetrical pictures across a dashed mirror line.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
How many lines of symmetry do each of the following shapes have? (a) An equilateral triangle, (b) A square, (c) A rectangle, (d) A circle, (e) A scalene triangle.
Lines of Symmetry in Plane Shapes
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Equilateral Triangle: 3 lines of symmetry (one from each vertex perpendicular to the opposite side).
(b) Square: 4 lines of symmetry (2 through midpoints of opposite sides + 2 along diagonals).
(c) Rectangle: 2 lines of symmetry (only through midpoints of opposite sides; diagonals are NOT lines of symmetry).
(d) Circle: Infinite lines of symmetry (any straight line passing through the centre is a line of symmetry).
(e) Scalene Triangle: 0 lines of symmetry (all sides and angles are unequal).
(b) Square: 4 lines of symmetry (2 through midpoints of opposite sides + 2 along diagonals).
(c) Rectangle: 2 lines of symmetry (only through midpoints of opposite sides; diagonals are NOT lines of symmetry).
(d) Circle: Infinite lines of symmetry (any straight line passing through the centre is a line of symmetry).
(e) Scalene Triangle: 0 lines of symmetry (all sides and angles are unequal).
CBSE Step-by-Step Marking Scheme
Correct counts for triangle, square, rectangle
1.5 M
Correct counts for circle (infinite) and scalene triangle (0)
1.5 M
Q2
Which of the following English capital letters look identical after a 1/2 turn (180° rotation)?
A, H, M, O, S, Z Rotational Symmetry • Turns and Angles 3 Marks
A, H, M, O, S, Z Rotational Symmetry • Turns and Angles 3 Marks
✅ Step-by-Step Model Answer & Solution:
Half-Turn (180°) Invariance Analysis:
Rotate each letter upside down by 180°:
• A: Turns upside down (∀) - NO.
• H: Remains exactly H - YES.
• M: Turns into W - NO.
• O: Remains exactly O - YES.
• S: Remains exactly S - YES.
• Z: Remains exactly Z - YES.
The letters that look identical after a 1/2 turn are H, O, S, and Z.
Rotate each letter upside down by 180°:
• A: Turns upside down (∀) - NO.
• H: Remains exactly H - YES.
• M: Turns into W - NO.
• O: Remains exactly O - YES.
• S: Remains exactly S - YES.
• Z: Remains exactly Z - YES.
The letters that look identical after a 1/2 turn are H, O, S, and Z.
CBSE Step-by-Step Marking Scheme
Correctly identifying all 4 letters (H, O, S, Z)
2.0 M
Accurately ruling out A and M
1.0 M
Q3
How many lines of symmetry do each of the following geometric shapes have?
(a) Equilateral triangle
(b) Square
(c) Circle Geometric Lines of Symmetry 3 Marks
(a) Equilateral triangle
(b) Square
(c) Circle Geometric Lines of Symmetry 3 Marks
✅ Step-by-Step Model Answer & Solution:
Lines of Symmetry:
• (a) Equilateral Triangle: 3 lines of symmetry (each passing from a vertex perpendicular to the opposite side).
• (b) Square: 4 lines of symmetry (2 bisecting opposite sides horizontally and vertically, and 2 along the diagonals).
• (c) Circle: Infinite (countless) lines of symmetry (any straight line passing through the centre point is a line of symmetry).
• (a) Equilateral Triangle: 3 lines of symmetry (each passing from a vertex perpendicular to the opposite side).
• (b) Square: 4 lines of symmetry (2 bisecting opposite sides horizontally and vertically, and 2 along the diagonals).
• (c) Circle: Infinite (countless) lines of symmetry (any straight line passing through the centre point is a line of symmetry).
CBSE Step-by-Step Marking Scheme
Equilateral triangle: 3
1.0 M
Square: 4
1.0 M
Circle: Infinite
1.0 M
Q4
Draw an imaginary mirror line through the digit '8' and explain why it has both horizontal and vertical symmetry.
Mirror Halves • Reflectional Symmetry
2 Marks
✅ Step-by-Step Model Answer & Solution:
Symmetry of Digit 8:
• Vertical Line of Symmetry: A vertical line dividing '8' through the middle produces two identical left and right halves that reflect each other perfectly.
• Horizontal Line of Symmetry: A horizontal line passing through the central intersection produces matching top and bottom loops.
Therefore, digit 8 possesses 2 lines of reflectional symmetry.
• Vertical Line of Symmetry: A vertical line dividing '8' through the middle produces two identical left and right halves that reflect each other perfectly.
• Horizontal Line of Symmetry: A horizontal line passing through the central intersection produces matching top and bottom loops.
Therefore, digit 8 possesses 2 lines of reflectional symmetry.
CBSE Step-by-Step Marking Scheme
Explanation of vertical reflection
1.0 M
Explanation of horizontal reflection
1.0 M
Q5
In Chapter 11 ('Fun with Symmetry'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Rangoli Mirror Pattern Creation
Real-World Math Context: Pooja draws half of a diya pattern on folded paper. When she opens the fold, both sides are perfectly identical.
Analytical Task: What is the crease of the paper called? If she cuts a heart shape along the fold, how many lines of symmetry will the heart have?
Answers:
1. The crease is called the Line of Symmetry (or Axis of Reflection).
2. A symmetrical heart shape has exactly 1 vertical line of symmetry running down the center.
1. The crease is called the Line of Symmetry (or Axis of Reflection).
2. A symmetrical heart shape has exactly 1 vertical line of symmetry running down the center.
CBSE Assessment Rubric: 1 Mark for Line of Symmetry; 1 Mark for 1 vertical line.
12
Unit 4: Time and Calendar Computations • Class 4 Mathematics (New NEP 2020)
Chapter 12: Ticking Clocks and Turning Calendar
12-Hour vs. 24-Hour Clocks, AM/PM, Elapsed Time & Calendar Logic
Chapter Highlights, Mathematical Ideas & Key Properties
- Reading time to the exact minute on analog and digital clocks.
- Converting between 12-hour (am/pm) and 24-hour railway time formats.
- Calculating elapsed time (start time, end time, duration).
- Understanding calendar months, leap years, manufacturing and expiry dates on packaged products.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Convert to 24-hour clock time: (a) 6:15 am, (b) 2:45 pm, (c) 11:20 pm, (d) 12:00 midnight. (e) If a train departs at 08:45 and arrives at 14:15, what is the journey duration?
Time Conversion & Calculation
4 Marks
✅ Step-by-Step Model Answer & Solution:
Part 1: Conversions to 24-Hour Time:
• (a) 6:15 am = 06:15 hours (am times before noon remain unchanged).
• (b) 2:45 pm = 2:45 + 12:00 = 14:45 hours.
• (c) 11:20 pm = 11:20 + 12:00 = 23:20 hours.
• (d) 12:00 midnight = 00:00 hours (or 24:00 hours).
Part 2: Train Journey Duration:
• Departure: 08:45 hours.
• From 08:45 to 09:00 = 15 minutes.
• From 09:00 to 14:00 = 5 hours.
• From 14:00 to 14:15 = 15 minutes.
• Total duration = 5 hours + 15 min + 15 min = 5 hours 30 minutes.
• (a) 6:15 am = 06:15 hours (am times before noon remain unchanged).
• (b) 2:45 pm = 2:45 + 12:00 = 14:45 hours.
• (c) 11:20 pm = 11:20 + 12:00 = 23:20 hours.
• (d) 12:00 midnight = 00:00 hours (or 24:00 hours).
Part 2: Train Journey Duration:
• Departure: 08:45 hours.
• From 08:45 to 09:00 = 15 minutes.
• From 09:00 to 14:00 = 5 hours.
• From 14:00 to 14:15 = 15 minutes.
• Total duration = 5 hours + 15 min + 15 min = 5 hours 30 minutes.
CBSE Step-by-Step Marking Scheme
Correct conversions for all 4 time formats
2.0 M
Accurate step-by-step elapsed time calculation (5h 30m)
2.0 M
Q2
Convert the following times between 12-hour clock (am/pm) and 24-hour railway clock:
(a) 07:45 am
(b) 03:20 pm
(c) 21:50 hours Time Arithmetic • 24-Hour Railway Clock 3 Marks
(a) 07:45 am
(b) 03:20 pm
(c) 21:50 hours Time Arithmetic • 24-Hour Railway Clock 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Conversions:
• (a) 07:45 am: Since it is am before noon, the time remains 07:45 hours.
• (b) 03:20 pm: Since it is pm after noon, add 12 hours: 3:20 + 12:00 = 15:20 hours.
• (c) 21:50 hours: Since it is greater than 12:00, subtract 12 hours: 21:50 - 12:00 = 09:50 pm.
• (a) 07:45 am: Since it is am before noon, the time remains 07:45 hours.
• (b) 03:20 pm: Since it is pm after noon, add 12 hours: 3:20 + 12:00 = 15:20 hours.
• (c) 21:50 hours: Since it is greater than 12:00, subtract 12 hours: 21:50 - 12:00 = 09:50 pm.
CBSE Step-by-Step Marking Scheme
(a) 07:45 hours
1.0 M
(b) 15:20 hours
1.0 M
(c) 09:50 pm
1.0 M
Q3
A superfast train departs from New Delhi at 06:15 am and arrives in Amritsar on the same day at 01:45 pm. What is the total duration of the train journey?
Elapsed Time • Journey Duration
3 Marks
✅ Step-by-Step Model Answer & Solution:
Elapsed Time Calculation:
• Departure Time: 06:15 am
• Arrival Time: 01:45 pm
1. From 06:15 am to 12:15 pm (noon) = 6 hours.
2. From 12:15 pm to 01:15 pm = 1 hour.
3. From 01:15 pm to 01:45 pm = 30 minutes.
Total Journey Time = 6 hours + 1 hour + 30 minutes = 7 hours 30 minutes.
• Departure Time: 06:15 am
• Arrival Time: 01:45 pm
1. From 06:15 am to 12:15 pm (noon) = 6 hours.
2. From 12:15 pm to 01:15 pm = 1 hour.
3. From 01:15 pm to 01:45 pm = 30 minutes.
Total Journey Time = 6 hours + 1 hour + 30 minutes = 7 hours 30 minutes.
CBSE Step-by-Step Marking Scheme
Decomposing time to noon milestone
1.5 M
Accurate sum: 7 hours 30 minutes
1.5 M
Q4
A packet of butter shows 'Manufacture Date: 15/04/2026' and 'Best before 180 days from packaging'. Can it be safely consumed on 15th October 2026? Show calculations.
Calendar Literacy • Expiry Dates
3 Marks
✅ Step-by-Step Model Answer & Solution:
Days Count Calculation:
• Days remaining in April (after 15th): 30 - 15 = 15 days.
• May: 31 days.
• June: 30 days.
• July: 31 days.
• August: 31 days.
• September: 30 days.
• Total days elapsed by Sept 30 = 15 + 31 + 30 + 31 + 31 + 30 = 168 days.
Remaining valid days for October = 180 - 168 = 12 days.
Hence, the product expires on 12th October 2026.
Therefore, on 15th October 2026 (183 days), the butter is expired and unsafe to consume.
• Days remaining in April (after 15th): 30 - 15 = 15 days.
• May: 31 days.
• June: 30 days.
• July: 31 days.
• August: 31 days.
• September: 30 days.
• Total days elapsed by Sept 30 = 15 + 31 + 30 + 31 + 31 + 30 = 168 days.
Remaining valid days for October = 180 - 168 = 12 days.
Hence, the product expires on 12th October 2026.
Therefore, on 15th October 2026 (183 days), the butter is expired and unsafe to consume.
CBSE Step-by-Step Marking Scheme
Accurate month-by-month day counting (168 days up to Sept 30)
1.5 M
Calculating expiry on Oct 12 and concluding unsafe on Oct 15
1.5 M
Q5
In Chapter 12 ('Ticking Clocks and Turning Calendar'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Medicine Expiry Date Verification
Real-World Math Context: A medicine bottle has manufacturing date 'MFG: 03/24' and states 'Best before 24 months from manufacture'.
Analytical Task: Can this medicine be safely consumed in February 2026? What is the last safe month?
Analysis:
• Manufacturing date = March 2024 (03/24).
• Adding 24 months (2 full years): March 2024 + 2 years = March 2026.
Conclusion:
Yes, it can be safely consumed in February 2026 because February 2026 falls before the expiry date of March 2026.
• Manufacturing date = March 2024 (03/24).
• Adding 24 months (2 full years): March 2024 + 2 years = March 2026.
Conclusion:
Yes, it can be safely consumed in February 2026 because February 2026 falls before the expiry date of March 2026.
CBSE Assessment Rubric: 1 Mark for calculating expiry month (March 2026); 1 Mark for valid consumption conclusion.
13
Unit 5: Financial Literacy, Fares & Travel Planning • Class 4 Mathematics (New NEP 2020)
Chapter 13: The Transport Museum
Ticket Booking, Travel Fares, Currency Operations (Rupees & Paise) & Timetables
Chapter Highlights, Mathematical Ideas & Key Properties
- Financial arithmetic involving Indian Currency: Rupees (₹) and Paise (p); 1 Rupee = 100 Paise.
- Reading and interpreting bus/train fare charts and ticket rates for adults and children.
- Calculating change returned by cashiers during purchases.
- Planning trip budgets and comparing transport choices.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
A family of 2 adults and 3 children visits the Transport Museum. Ticket rates are ₹85 per adult and ₹40 per child. (a) What is the total ticket cost? (b) The father pays with a ₹500 currency note. How much change does the booking clerk return?
Currency Operations & Change Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Total Ticket Cost:
• Cost for 2 adults = 2 × ₹85 = ₹170.
• Cost for 3 children = 3 × ₹40 = ₹120.
• Total cost = ₹170 + ₹120 = ₹290.
(b) Change Returned:
• Amount given = ₹500.
• Total bill = ₹290.
• Change = ₹500 - ₹290 = ₹210.
• Cost for 2 adults = 2 × ₹85 = ₹170.
• Cost for 3 children = 3 × ₹40 = ₹120.
• Total cost = ₹170 + ₹120 = ₹290.
(b) Change Returned:
• Amount given = ₹500.
• Total bill = ₹290.
• Change = ₹500 - ₹290 = ₹210.
CBSE Step-by-Step Marking Scheme
Correct adult and child ticket total (₹290)
1.5 M
Correct change calculation (₹210)
1.5 M
Q2
At the transport museum gift shop, Kabir buys 3 toy vintage cars at ₹125 each, 2 model aeroplanes at ₹240 each, and 4 souvenir keychains at ₹35 each. Prepare a cash memo and calculate the total bill.
Financial Literacy • Creating a Cash Bill
3 Marks
✅ Step-by-Step Model Answer & Solution:
Cash Memo / Bill Preparation:
-----------------------------------------------------------
Item Quantity Rate (₹) Amount (₹)
-----------------------------------------------------------
1. Toy Vintage Cars 3 ₹125 ₹375
2. Model Aeroplanes 2 ₹240 ₹480
3. Souvenir Keychains 4 ₹35 ₹140
-----------------------------------------------------------
Total Bill Amount = ₹375 + ₹480 + ₹140 = ₹995.
If Kabir pays with a ₹1,000 note, change returned = ₹1,000 - ₹995 = ₹5.
-----------------------------------------------------------
Item Quantity Rate (₹) Amount (₹)
-----------------------------------------------------------
1. Toy Vintage Cars 3 ₹125 ₹375
2. Model Aeroplanes 2 ₹240 ₹480
3. Souvenir Keychains 4 ₹35 ₹140
-----------------------------------------------------------
Total Bill Amount = ₹375 + ₹480 + ₹140 = ₹995.
If Kabir pays with a ₹1,000 note, change returned = ₹1,000 - ₹995 = ₹5.
CBSE Step-by-Step Marking Scheme
Correct subtotal for all three items
1.5 M
Correct grand total of ₹995 and change ₹5
1.5 M
Q3
If 8 bus tickets from the city centre to the museum cost ₹360, how much will 15 tickets cost?
Unitary Method • Real-World Math
2 Marks
✅ Step-by-Step Model Answer & Solution:
Unitary Method Solution:
1. Cost of 1 ticket:
₹360 ÷ 8 = ₹45 per ticket.
2. Cost of 15 tickets:
15 × ₹45 = ₹675.
The cost of 15 bus tickets is ₹675.
1. Cost of 1 ticket:
₹360 ÷ 8 = ₹45 per ticket.
2. Cost of 15 tickets:
15 × ₹45 = ₹675.
The cost of 15 bus tickets is ₹675.
CBSE Step-by-Step Marking Scheme
Unit cost calculation: ₹360 ÷ 8 = ₹45
1.0 M
Final cost calculation: 15 × ₹45 = ₹675
1.0 M
Q4
How many ₹50 notes make ₹2,500? How many ₹200 notes make ₹1,600?
Money Arithmetic • Currency Denominations
2 Marks
✅ Step-by-Step Model Answer & Solution:
Currency Calculations:
• (a) ₹2,500 ÷ ₹50 = 50 notes of ₹50.
• (b) ₹1,600 ÷ ₹200 = 8 notes of ₹200.
• (a) ₹2,500 ÷ ₹50 = 50 notes of ₹50.
• (b) ₹1,600 ÷ ₹200 = 8 notes of ₹200.
CBSE Step-by-Step Marking Scheme
(a) 50 notes
1.0 M
(b) 8 notes
1.0 M
Q5
In Chapter 13 ('The Transport Museum'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Toy Train Ride Booking
Real-World Math Context: The museum toy train operates every 20 minutes from 10:00 am. It accommodates 32 passengers per trip.
Analytical Task: How many trips will the train make between 10:00 am and 12:00 noon, and what is the maximum number of visitors it can carry?
Trip Calculation:
• Duration from 10:00 am to 12:00 noon = 2 hours = 120 minutes.
• Number of trips = 120 min ÷ 20 min = 6 trips (at 10:00, 10:20, 10:40, 11:00, 11:20, 11:40).
• Maximum visitors = 6 trips × 32 passengers = 192 passengers.
• Duration from 10:00 am to 12:00 noon = 2 hours = 120 minutes.
• Number of trips = 120 min ÷ 20 min = 6 trips (at 10:00, 10:20, 10:40, 11:00, 11:20, 11:40).
• Maximum visitors = 6 trips × 32 passengers = 192 passengers.
CBSE Assessment Rubric: 1 Mark for 6 trips; 1 Mark for 192 total passengers.
14
Unit 5: Data Representation & Interpretation • Class 4 Mathematics (New NEP 2020)
Chapter 14: Data Handling
Pictographs, Bar Graphs, Tally Tables & Frequency Distribution
Chapter Highlights, Mathematical Ideas & Key Properties
- Representing information using pictographs with a defined scale key (e.g., 1 icon = 5 students).
- Drawing and reading vertical and horizontal bar graphs with labeled axes.
- Finding maximum, minimum, and difference values from graphical data.
- Drawing valid conclusions and inferences from statistical representations.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
In a pictograph, the symbol 📚 represents 6 library books borrowed. Look at the data: Class 4A has 5 symbols; Class 4B has 4 symbols; Class 4C has 6 symbols; Class 4D has 3 and a half symbols. (a) How many books were borrowed by each class? (b) What is the total number of books borrowed?
Pictograph & Scale Interpretation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Scale: 1 symbol 📚 = 6 books.
Half symbol = 6 ÷ 2 = 3 books.
(a) Books borrowed by each section:
• Class 4A: 5 × 6 = 30 books.
• Class 4B: 4 × 6 = 24 books.
• Class 4C: 6 × 6 = 36 books.
• Class 4D: (3 × 6) + 3 = 18 + 3 = 21 books.
(b) Total books borrowed:
Total = 30 + 24 + 36 + 21 = 111 books.
Half symbol = 6 ÷ 2 = 3 books.
(a) Books borrowed by each section:
• Class 4A: 5 × 6 = 30 books.
• Class 4B: 4 × 6 = 24 books.
• Class 4C: 6 × 6 = 36 books.
• Class 4D: (3 × 6) + 3 = 18 + 3 = 21 books.
(b) Total books borrowed:
Total = 30 + 24 + 36 + 21 = 111 books.
CBSE Step-by-Step Marking Scheme
Correct calculation for all 4 sections with half-symbol logic
2.0 M
Accurate sum of 111 books
1.0 M
Q2
In a school library pictograph, one symbol 📖 represents 10 books. The records show:
• Science: 📖 📖 📖 📖
• Maths: 📖 📖 📖 📖 📖 📖
• Storybooks: 📖 📖 📖 📖 📖 📖 📖 📖
(a) How many Maths books are there? (b) How many more Storybooks are there than Science books? Data Handling • Pictograph Interpretation 3 Marks
• Science: 📖 📖 📖 📖
• Maths: 📖 📖 📖 📖 📖 📖
• Storybooks: 📖 📖 📖 📖 📖 📖 📖 📖
(a) How many Maths books are there? (b) How many more Storybooks are there than Science books? Data Handling • Pictograph Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Pictograph Reading (Key: 📖 = 10 books):
• Science = 4 symbols × 10 = 40 books.
• Maths = 6 symbols × 10 = 60 books.
• Storybooks = 8 symbols × 10 = 80 books.
1. (a) Number of Maths books: 60 books.
2. (b) Difference between Storybooks and Science:
80 - 40 = 40 more Storybooks.
• Science = 4 symbols × 10 = 40 books.
• Maths = 6 symbols × 10 = 60 books.
• Storybooks = 8 symbols × 10 = 80 books.
1. (a) Number of Maths books: 60 books.
2. (b) Difference between Storybooks and Science:
80 - 40 = 40 more Storybooks.
CBSE Step-by-Step Marking Scheme
Using key scale of 10 books accurately
1.0 M
Maths books count = 60
1.0 M
Difference = 40 books
1.0 M
Q3
A survey of 40 children about their favourite sport revealed: 20 like Cricket, 10 like Football, and 10 like Badminton. Represent this data as fractions on a circular Chapati Chart.
Data Visualization • Chapati (Pie) Chart
3 Marks
✅ Step-by-Step Model Answer & Solution:
Circular Chart Representation (Total = 40 children):
• Cricket: 20 out of 40 = 20/40 = 1/2 (Half of the circle).
• Football: 10 out of 40 = 10/40 = 1/4 (One-fourth / quarter of the circle).
• Badminton: 10 out of 40 = 10/40 = 1/4 (One-fourth / quarter of the circle).
On the circular chart, draw a straight diameter dividing the circle into two halves; label one half 'Cricket (1/2)'. Divide the other half into two equal quarters; label one 'Football (1/4)' and the other 'Badminton (1/4)'.
• Cricket: 20 out of 40 = 20/40 = 1/2 (Half of the circle).
• Football: 10 out of 40 = 10/40 = 1/4 (One-fourth / quarter of the circle).
• Badminton: 10 out of 40 = 10/40 = 1/4 (One-fourth / quarter of the circle).
On the circular chart, draw a straight diameter dividing the circle into two halves; label one half 'Cricket (1/2)'. Divide the other half into two equal quarters; label one 'Football (1/4)' and the other 'Badminton (1/4)'.
CBSE Step-by-Step Marking Scheme
Calculating correct fractional share (1/2, 1/4, 1/4)
1.5 M
Describing accurate geometric sector partition of circle
1.5 M
Q4
Represent the number 18 using standard 5-bar tally marks.
Tally Marks • Organizing Raw Data
2 Marks
✅ Step-by-Step Model Answer & Solution:
Tally Marks for 18:
Standard tally marks group in clusters of five (four vertical bars crossed by a diagonal fifth bar||||):
• 18 = 5 + 5 + 5 + 3
•|||| |||| |||| |||
(Three groups of five plus three individual tally bars).
Standard tally marks group in clusters of five (four vertical bars crossed by a diagonal fifth bar
• 18 = 5 + 5 + 5 + 3
•
(Three groups of five plus three individual tally bars).
CBSE Step-by-Step Marking Scheme
Three groups of 5 tallies plus 3 singles correctly written
2.0 M
Q5
In Chapter 14 ('Data Handling'), a classroom project investigates real-world mathematics: If a school bus travels 48 kilometres on 4 litres of diesel, what is the mileage (kilometres per litre) of the bus? How much diesel is needed for a 120-kilometre journey?
Textbook Exercise • Real-World Context
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
1. Mileage calculation:
• Distance = 48 km, Diesel used = 4 L.
• Mileage = 48 ÷ 4 = 12 km per litre.
2. Diesel for 120 km:
• Required diesel = Total distance ÷ Mileage = 120 ÷ 12 = 10 litres.
CBSE Step-by-Step Marking Scheme
Mileage = 12 km/L
1.5 M
Diesel needed = 10 L
1.5 M
Q6
Convert the following measurements into standard units:
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams. Practice Time • Measurement & Conversions 3 Marks
✅ Step-by-Step Model Answer & Solution:
Conversions:
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
• (a) 1 m = 100 cm → (4 × 100) + 65 = 465 cm.
• (b) 1000 mL = 1 L → 3500 mL = 3 L 500 mL.
• (c) 1 kg = 1000 g → (2 × 1000) + 750 = 2750 g.
CBSE Step-by-Step Marking Scheme
465 cm
1 M
3 L 500 mL
1 M
2750 g
1 M
Q7
Look at a solid brick:
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
(a) How many faces does a brick have?
(b) What is the shape of each face?
(c) How many straight edges and how many corners (vertices) does a brick have? Try These • Geometry and Shapes 3 Marks
✅ Step-by-Step Model Answer & Solution:
Properties of a Brick (Cuboid):
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
• (a) Faces: A brick has 6 flat faces.
• (b) Shape of faces: Each face is a rectangle.
• (c) Edges and Corners: It has 12 straight edges and 8 corners (vertices).
CBSE Step-by-Step Marking Scheme
6 faces
1 M
Rectangular faces
1 M
12 edges and 8 corners
1 M
Q8
At a recycling shop, the rate list shows: Waste paper = ₹12 per kg, Plastic = ₹18 per kg, Iron = ₹25 per kg.
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
Ramesh sells 10 kg of waste paper, 5 kg of plastic, and 4 kg of iron.
(a) Find the cost of each item sold.
(b) What is the total money Ramesh earns? Money & Accounts • Rate List Calculation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
• Waste paper: 10 × ₹12 = ₹120.
• Plastic: 5 × ₹18 = ₹90.
• Iron: 4 × ₹25 = ₹100.
• Total Earnings: ₹120 + ₹90 + ₹100 = ₹310.
CBSE Step-by-Step Marking Scheme
Individual costs (₹120, ₹90, ₹100)
1.5 M
Total = ₹310
1.5 M
Q9
A rectangular chocolate bar has 16 equal pieces. Reena gives 1/4 of the chocolate to her brother and 1/2 of it to her friend.
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
(a) How many pieces does her brother receive?
(b) How many pieces does her friend receive?
(c) How many pieces are left for Reena? Fractions Exploration • Parts of a Whole 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Breakdown:
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
• Total pieces = 16.
• Brother's share (1/4): 16 ÷ 4 = 4 pieces.
• Friend's share (1/2): 16 ÷ 2 = 8 pieces.
• Remaining for Reena: 16 - (4 + 8) = 16 - 12 = 4 pieces (which is 1/4 of the bar).
CBSE Step-by-Step Marking Scheme
Brother = 4 pieces
1 M
Friend = 8 pieces
1 M
Reena = 4 pieces
1 M
Q10
A school cricket match began at 9:30 AM and concluded at 1:15 PM.
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last? Time & Clocks • Elapsed Time 3 Marks
✅ Step-by-Step Model Answer & Solution:
Time Calculations:
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
• (a) 24-hour time: 1:15 PM = 12:00 + 1:15 = 13:15 hours.
• (b) Duration:
• From 9:30 AM to 12:30 PM = 3 hours.
• From 12:30 PM to 1:15 PM = 45 minutes.
• Total duration = 3 hours and 45 minutes.
CBSE Step-by-Step Marking Scheme
13:15 hours in 24-hr clock
1 M
Duration = 3 hours 45 minutes with steps
2 M
Q11
A square vegetable garden has a side length of 15 metres.
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
(a) What is the total length of wire fence needed to go around the garden once?
(b) If fencing costs ₹20 per metre, find the total cost of fencing. Perimeter & Area • Fencing a Field 3 Marks
✅ Step-by-Step Model Answer & Solution:
Perimeter & Cost:
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
• (a) Perimeter of square: 4 × Side = 4 × 15 m = 60 metres.
• (b) Total Cost: Perimeter × Rate = 60 m × ₹20/m = ₹1,200.
CBSE Step-by-Step Marking Scheme
Perimeter = 60 m
1.5 M
Cost = ₹1,200
1.5 M
Q12
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ? Mental Math • Division and Multiplication 2 Marks
✅ Step-by-Step Model Answer & Solution:
Solutions:
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
• (a) 72 ÷ 6 = (60 ÷ 6) + (12 ÷ 6) = 10 + 2 = 12.
• (b) 15 × 8 = (10 × 8) + (5 × 8) = 80 + 40 = 120.
• (c) 25 × 40 = (25 × 4) × 10 = 100 × 10 = 1000.
• (d) 96 ÷ 8 = (80 ÷ 8) + (16 ÷ 8) = 10 + 2 = 12.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q13
Look at the letter 'H' and the letter 'N':
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
(a) What does each look like after a half-turn (180° rotation)?
(b) What does each look like after a quarter-turn (90° rotation)? Patterns & Symmetries • Rotational Turns 2 Marks
✅ Step-by-Step Model Answer & Solution:
Rotational Symmetry:
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
• (a) Half-turn (180°): Both 'H' and 'N' look exactly the same after a half-turn.
• (b) Quarter-turn (90°): 'H' rotates to look like 'I' with sleeping bars, and 'N' rotates to look like 'Z'.
CBSE Step-by-Step Marking Scheme
Half-turn explanation (same)
1 M
Quarter-turn explanation
1 M
Q14
In a Class 4 survey of 40 children, 20 like Cricket, 10 like Football, and 10 like Badminton.
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data. Smart Charts • Data Interpretation 3 Marks
✅ Step-by-Step Model Answer & Solution:
Data & Chapati Chart:
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
• (a) Fraction: 20 out of 40 = 20/40 = 1/2 (half of the class).
• (b) Chapati Chart: A circle divided in half represents Cricket (1/2). The other half is split equally into two quarters (1/4 for Football and 1/4 for Badminton).
CBSE Step-by-Step Marking Scheme
Fraction = 1/2 for cricket
1.5 M
Pie chart sectors explained (1/2, 1/4, 1/4)
1.5 M
Q15
State True or False:
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
(a) A circle has no corners and no straight edges.
(b) 1 litre is equal to 100 millilitres.
(c) The perimeter of any rectangle is 2 × (Length + Breadth). Chapter Review • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
• (a) True: A circle is a smooth curve with 0 corners.
• (b) False: 1 Litre is equal to 1000 millilitres.
• (c) True: Perimeter = 2 × (L + B).
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
School Canteen Drink Preferences
Real-World Math Context: A bar graph shows fruit juice sales: Lemonade = 45 glasses, Apple Juice = 30 glasses, Orange Juice = 55 glasses, and Coconut Water = 70 glasses.
Analytical Task: Which drink is the most popular, and how many more glasses of coconut water were sold than apple juice?
Analysis:
• Most popular drink = Coconut Water (70 glasses).
• Difference between coconut water and apple juice = 70 - 30 = 40 glasses.
• Most popular drink = Coconut Water (70 glasses).
• Difference between coconut water and apple juice = 70 - 30 = 40 glasses.
CBSE Assessment Rubric: 1 Mark for identifying coconut water; 1 Mark for 40 glasses difference.
1
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 1: Building with Bricks
Brick Patterns, Arch Designs (Mehrab, Jharokha), Brick Geometry & Brick Kiln Arithmetic
Chapter Highlights, Mathematical Ideas & Key Properties
- Architectural brick patterns from Jagriti School, Murshidabad: floor patterns, circular patterns, and mirror patterns.
- Geometric dimensions and faces of a standard brick: 6 rectangular faces, 12 edges, 8 corners.
- Traditional Indian architectural arches: Mehrab, circular arches, and decorative Jharokhas.
- Large number calculations: Indian brick kilns producing 1,00,000 (one lakh) bricks; calculating the cost of thousands of bricks.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Answer the following questions about a brick: (a) How many faces does a brick have? (b) Is any face of a standard brick a square? (c) Draw the smallest face of a brick. (d) Which of the following shapes can be a face of a brick: Triangle, Square, Rectangle, Circle?
Textbook Exercise • Geometric Properties of a Brick
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) A standard brick has 6 rectangular faces.
(b) No, in standard construction bricks, all 6 faces are rectangles of varying dimensions (length × width, length × height, width × height). None of the faces is a square.
(c) Smallest face: The side face measuring width × height (approximately 10 cm × 7 cm) is the smallest face.
(d) Face shape: Only a Rectangle can be a face of a standard brick (triangles and circles cannot form brick faces).
(b) No, in standard construction bricks, all 6 faces are rectangles of varying dimensions (length × width, length × height, width × height). None of the faces is a square.
(c) Smallest face: The side face measuring width × height (approximately 10 cm × 7 cm) is the smallest face.
(d) Face shape: Only a Rectangle can be a face of a standard brick (triangles and circles cannot form brick faces).
CBSE Step-by-Step Marking Scheme
Correct face count (6) and shape verification
1.5 M
Smallest face description and rectangle identification
1.5 M
Q2
Bhajan went to buy bricks. The rate was ₹1,800 for 1,000 old bricks, ₹2,000 for 1,000 new bricks from Brickabad, and ₹1,200 for 1,000 bricks from Itapur. If Bhajan buys 3,000 new bricks from Brickabad and 500 old bricks, how much money will he pay in total?
Brick Kiln Cost Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step 1: Cost of 3,000 new bricks from Brickabad:
• Cost of 1,000 new bricks = ₹2,000.
• Cost of 3,000 new bricks = 3 × ₹2,000 = ₹6,000.
Step 2: Cost of 500 old bricks:
• Cost of 1,000 old bricks = ₹1,800.
• Cost of 500 bricks (half of 1,000) = ₹1,800 ÷ 2 = ₹900.
Step 3: Total Payment:
• Total = ₹6,000 + ₹900 = ₹6,900.
• Cost of 1,000 new bricks = ₹2,000.
• Cost of 3,000 new bricks = 3 × ₹2,000 = ₹6,000.
Step 2: Cost of 500 old bricks:
• Cost of 1,000 old bricks = ₹1,800.
• Cost of 500 bricks (half of 1,000) = ₹1,800 ÷ 2 = ₹900.
Step 3: Total Payment:
• Total = ₹6,000 + ₹900 = ₹6,900.
CBSE Step-by-Step Marking Scheme
Calculation for 3,000 new bricks (₹6,000)
1.0 M
Calculation for 500 old bricks (₹900)
1.0 M
Total payment ₹6,900 with clear working
1.0 M
Q3
What is an 'Arch' (कमान) in brick architecture? Where can you see traditional brick jali patterns in historical Indian monuments?
Architectural Patterns • Arches & Jali
3 Marks
✅ Step-by-Step Model Answer & Solution:
1. Brick Arch (Kaman):
An arch is a curved symmetrical structural opening built of wedge-shaped bricks arranged over an entrance or bridge. The bricks support each other by pressing against one another, transferring heavy downward weight safely to the side pillars without needing a horizontal wooden beam.
2. Traditional Brick Jali (Lattice):
Brick jalis are decorative screen walls created by leaving systematic hollow spaces between bricks during masonry. They allow cool breeze and soft geometric light patterns to enter while keeping harsh sun and rain out. Famous examples include the Jaagrithi School in Murshidabad (West Bengal) and historical Mughal monuments.
An arch is a curved symmetrical structural opening built of wedge-shaped bricks arranged over an entrance or bridge. The bricks support each other by pressing against one another, transferring heavy downward weight safely to the side pillars without needing a horizontal wooden beam.
2. Traditional Brick Jali (Lattice):
Brick jalis are decorative screen walls created by leaving systematic hollow spaces between bricks during masonry. They allow cool breeze and soft geometric light patterns to enter while keeping harsh sun and rain out. Famous examples include the Jaagrithi School in Murshidabad (West Bengal) and historical Mughal monuments.
CBSE Step-by-Step Marking Scheme
Structural principle of brick arch and weight distribution
1.5 M
Jali pattern description and historical monument examples
1.5 M
Q4
Bhajan went to buy bricks. The price of new bricks from Brickabad was ₹2,000 for 1,000 bricks. He bought 3,000 bricks. If he also bought 500 old bricks at ₹1,200 for 1,000 bricks, how much total money did he pay?
Commercial Arithmetic • Cost of Bricks
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Calculation:
1. Cost of New Bricks from Brickabad:
• Cost of 1,000 bricks = ₹2,000.
• Cost of 3,000 bricks = 3 × ₹2,000 = ₹6,000.
2. Cost of Old Bricks:
• Cost of 1,000 bricks = ₹1,200.
• Cost of 500 bricks (half of 1,000) = ₹1,200 ÷ 2 = ₹600.
3. Total Money Paid:
₹6,000 + ₹600 = ₹6,600.
1. Cost of New Bricks from Brickabad:
• Cost of 1,000 bricks = ₹2,000.
• Cost of 3,000 bricks = 3 × ₹2,000 = ₹6,000.
2. Cost of Old Bricks:
• Cost of 1,000 bricks = ₹1,200.
• Cost of 500 bricks (half of 1,000) = ₹1,200 ÷ 2 = ₹600.
3. Total Money Paid:
₹6,000 + ₹600 = ₹6,600.
CBSE Step-by-Step Marking Scheme
Cost of new bricks (₹6,000)
1.0 M
Cost of old bricks (₹600)
1.0 M
Total sum: ₹6,600
1.0 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Estimating Bricks for a Compound Wall
Real-World Math Context: A mason calculates that 1 metre length of a 1-metre high boundary wall requires 100 bricks. The school desires to construct a 45-metre long and 1-metre high wall.
Analytical Task: How many bricks should the school order? If each truck carries 2,500 bricks, how many truckloads are needed?
Step 1: Total bricks needed:
45 m × 100 bricks/m = 4,500 bricks.
Step 2: Number of truckloads:
4,500 ÷ 2,500 = 1 full truck (2,500 bricks) with 2,000 bricks remaining.
Therefore, 2 truckloads must be ordered so the project has enough bricks.
45 m × 100 bricks/m = 4,500 bricks.
Step 2: Number of truckloads:
4,500 ÷ 2,500 = 1 full truck (2,500 bricks) with 2,000 bricks remaining.
Therefore, 2 truckloads must be ordered so the project has enough bricks.
CBSE Assessment Rubric: 1 Mark for 4,500 bricks; 1 Mark for practical answer of 2 truckloads.
2
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 2: Long and Short
Measuring Heights, Distances, Conversions (cm, m, km), Sports Records & Marathon Math
Chapter Highlights, Mathematical Ideas & Key Properties
- Comparing lengths visually and measuring accurately using a ruler and measuring tape.
- Units of length: 1 m = 100 cm; 1 km = 1,000 m.
- Analyzing world records and Indian records in high jump and long jump.
- Calculating distances in round tracks and solving marathon running problems.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Look at the athletic records: Javier S. holds the Men's World Record for High Jump at 2 m 45 cm. Chandrapal holds the Indian Record for High Jump at 2 m 17 cm. (a) How many more centimetres must Chandrapal jump to equal Javier's world record? (b) How many centimetres short of 2 and a half metres is Javier's jump?
Sports Records Comparison
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Difference between World and Indian High Jump records:
• Javier S. (World Record) = 2 m 45 cm = 245 cm.
• Chandrapal (Indian Record) = 2 m 17 cm = 217 cm.
• Difference = 245 cm - 217 cm = 28 cm.
Chandrapal must jump 28 cm higher.
(b) Short of 2 and a half metres (2 m 50 cm):
• 2 and a half metres = 2 m 50 cm = 250 cm.
• Javier's jump = 245 cm.
• Difference = 250 cm - 245 cm = 5 cm.
Javier's jump is only 5 cm short of 2.5 metres.
• Javier S. (World Record) = 2 m 45 cm = 245 cm.
• Chandrapal (Indian Record) = 2 m 17 cm = 217 cm.
• Difference = 245 cm - 217 cm = 28 cm.
Chandrapal must jump 28 cm higher.
(b) Short of 2 and a half metres (2 m 50 cm):
• 2 and a half metres = 2 m 50 cm = 250 cm.
• Javier's jump = 245 cm.
• Difference = 250 cm - 245 cm = 5 cm.
Javier's jump is only 5 cm short of 2.5 metres.
CBSE Step-by-Step Marking Scheme
Correct difference of 28 cm with conversion
1.5 M
Correct calculation showing 5 cm short of 2.5 m
1.5 M
Q2
A stadium running track is 400 metres long for one complete lap. People run a marathon race of 40 kilometres. How many complete rounds of the stadium track must a runner make to complete the 40 km marathon?
Marathon & Stadium Track Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step 1: Convert marathon distance into metres:
• 1 kilometre = 1,000 metres.
• 40 km = 40 × 1,000 = 40,000 metres.
Step 2: Calculate number of rounds:
• Length of 1 round of stadium = 400 metres.
• Number of rounds = Total distance ÷ Track length
• Number of rounds = 40,000 ÷ 400 = 100 rounds.
A runner must complete exactly 100 rounds of the stadium track.
• 1 kilometre = 1,000 metres.
• 40 km = 40 × 1,000 = 40,000 metres.
Step 2: Calculate number of rounds:
• Length of 1 round of stadium = 400 metres.
• Number of rounds = Total distance ÷ Track length
• Number of rounds = 40,000 ÷ 400 = 100 rounds.
A runner must complete exactly 100 rounds of the stadium track.
CBSE Step-by-Step Marking Scheme
Unit conversion 40 km = 40,000 m
1.5 M
Division 40,000 ÷ 400 = 100 rounds
1.5 M
Q3
In high jump, Javier S. holds the world record of 2 m 45 cm, and Chandra Pal holds the Indian record of 2 m 17 cm. How many centimetres higher must Chandra Pal jump to equal the world record?
Sports Arithmetic • High Jump & Long Jump
2 Marks
✅ Step-by-Step Model Answer & Solution:
Difference Calculation:
• World Record = 2 m 45 cm = 245 cm
• Indian Record = 2 m 17 cm = 217 cm
Difference = 245 cm - 217 cm = 28 cm.
Chandra Pal must jump 28 centimetres higher to equal the world record.
• World Record = 2 m 45 cm = 245 cm
• Indian Record = 2 m 17 cm = 217 cm
Difference = 245 cm - 217 cm = 28 cm.
Chandra Pal must jump 28 centimetres higher to equal the world record.
CBSE Step-by-Step Marking Scheme
Conversion to centimetres (245 cm and 217 cm)
1.0 M
Correct difference of 28 cm
1.0 M
Q4
A doctor tells Devi Prasad to run 2 km every day to stay fit. He runs around a square field with each side 500 metres long. (a) How many rounds of this field must he take to complete 2 km? (b) If he instead runs on a 400-metre circular stadium track, how many rounds are needed?
Marathon & Distance • Stadium Track
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution (Target = 2 km = 2,000 m):
1. (a) Square Field:
• Side = 500 m
• Perimeter of square = 4 × 500 m = 2,000 m.
• Number of rounds = 2,000 m ÷ 2,000 m = 1 round.
2. (b) 400-metre Stadium Track:
• Number of rounds = 2,000 m ÷ 400 m = 5 rounds.
1. (a) Square Field:
• Side = 500 m
• Perimeter of square = 4 × 500 m = 2,000 m.
• Number of rounds = 2,000 m ÷ 2,000 m = 1 round.
2. (b) 400-metre Stadium Track:
• Number of rounds = 2,000 m ÷ 400 m = 5 rounds.
CBSE Step-by-Step Marking Scheme
Square field perimeter (2,000 m) = 1 round
1.5 M
Stadium track calculation: 2,000 ÷ 400 = 5 rounds
1.5 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Daily Walking Distance Goal
Real-World Math Context: Doctor advises grandfather to walk 2 kilometres every day to stay fit. Grandfather walks around a square park that measures 125 metres on each side.
Analytical Task: How many complete rounds of the park must grandfather take to achieve his 2 km goal?
Step 1: Perimeter of square park:
Perimeter = 4 × 125 m = 500 metres per round.
Step 2: Rounds for 2 km:
2 km = 2,000 metres.
Rounds required = 2,000 m ÷ 500 m = 4 rounds.
Grandfather must walk 4 complete rounds.
Perimeter = 4 × 125 m = 500 metres per round.
Step 2: Rounds for 2 km:
2 km = 2,000 metres.
Rounds required = 2,000 m ÷ 500 m = 4 rounds.
Grandfather must walk 4 complete rounds.
CBSE Assessment Rubric: 1 Mark for park perimeter 500 m; 1 Mark for 4 rounds.
3
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 3: A Trip to Bhopal
Excursion Planning, Bus Seating, Petrol Pumps, Narmada Bridge & Bhimbetka Time Math
Chapter Highlights, Mathematical Ideas & Key Properties
- Calculating bus requirements based on total students and seat capacities (50-seater vs 35-seater mini-buses).
- Bridge length, river water level differences, and speed calculations over the Narmada River.
- Fuel costs, diesel filling rates, and time taken at petrol pumps.
- Prehistoric cave paintings at Bhimbetka: counting animal and human figures; boat ride ticket budgeting at Upper Lake Bhopal.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Total students going on the Bhopal trip from Class 1 to Class 5 are: Class 1: 33, Class 2: 32, Class 3: 42, Class 4: 50, Class 5: 53. (a) How many total children are going on the trip? (b) If the school hires 4 buses with 50 seats each, how many children will get seats? (c) How many children will be left without seats?
Excursion Bus Seating Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Total Children Going on the Trip:
33 (Class 1)
+ 32 (Class 2)
+ 42 (Class 3)
+ 50 (Class 4)
+ 53 (Class 5)
-------
210 total children.
(b) Seating Capacity of 4 Buses:
• Each bus has 50 seats.
• 4 buses have 4 × 50 = 200 seats.
So, 200 children will get seats.
(c) Children Left Without Seats:
• 210 - 200 = 10 children will be left without seats.
(They will share seats with classmates).
33 (Class 1)
+ 32 (Class 2)
+ 42 (Class 3)
+ 50 (Class 4)
+ 53 (Class 5)
-------
210 total children.
(b) Seating Capacity of 4 Buses:
• Each bus has 50 seats.
• 4 buses have 4 × 50 = 200 seats.
So, 200 children will get seats.
(c) Children Left Without Seats:
• 210 - 200 = 10 children will be left without seats.
(They will share seats with classmates).
CBSE Step-by-Step Marking Scheme
Correct sum of 210 children
1.0 M
Correct calculation of 200 seats in 4 buses
1.0 M
Difference of 10 children without seats
1.0 M
Q2
At the Bhopal lake, ticket prices are: Double-Decker Boat: ₹30 (45 mins), Motor Boat: ₹25 (20 mins), Paddle Boat: ₹15 (30 mins), Oar Boat: ₹15 (45 mins). (a) Indra and Bhanu first took the motor boat and then the oar boat. How much total did they pay for both? (b) Which boat makes two trips in 1 hour?
Boat Ride Rates & Time Budgeting
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Cost for Indra and Bhanu:
• Motor boat: Ticket = ₹25 per person. For 2 persons = 2 × ₹25 = ₹50.
• Oar boat: Ticket = ₹15 per person. For 2 persons = 2 × ₹15 = ₹30.
• Total amount paid = ₹50 + ₹30 = ₹80.
(b) Boat that makes 2 trips in 1 hour:
• 1 hour = 60 minutes.
• Time for 1 trip must be 60 ÷ 2 = 30 minutes.
• Looking at the table, the Paddle Boat has a trip duration of 30 minutes. Hence, the paddle boat makes two trips in 1 hour.
• Motor boat: Ticket = ₹25 per person. For 2 persons = 2 × ₹25 = ₹50.
• Oar boat: Ticket = ₹15 per person. For 2 persons = 2 × ₹15 = ₹30.
• Total amount paid = ₹50 + ₹30 = ₹80.
(b) Boat that makes 2 trips in 1 hour:
• 1 hour = 60 minutes.
• Time for 1 trip must be 60 ÷ 2 = 30 minutes.
• Looking at the table, the Paddle Boat has a trip duration of 30 minutes. Hence, the paddle boat makes two trips in 1 hour.
CBSE Step-by-Step Marking Scheme
Correct total fare of ₹80 for 2 children
1.5 M
Correct identification of Paddle Boat with 30 min duration
1.5 M
Q3
At the Bhopal lake, a motorboat charges ₹25 per person for a 20-minute ride, and a paddle boat charges ₹15 per person for a 45-minute ride. A group of 4 children have ₹100 and 40 minutes time. Which boat ride can they take?
Travel Budget • Boating Rates
3 Marks
✅ Step-by-Step Model Answer & Solution:
Comparison of Boating Options for 4 Children:
Available Budget = ₹100, Available Time = 40 minutes.
1. Motorboat Option:
• Total Cost = 4 × ₹25 = ₹100 (Within budget).
• Duration = 20 minutes (Well within 40 minutes).
2. Paddle Boat Option:
• Total Cost = 4 × ₹15 = ₹60 (Within budget).
• Duration = 45 minutes (Exceeds available 40 minutes).
Conclusion: They can only take the motorboat ride because the paddle boat exceeds their 40-minute time limit.
Available Budget = ₹100, Available Time = 40 minutes.
1. Motorboat Option:
• Total Cost = 4 × ₹25 = ₹100 (Within budget).
• Duration = 20 minutes (Well within 40 minutes).
2. Paddle Boat Option:
• Total Cost = 4 × ₹15 = ₹60 (Within budget).
• Duration = 45 minutes (Exceeds available 40 minutes).
Conclusion: They can only take the motorboat ride because the paddle boat exceeds their 40-minute time limit.
CBSE Step-by-Step Marking Scheme
Budget calculation for both boats (₹100 vs ₹60)
1.5 M
Time limit comparison selecting motorboat (20 mins vs 45 mins)
1.5 M
Q4
At a highway petrol pump, the driver filled 65 litres of diesel into a bus tank. If the diesel price was ₹84 per litre, calculate the total amount the school paid for the diesel.
Fuel Arithmetic • Filling Bus Tanks
2 Marks
✅ Step-by-Step Model Answer & Solution:
Multiplication Calculation:
6 5 litres
× 8 4 rupees
-----------
2 6 0 (65 × 4)
+ 5 2 0 0 (65 × 80)
-----------
5 4 6 0
The school paid ₹5,460 for the diesel.
6 5 litres
× 8 4 rupees
-----------
2 6 0 (65 × 4)
+ 5 2 0 0 (65 × 80)
-----------
5 4 6 0
The school paid ₹5,460 for the diesel.
CBSE Step-by-Step Marking Scheme
Correct partial products (260 and 5200)
1.0 M
Final total bill of ₹5,460
1.0 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Petrol Pump Refueling Time
Real-World Math Context: Two buses stop at a petrol pump to refill diesel. Each bus needs 50 litres of diesel. 1 litre of diesel costs ₹45. The pump fills diesel at a rate of 10 litres per minute.
Analytical Task: What is the total bill for both buses, and how long does it take to fill both buses?
Step 1: Total diesel required:
2 buses × 50 litres = 100 litres.
Step 2: Total cost:
100 litres × ₹45/litre = ₹4,500.
Step 3: Total filling time:
100 litres ÷ 10 litres/min = 10 minutes.
2 buses × 50 litres = 100 litres.
Step 2: Total cost:
100 litres × ₹45/litre = ₹4,500.
Step 3: Total filling time:
100 litres ÷ 10 litres/min = 10 minutes.
CBSE Assessment Rubric: 1 Mark for cost ₹4,500; 1 Mark for time 10 minutes.
4
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 4: Tick-Tick-Tick
Clock Reading, Movement of Minute Hand, 12h vs 24h Formats & Expiry Date Verification
Chapter Highlights, Mathematical Ideas & Key Properties
- Understanding clock mechanics: the minute hand moves 1 small mark (6°) in 1 minute, 5 marks (30°) from one number to the next.
- Calculating the time taken by the minute hand to move from one digit to another.
- Differentiating morning (am) and afternoon/evening (pm).
- Reading manufacturing (MFG) and expiry dates on ghee tins, medicines, and butter packets.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
How many minutes does it take the minute hand to move from: (a) 2 to 7, (b) 12 to 8, (c) 1 to 4, (d) 7 to 10?
Minute Hand Movement
3 Marks
✅ Step-by-Step Model Answer & Solution:
Each number on the clock represents 5 minutes.
• (a) From 2 to 7: (7 - 2) = 5 numbers. 5 × 5 = 25 minutes.
• (b) From 12 to 8: 8 numbers forward. 8 × 5 = 40 minutes.
• (c) From 1 to 4: (4 - 1) = 3 numbers. 3 × 5 = 15 minutes.
• (d) From 7 to 10: (10 - 7) = 3 numbers. 3 × 5 = 15 minutes.
• (a) From 2 to 7: (7 - 2) = 5 numbers. 5 × 5 = 25 minutes.
• (b) From 12 to 8: 8 numbers forward. 8 × 5 = 40 minutes.
• (c) From 1 to 4: (4 - 1) = 3 numbers. 3 × 5 = 15 minutes.
• (d) From 7 to 10: (10 - 7) = 3 numbers. 3 × 5 = 15 minutes.
CBSE Step-by-Step Marking Scheme
Correct answers for (a) and (b)
1.5 M
Correct answers for (c) and (d)
1.5 M
Q2
Amrit bought butter on 15 May 2026. It was written on the packet 'Best before 180 days from the date of packing'. The date of packing was 15/01/2026. Should Amrit eat this butter or not? Explain your calculation.
Product Expiry Date Check
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step 1: Calculate days from 15 January 2026 to 15 May 2026:
• January: 31 - 15 = 16 days remaining.
• February 2026 (non-leap year) = 28 days.
• March = 31 days.
• April = 30 days.
• May (up to 15th) = 15 days.
• Total days passed = 16 + 28 + 31 + 30 + 15 = 120 days.
Step 2: Compare with expiry limit:
• The packet is safe for 180 days.
• Since 120 days < 180 days, the butter has NOT expired.
• Conclusion: Yes, Amrit can safely eat the butter.
• January: 31 - 15 = 16 days remaining.
• February 2026 (non-leap year) = 28 days.
• March = 31 days.
• April = 30 days.
• May (up to 15th) = 15 days.
• Total days passed = 16 + 28 + 31 + 30 + 15 = 120 days.
Step 2: Compare with expiry limit:
• The packet is safe for 180 days.
• Since 120 days < 180 days, the butter has NOT expired.
• Conclusion: Yes, Amrit can safely eat the butter.
CBSE Step-by-Step Marking Scheme
Accurate monthly day count sum = 120 days
2.0 M
Valid comparison and safe consumption verdict
1.0 M
Q3
Munia was born on 5th March 2025. She cut her first tooth on 15th September 2025 and started walking on 2nd February 2026. (a) How old was she in completed months when she cut her first tooth? (b) How many months after birth did she start walking?
Developmental Timeline • Munia's Milestones
3 Marks
✅ Step-by-Step Model Answer & Solution:
Timeline Milestones:
Date of Birth: 5th March 2025
1. (a) First Tooth (15th September 2025):
From March to September = 6 months (March 5 to Sept 5 = 6 months) + 10 days.
Munia was 6 months and 10 days old.
2. (b) Walking (2nd February 2026):
From March 2025 to January 2026 = 10 months. Adding up to Feb 2 = nearly 11 months old.
Date of Birth: 5th March 2025
1. (a) First Tooth (15th September 2025):
From March to September = 6 months (March 5 to Sept 5 = 6 months) + 10 days.
Munia was 6 months and 10 days old.
2. (b) Walking (2nd February 2026):
From March 2025 to January 2026 = 10 months. Adding up to Feb 2 = nearly 11 months old.
CBSE Step-by-Step Marking Scheme
First tooth age: 6 months 10 days
1.5 M
Walking milestone age: approx 11 months
1.5 M
Q4
Is the year 2028 a leap year? How many days will the months of February and the entire year 2028 have?
Calendar Math • Number of Days in a Year
2 Marks
✅ Step-by-Step Model Answer & Solution:
Leap Year Test:
A year is a leap year if its last two digits are divisible by 4.
• 28 ÷ 4 = 7 (completely divisible, remainder 0).
Therefore, 2028 is a leap year.
Days Count:
• February 2028 will have 29 days.
• The entire year 2028 will have 366 days (instead of the normal 365 days).
A year is a leap year if its last two digits are divisible by 4.
• 28 ÷ 4 = 7 (completely divisible, remainder 0).
Therefore, 2028 is a leap year.
Days Count:
• February 2028 will have 29 days.
• The entire year 2028 will have 366 days (instead of the normal 365 days).
CBSE Step-by-Step Marking Scheme
Divisibility rule proving 2028 is a leap year
1.0 M
February has 29 days and total year has 366 days
1.0 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Missing a Train Due to 24-Hour Time Format
Real-World Math Context: Ranjit has a train ticket with departure time printed as '05:30'. He reaches the railway station at 5:00 in the evening on the same day.
Analytical Task: Did Ranjit catch his train or miss it? Explain why the railway ticket printed 05:30.
Ranjit missed his train.
Explanation: Indian Railways uses the 24-hour clock. '05:30' represents 5:30 am in the early morning. If the train were at 5:30 in the evening, the ticket would have printed '17:30'. Since Ranjit arrived at 5:00 pm (17:00), his train had already departed 11 hours and 30 minutes earlier.
Explanation: Indian Railways uses the 24-hour clock. '05:30' represents 5:30 am in the early morning. If the train were at 5:30 in the evening, the ticket would have printed '17:30'. Since Ranjit arrived at 5:00 pm (17:00), his train had already departed 11 hours and 30 minutes earlier.
CBSE Assessment Rubric: 1 Mark for missed train conclusion; 1 Mark for explaining 05:30 am vs 17:30 pm.
5
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 5: The Way The World Looks
Gappu's Balloon Journey, Aerial Maps, Matching Top Views & Perspective Drawing
Chapter Highlights, Mathematical Ideas & Key Properties
- Perspective changes with distance: objects look big and wide at the near end, but small and narrow at the distant end.
- Gappu's view from a gas balloon: seeing the top of the bed, fan blades, chairs, and park benches.
- Matching top view (bird's-eye view) with ground view for bowls, shoes, cars, and railway lines.
- Navigating classroom floor maps and finding doors, windows, and blackboards.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Why do the two sides of a railway track or road look wide and far apart near your feet, but appear to meet at a single point in the far distance?
Perspective Illusion Explanation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Scientific & Geometric Reason:
This phenomenon is called Perspective Convergence.
• Objects or distances that are close to our eyes subtend a larger visual angle, so they appear wider and larger.
• As objects move farther away, their visual angle shrinks, so they appear smaller and narrower.
• Although the two rails of a train track are strictly parallel and always equal distance apart on the ground, our eye's perspective causes them to appear to converge toward a 'vanishing point' on the horizon.
This phenomenon is called Perspective Convergence.
• Objects or distances that are close to our eyes subtend a larger visual angle, so they appear wider and larger.
• As objects move farther away, their visual angle shrinks, so they appear smaller and narrower.
• Although the two rails of a train track are strictly parallel and always equal distance apart on the ground, our eye's perspective causes them to appear to converge toward a 'vanishing point' on the horizon.
CBSE Step-by-Step Marking Scheme
Mentions perspective / visual angle effect
1.5 M
Explains parallel lines appearing to converge at horizon
1.5 M
Q2
Draw or describe: (a) The top view of a teacup, (b) The side view of a pressure cooker, (c) The top view of a railway track.
Perspective Views • Everyday Objects
3 Marks
✅ Step-by-Step Model Answer & Solution:
Perspective Projections:
• (a) Top View of a Teacup: Shows two concentric circles (the inner circle representing the cup rim and the outer circle representing the saucer) with a small oval loop on one side representing the handle.
• (b) Side View of a Pressure Cooker: Shows the cylindrical metallic body, the side handle, the lid clamp, and the safety weight (whistle) sitting on the top vent pipe.
• (c) Top View of a Railway Track: Shows two parallel vertical lines with horizontal wooden or concrete sleepers spaced evenly across them like a ladder.
• (a) Top View of a Teacup: Shows two concentric circles (the inner circle representing the cup rim and the outer circle representing the saucer) with a small oval loop on one side representing the handle.
• (b) Side View of a Pressure Cooker: Shows the cylindrical metallic body, the side handle, the lid clamp, and the safety weight (whistle) sitting on the top vent pipe.
• (c) Top View of a Railway Track: Shows two parallel vertical lines with horizontal wooden or concrete sleepers spaced evenly across them like a ladder.
CBSE Step-by-Step Marking Scheme
Accurate geometric description of teacup top view
1.0 M
Accurate side view of cooker
1.0 M
Accurate top view of railway track
1.0 M
Q3
On a neighbourhood map, Neha starts at the Park facing East. She walks 50 metres straight, turns 90° right, walks 30 metres, and enters the Library. (a) In which direction did she walk after turning? (b) In which direction is the Library from the Park?
Grid Map Navigation • Directions
3 Marks
✅ Step-by-Step Model Answer & Solution:
Spatial Navigation:
1. Direction after turning:
Starting facing East, turning 90° to the right means she is now facing South. She walked 30 metres South.
2. Position of Library relative to Park:
The Library is 50 m East and 30 m South of the Park. Therefore, the Library is located to the South-East of the Park.
1. Direction after turning:
Starting facing East, turning 90° to the right means she is now facing South. She walked 30 metres South.
2. Position of Library relative to Park:
The Library is 50 m East and 30 m South of the Park. Therefore, the Library is located to the South-East of the Park.
CBSE Step-by-Step Marking Scheme
Right turn from East = South
1.5 M
Combined position = South-East
1.5 M
Q4
A boy looks at a dice. The sum of opposite faces of a standard dice is always 7. If the top face shows 3 and the front face shows 2, what numbers are on: (a) the bottom face, (b) the back face?
Isometric 3D Blocks • Visual Reasoning
2 Marks
✅ Step-by-Step Model Answer & Solution:
Opposite Face Rule (Sum = 7):
• (a) Bottom Face: Opposite to the top face (3).
Bottom = 7 - 3 = 4.
• (b) Back Face: Opposite to the front face (2).
Back = 7 - 2 = 5.
• (a) Bottom Face: Opposite to the top face (3).
Bottom = 7 - 3 = 4.
• (b) Back Face: Opposite to the front face (2).
Back = 7 - 2 = 5.
CBSE Step-by-Step Marking Scheme
Bottom face = 4
1.0 M
Back face = 5
1.0 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Classroom Blackboard Location Map
Real-World Math Context: In a classroom top-view plan, the teacher's table is at (3, 5), the entrance door is at (1, 1), and student benches are arranged in 4 columns from X = 2 to 5.
Analytical Task: If a student enters through the door and walks straight North along the left aisle, which direction should she turn to face the teacher's table?
She should walk North up to Y = 5, and then turn Right (East) to face the teacher's table at (3, 5).
CBSE Assessment Rubric: 1 Mark for North direction; 1 Mark for Right / East turn.
6
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 6: The Junk Seller
Kiran's Junk Shop, Rate Lists, Loan Interest, Calculating Earnings & Column Multiplication
Chapter Highlights, Mathematical Ideas & Key Properties
- Real-life entrepreneurship: Kiran's story of establishing a junk shop in Patna.
- Understanding bank loans vs. moneylenders: calculating simple interest and monthly installments.
- Rate lists for scrap materials: waste paper, newspaper, iron, brass, plastic.
- Multiplication of currency and mental math strategies (e.g., 9 × 12 = 9 × 10 + 9 × 2).
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Hari and Babu each wanted to buy a handcart worth ₹300. (a) Hari took a loan of ₹300 from a bank. He pays back ₹51 every month for 6 months. How much does he pay back in total? (b) Babu took a loan of ₹300 from Chuni Lal (moneylender). After 6 months, he pays back ₹360. Who has to pay back more money, and by how much?
Loan Comparison: Bank vs. Moneylender
4 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Hari's Bank Loan Repayment:
• Monthly installment = ₹51.
• Duration = 6 months.
• Total paid = 6 × ₹51 = ₹306.
(Extra interest paid to bank = ₹306 - ₹300 = ₹6).
(b) Babu's Moneylender Loan Repayment:
• Total paid to Chuni Lal = ₹360.
(Extra interest paid to moneylender = ₹360 - ₹300 = ₹60).
Comparison:
• Babu pays back more money.
• Difference = ₹360 - ₹306 = ₹54 more.
This demonstrates why institutional bank loans are far fairer than unregulated moneylenders.
• Monthly installment = ₹51.
• Duration = 6 months.
• Total paid = 6 × ₹51 = ₹306.
(Extra interest paid to bank = ₹306 - ₹300 = ₹6).
(b) Babu's Moneylender Loan Repayment:
• Total paid to Chuni Lal = ₹360.
(Extra interest paid to moneylender = ₹360 - ₹300 = ₹60).
Comparison:
• Babu pays back more money.
• Difference = ₹360 - ₹306 = ₹54 more.
This demonstrates why institutional bank loans are far fairer than unregulated moneylenders.
CBSE Step-by-Step Marking Scheme
Hari's total repayment ₹306
1.5 M
Babu's total repayment ₹360
1.0 M
Comparison showing Babu pays ₹54 more
1.5 M
Q2
Using Kiran's rate list (Newspaper: ₹5/kg, Iron: ₹12/kg, Brass: ₹180/kg, Plastic: ₹10/kg), calculate the total amount Kiran pays for: (a) 42 kg of newspaper, (b) 25 kg of iron, (c) 3 kg of brass.
Scrap Rate Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) 42 kg of Newspaper at ₹5/kg:
• 42 × 5 = 42 × (10 ÷ 2) = 420 ÷ 2 = ₹210.
(b) 25 kg of Iron at ₹12/kg:
• 25 × 12 = 25 × (10 + 2) = 250 + 50 = ₹300.
(c) 3 kg of Brass at ₹180/kg:
• 3 × 180 = ₹540.
Total amount Kiran pays:
Total = ₹210 + ₹300 + ₹540 = ₹1,050.
• 42 × 5 = 42 × (10 ÷ 2) = 420 ÷ 2 = ₹210.
(b) 25 kg of Iron at ₹12/kg:
• 25 × 12 = 25 × (10 + 2) = 250 + 50 = ₹300.
(c) 3 kg of Brass at ₹180/kg:
• 3 × 180 = ₹540.
Total amount Kiran pays:
Total = ₹210 + ₹300 + ₹540 = ₹1,050.
CBSE Step-by-Step Marking Scheme
Correct calculation for all three items
2.0 M
Total bill sum ₹1,050
1.0 M
Q3
Kiran the junk seller buys scrap from collectors at these rates:
• Newspaper: ₹14/kg
• Iron: ₹22/kg
• Brass: ₹280/kg
Calculate the total amount Kiran pays for 40 kg newspaper, 15 kg iron, and 2 kg brass. Commercial Math • Kiran's Rate List 3 Marks
• Newspaper: ₹14/kg
• Iron: ₹22/kg
• Brass: ₹280/kg
Calculate the total amount Kiran pays for 40 kg newspaper, 15 kg iron, and 2 kg brass. Commercial Math • Kiran's Rate List 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Bill Calculation:
1. Newspaper (40 kg): 40 × ₹14 = ₹560.
2. Iron (15 kg): 15 × ₹22 = ₹330.
3. Brass (2 kg): 2 × ₹280 = ₹560.
Total Amount Paid:
₹560 + ₹330 + ₹560 = ₹1,450.
1. Newspaper (40 kg): 40 × ₹14 = ₹560.
2. Iron (15 kg): 15 × ₹22 = ₹330.
3. Brass (2 kg): 2 × ₹280 = ₹560.
Total Amount Paid:
₹560 + ₹330 + ₹560 = ₹1,450.
CBSE Step-by-Step Marking Scheme
Newspaper (₹560) and Iron (₹330)
1.0 M
Brass (₹560)
1.0 M
Total bill = ₹1,450
1.0 M
Q4
Hariyal took a loan of ₹300 from a bank and repaid ₹340 after 6 months. Babu took a loan of ₹300 from a moneylender and paid ₹60 every month for 6 months. Who paid back more money, and by how much?
Loan & Interest • Financial Comparison
3 Marks
✅ Step-by-Step Model Answer & Solution:
Comparison of Repayments:
• Hariyal (Bank): Total paid back = ₹340.
• Babu (Moneylender):
Paid ₹60 every month for 6 months = 6 × ₹60 = ₹360.
Difference:
₹360 - ₹340 = ₹20.
Babu paid back ₹20 more than Hariyal because of the moneylender's higher interest rate.
• Hariyal (Bank): Total paid back = ₹340.
• Babu (Moneylender):
Paid ₹60 every month for 6 months = 6 × ₹60 = ₹360.
Difference:
₹360 - ₹340 = ₹20.
Babu paid back ₹20 more than Hariyal because of the moneylender's higher interest rate.
CBSE Step-by-Step Marking Scheme
Babu's total payment calculation (6 × 60 = 360)
1.5 M
Correct comparison: Babu paid ₹20 more
1.5 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Kiran's Reselling Profit Margin
Real-World Math Context: Kiran buys 152 kg of plastic from scrap collectors at ₹10 per kg. She transports it to a big recycling factory and sells it at ₹12 per kg.
Analytical Task: How much money does Kiran earn as profit on this plastic sale?
Step 1: Profit per kg:
Selling Price - Cost Price = ₹12 - ₹10 = ₹2 per kg.
Step 2: Total profit on 152 kg:
152 kg × ₹2/kg = ₹304 profit.
Selling Price - Cost Price = ₹12 - ₹10 = ₹2 per kg.
Step 2: Total profit on 152 kg:
152 kg × ₹2/kg = ₹304 profit.
CBSE Assessment Rubric: 1 Mark for ₹2/kg margin; 1 Mark for ₹304 total profit.
7
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 7: Jugs and Mugs
Bunny and Banno's Wedding Feast, Capacity in Litres & Millilitres & Medical Doses
Chapter Highlights, Mathematical Ideas & Key Properties
- Bunny and Banno celebrate their wedding anniversary: animals drink kheer in millilitres and litres.
- Capacity conversion: 1 Litre (l) = 1,000 Millilitres (ml).
- Combinations that make 1 Litre: 500 ml + 500 ml; 250 ml × 4; 200 ml × 5; 100 ml × 10.
- Estimating liquid usage: water used in bathing, cooking, washing clothes, and eye-drop droppers.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
At the wedding party: (a) 1,000 ants arrive. Each ant drinks only 1 ml of kheer. How much kheer do all 1,000 ants drink together? (b) A donkey wonders how 1,000 ants can drink kheer. 10 frogs also arrive, and each frog drinks 100 ml. How much kheer do 10 frogs drink?
Bunny and Banno's Wedding Feast Arithmetic
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Kheer for 1,000 ants:
• Each ant drinks 1 ml.
• Total kheer = 1,000 × 1 ml = 1,000 ml = 1 Litre.
(b) Kheer for 10 frogs:
• Each frog drinks 100 ml.
• Total kheer = 10 × 100 ml = 1,000 ml = 1 Litre.
Interesting observation: Both the 1,000 tiny ants and the 10 frogs drink the exact same total amount of kheer (1 Litre each!).
• Each ant drinks 1 ml.
• Total kheer = 1,000 × 1 ml = 1,000 ml = 1 Litre.
(b) Kheer for 10 frogs:
• Each frog drinks 100 ml.
• Total kheer = 10 × 100 ml = 1,000 ml = 1 Litre.
Interesting observation: Both the 1,000 tiny ants and the 10 frogs drink the exact same total amount of kheer (1 Litre each!).
CBSE Step-by-Step Marking Scheme
Correct calculation for ants (1,000 ml = 1 l)
1.5 M
Correct calculation for frogs (1,000 ml = 1 l)
1.5 M
Q2
Look at the table of water used by a family of 4 people in one day: Cooking and drinking: 30 l, Washing clothes: 40 l, Cleaning pots and pans: 20 l, Bathing: 75 l. (a) What is the total water used by the family in one day? (b) How much water will they use in 1 week (7 days)?
Household Water Usage & Conservation
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Total water used in 1 day:
30 l (cooking/drinking)
+ 40 l (washing clothes)
+ 20 l (cleaning pans)
+ 75 l (bathing)
-------
165 Litres per day.
(b) Water used in 1 week (7 days):
• 165 l × 7 days = 1,155 Litres.
(Working: 100 × 7 = 700; 60 × 7 = 420; 5 × 7 = 35; 700 + 420 + 35 = 1,155 l).
30 l (cooking/drinking)
+ 40 l (washing clothes)
+ 20 l (cleaning pans)
+ 75 l (bathing)
-------
165 Litres per day.
(b) Water used in 1 week (7 days):
• 165 l × 7 days = 1,155 Litres.
(Working: 100 × 7 = 700; 60 × 7 = 420; 5 × 7 = 35; 700 + 420 + 35 = 1,155 l).
CBSE Step-by-Step Marking Scheme
Correct sum of 165 Litres for 1 day
1.5 M
Accurate multiplication 165 × 7 = 1,155 Litres
1.5 M
Q3
At Bunny's wedding feast, 1,000 ants arrived to drink kheer. Each ant drinks only 1 mL of kheer. (a) How many millilitres of kheer do 1,000 ants drink in total? (b) Convert this quantity into litres.
Capacity Multiples • Bunny's Wedding Feast
2 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Calculation:
1. Total Millilitres:
1,000 ants × 1 mL = 1,000 mL.
2. Convert to Litres:
Since 1,000 mL = 1 Litre,
1,000 mL ÷ 1,000 = 1 Litre of kheer in total.
1. Total Millilitres:
1,000 ants × 1 mL = 1,000 mL.
2. Convert to Litres:
Since 1,000 mL = 1 Litre,
1,000 mL ÷ 1,000 = 1 Litre of kheer in total.
CBSE Step-by-Step Marking Scheme
Multiplication (1,000 mL)
1.0 M
Conversion to 1 Litre
1.0 M
Q4
A family uses 6 buckets of water for bathing (each bucket holds 15 L), 3 buckets for washing clothes (each holds 20 L), and 45 L for cooking and drinking. What is the family's total daily water consumption?
Water Measurement • Daily Household Usage
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Total Usage:
1. Bathing: 6 buckets × 15 L = 90 L.
2. Washing Clothes: 3 buckets × 20 L = 60 L.
3. Cooking & Drinking: = 45 L.
Total Daily Consumption:
90 L + 60 L + 45 L = 195 Litres.
1. Bathing: 6 buckets × 15 L = 90 L.
2. Washing Clothes: 3 buckets × 20 L = 60 L.
3. Cooking & Drinking: = 45 L.
Total Daily Consumption:
90 L + 60 L + 45 L = 195 Litres.
CBSE Step-by-Step Marking Scheme
Bathing (90 L) and clothes (60 L) calculated
1.5 M
Grand total sum of 195 Litres
1.5 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Hospital Intravenous (IV) Saline Bottle Rate
Real-World Math Context: A hospital saline bottle holds 500 ml of fluid. A nurse sets the drip so that the patient receives 2 ml of saline every minute.
Analytical Task: How many minutes will it take for the entire 500 ml bottle to finish? Express your answer in hours and minutes.
Step 1: Calculate total minutes:
500 ml ÷ 2 ml/min = 250 minutes.
Step 2: Convert into hours and minutes:
250 ÷ 60 = 4 with a remainder of 10.
So, 250 minutes = 4 hours and 10 minutes.
500 ml ÷ 2 ml/min = 250 minutes.
Step 2: Convert into hours and minutes:
250 ÷ 60 = 4 with a remainder of 10.
So, 250 minutes = 4 hours and 10 minutes.
CBSE Assessment Rubric: 1 Mark for 250 minutes; 1 Mark for 4 hours 10 minutes.
8
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 8: Carts and Wheels
Circles, Centre, Radius, Diameter, Compass Drawing & Spinning Tops (Charkhi)
Chapter Highlights, Mathematical Ideas & Key Properties
- Identifying round circular objects: bullock cart wheels, bicycle wheels, bangles, coins, chapati.
- Key circle vocabulary: Centre, Radius (r), Diameter (d), and Circumference.
- Relationship between radius and diameter: Diameter = 2 × Radius; Radius = Diameter ÷ 2.
- Technique for drawing a circle using a nail and string, or a geometric compass.
- Making spinning tops (charkhi) and balancing the stick at the exact centre.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Fill in the blanks: (a) If the radius of a circle is 4 cm, its diameter is __ cm. (b) If the diameter of a wheel is 18 cm, its radius is __ cm. (c) Which circle is larger: Circle A with radius 6 cm or Circle B with diameter 10 cm?
Radius and Diameter Relationships
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Formula: Diameter = 2 × Radius
• Diameter = 2 × 4 cm = 8 cm.
(b) Formula: Radius = Diameter ÷ 2
• Radius = 18 cm ÷ 2 = 9 cm.
(c) Comparison between Circle A and Circle B:
• Circle A radius = 6 cm (so Diameter = 2 × 6 = 12 cm).
• Circle B diameter = 10 cm (so Radius = 10 ÷ 2 = 5 cm).
• Since 6 cm > 5 cm, Circle A is larger.
• Diameter = 2 × 4 cm = 8 cm.
(b) Formula: Radius = Diameter ÷ 2
• Radius = 18 cm ÷ 2 = 9 cm.
(c) Comparison between Circle A and Circle B:
• Circle A radius = 6 cm (so Diameter = 2 × 6 = 12 cm).
• Circle B diameter = 10 cm (so Radius = 10 ÷ 2 = 5 cm).
• Since 6 cm > 5 cm, Circle A is larger.
CBSE Step-by-Step Marking Scheme
Correct answers for (a) and (b)
1.5 M
Accurate comparison showing Circle A is larger
1.5 M
Q2
Zakir, Appu, Naina, and Guddo made cardboard spinning tops. Zakir put his stick near the edge, Appu put it halfway between center and edge, Naina put it slightly off-center, while Guddo put her stick at the exact geometric centre. (a) Whose top will not spin at all? (b) Whose top will spin the best? Explain why.
Spinning Top Physics & Circle Centre
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Top that will not spin at all:
Zakir's top will not spin at all (or will wobble and instantly fall over) because placing the stick at the outer edge creates an extreme weight imbalance.
(b) Top that will spin the best:
Guddo's top will spin the best.
• Reason: When the pivot stick is placed at the exact center of the circle, the radius is equal in all directions. This distributes mass uniformly and balances the gravitational forces evenly around the axis of rotation, allowing the top to spin smoothly and stably for a long time.
Zakir's top will not spin at all (or will wobble and instantly fall over) because placing the stick at the outer edge creates an extreme weight imbalance.
(b) Top that will spin the best:
Guddo's top will spin the best.
• Reason: When the pivot stick is placed at the exact center of the circle, the radius is equal in all directions. This distributes mass uniformly and balances the gravitational forces evenly around the axis of rotation, allowing the top to spin smoothly and stably for a long time.
CBSE Step-by-Step Marking Scheme
Identifies Zakir's top as failing
1.0 M
Identifies Guddo's top as best with center balance explanation
2.0 M
Q3
If the radius of a bicycle wheel is 35 cm, what is its diameter? If the diameter of a giant Ferris wheel is 24 metres, what is its radius?
Circle Geometry • Radius & Diameter
2 Marks
✅ Step-by-Step Model Answer & Solution:
Formula: Diameter = 2 × Radius | Radius = Diameter ÷ 2
1. Bicycle Wheel:
Radius = 35 cm
Diameter = 2 × 35 cm = 70 cm.
2. Giant Ferris Wheel:
Diameter = 24 m
Radius = 24 m ÷ 2 = 12 metres.
1. Bicycle Wheel:
Radius = 35 cm
Diameter = 2 × 35 cm = 70 cm.
2. Giant Ferris Wheel:
Diameter = 24 m
Radius = 24 m ÷ 2 = 12 metres.
CBSE Step-by-Step Marking Scheme
Bicycle diameter: 70 cm
1.0 M
Ferris wheel radius: 12 m
1.0 M
Q4
Describe how to draw a circle of radius 4 cm using a ruler and a geometric compass. What is the role of the fixed sharp point?
Compass Construction • Drawing Circles
3 Marks
✅ Step-by-Step Model Answer & Solution:
Steps to Draw a Circle:
1. Setting the Radius: Open the arms of the compass. Place the sharp metal pointer at 0 cm mark on the ruler and expand the pencil tip to exactly the 4 cm mark.
2. Marking the Centre: Press the sharp metal pointer firmly onto paper without shifting; this point is the Centre (O) of the circle.
3. Drawing: Holding the compass strictly by the top handle, rotate the pencil 360° smoothly around the centre to trace the circular boundary.
The fixed sharp point ensures that every point on the circumference remains at an exact constant distance of 4 cm from the centre.
1. Setting the Radius: Open the arms of the compass. Place the sharp metal pointer at 0 cm mark on the ruler and expand the pencil tip to exactly the 4 cm mark.
2. Marking the Centre: Press the sharp metal pointer firmly onto paper without shifting; this point is the Centre (O) of the circle.
3. Drawing: Holding the compass strictly by the top handle, rotate the pencil 360° smoothly around the centre to trace the circular boundary.
The fixed sharp point ensures that every point on the circumference remains at an exact constant distance of 4 cm from the centre.
CBSE Step-by-Step Marking Scheme
Setting 4 cm measurement on ruler
1.0 M
Center anchor and 360° pencil rotation
1.0 M
Explaining constant distance from center
1.0 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Playground Circle Marker with String
Real-World Math Context: The sports teacher needs to draw a circular kabaddi ring on the ground with a diameter of 8 metres. She has a wooden peg and a coil of rope.
Analytical Task: How long should she cut the rope to tie between the central peg and the chalk stick?
Answer: 4 metres.
Explanation: The length of the rope between the central fixed peg (centre) and the rotating chalk stick represents the radius of the circle.
Radius = Diameter ÷ 2 = 8 m ÷ 2 = 4 metres.
Explanation: The length of the rope between the central fixed peg (centre) and the rotating chalk stick represents the radius of the circle.
Radius = Diameter ÷ 2 = 8 m ÷ 2 = 4 metres.
CBSE Assessment Rubric: 1 Mark for identifying rope as radius; 1 Mark for calculating 4 metres.
9
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 9: Halves and Quarters
Fractions: 1/2, 1/4, 3/4, Fraction Walls, Splitting Objects & Metric Fractions
Chapter Highlights, Mathematical Ideas & Key Properties
- Concept of a fraction: equal parts of a whole.
- Half (1/2), One-quarter (1/4), and Three-quarters (3/4).
- Two quarters make one half: 1/4 + 1/4 = 2/4 = 1/2.
- Four quarters make one whole: 4/4 = 1.
- Fractions of collections (e.g., half of 20 apples = 10; quarter of ₹100 = ₹25).
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Calculate: (a) 1/2 of ₹100, (b) 1/4 of a metre (in cm), (c) 3/4 of a kilogram (in grams), (d) 1/2 of a litre (in ml).
Fraction of Amounts & Metric Conversions
4 Marks
✅ Step-by-Step Model Answer & Solution:
(a) 1/2 of ₹100:
• ₹100 ÷ 2 = ₹50.
(b) 1/4 of a metre:
• 1 m = 100 cm.
• 100 cm ÷ 4 = 25 cm.
(c) 3/4 of a kilogram:
• 1 kg = 1,000 g.
• 1/4 of 1,000 g = 250 g.
• 3/4 = 3 × 250 g = 750 grams.
(d) 1/2 of a litre:
• 1 l = 1,000 ml.
• 1,000 ml ÷ 2 = 500 ml.
• ₹100 ÷ 2 = ₹50.
(b) 1/4 of a metre:
• 1 m = 100 cm.
• 100 cm ÷ 4 = 25 cm.
(c) 3/4 of a kilogram:
• 1 kg = 1,000 g.
• 1/4 of 1,000 g = 250 g.
• 3/4 = 3 × 250 g = 750 grams.
(d) 1/2 of a litre:
• 1 l = 1,000 ml.
• 1,000 ml ÷ 2 = 500 ml.
CBSE Step-by-Step Marking Scheme
Correct values for (a) and (b)
2.0 M
Correct values for (c) and (d)
2.0 M
Q2
Rani had a chocolate bar with 12 equal pieces. She gave 1/4 of it to Reena, 1/3 of it to Sugatha, and ate the rest herself. How many pieces did each girl get?
Word Problem on Splitting Food
3 Marks
✅ Step-by-Step Model Answer & Solution:
Total pieces in chocolate bar = 12.
• Reena's share: 1/4 of 12 = 12 ÷ 4 = 3 pieces.
• Sugatha's share: 1/3 of 12 = 12 ÷ 3 = 4 pieces.
• Pieces given away: 3 + 4 = 7 pieces.
• Rani's share: 12 - 7 = 5 pieces.
Check: 3 + 4 + 5 = 12 pieces. Correct!
• Reena's share: 1/4 of 12 = 12 ÷ 4 = 3 pieces.
• Sugatha's share: 1/3 of 12 = 12 ÷ 3 = 4 pieces.
• Pieces given away: 3 + 4 = 7 pieces.
• Rani's share: 12 - 7 = 5 pieces.
Check: 3 + 4 + 5 = 12 pieces. Correct!
CBSE Step-by-Step Marking Scheme
Reena = 3 pieces; Sugatha = 4 pieces
2.0 M
Rani = 5 pieces with verification
1.0 M
Q3
Look at the vegetable price list:
• Tomato: ₹16 per kg
• Potato: ₹20 per kg
• Carrot: ₹32 per kg
Calculate the total cost of 1/2 kg tomatoes, 3/4 kg potatoes, and 1 1/4 kg carrots. Fractional Pricing • Vegetable Market 3 Marks
• Tomato: ₹16 per kg
• Potato: ₹20 per kg
• Carrot: ₹32 per kg
Calculate the total cost of 1/2 kg tomatoes, 3/4 kg potatoes, and 1 1/4 kg carrots. Fractional Pricing • Vegetable Market 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Pricing:
1. Cost of 1/2 kg Tomatoes: 1/2 × ₹16 = ₹8.
2. Cost of 3/4 kg Potatoes: 3/4 × ₹20 = 3 × (20 ÷ 4) = 3 × ₹5 = ₹15.
3. Cost of 1 1/4 kg Carrots:
• 1 kg = ₹32
• 1/4 kg = ₹32 ÷ 4 = ₹8
• Total = ₹32 + ₹8 = ₹40.
Grand Total Bill:
₹8 + ₹15 + ₹40 = ₹63.
1. Cost of 1/2 kg Tomatoes: 1/2 × ₹16 = ₹8.
2. Cost of 3/4 kg Potatoes: 3/4 × ₹20 = 3 × (20 ÷ 4) = 3 × ₹5 = ₹15.
3. Cost of 1 1/4 kg Carrots:
• 1 kg = ₹32
• 1/4 kg = ₹32 ÷ 4 = ₹8
• Total = ₹32 + ₹8 = ₹40.
Grand Total Bill:
₹8 + ₹15 + ₹40 = ₹63.
CBSE Step-by-Step Marking Scheme
Tomatoes (₹8) and Potatoes (₹15)
1.0 M
Carrots (₹40)
1.0 M
Total bill = ₹63
1.0 M
Q4
A square sheet of paper is folded in half diagonally, and then folded in half again. (a) What fraction of the original sheet is each small triangle? (b) How many such small triangles make three-quarters (3/4) of the sheet?
Fraction Arithmetic • Cutting Shapes
2 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Folding:
1. First diagonal fold divides the square into 2 equal halves (1/2 each).
2. Second fold divides the halves into 4 equal triangles (1/4 each).
• (a) Fraction of each small triangle: 1/4 of the original square sheet.
• (b) To make 3/4: Exactly 3 small triangles make 3/4 of the sheet (3 × 1/4 = 3/4).
1. First diagonal fold divides the square into 2 equal halves (1/2 each).
2. Second fold divides the halves into 4 equal triangles (1/4 each).
• (a) Fraction of each small triangle: 1/4 of the original square sheet.
• (b) To make 3/4: Exactly 3 small triangles make 3/4 of the sheet (3 × 1/4 = 3/4).
CBSE Step-by-Step Marking Scheme
Part (a): 1/4 fraction
1.0 M
Part (b): 3 small triangles
1.0 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Vegetable Price List Fraction Math
Real-World Math Context: At the sabzi mandi: Tomato costs ₹16 per kg, Potato costs ₹20 per kg, and Onion costs ₹24 per kg. Mrs. Sharma buys 1/2 kg tomatoes, 3/4 kg potatoes, and 1/4 kg onions.
Analytical Task: How much total money does Mrs. Sharma spend?
Cost breakdown:
• Tomatoes: 1/2 × ₹16 = ₹8.
• Potatoes: 3/4 × ₹20 = 3 × ₹5 = ₹15.
• Onions: 1/4 × ₹24 = ₹6.
• Total spent = ₹8 + ₹15 + ₹6 = ₹29.
• Tomatoes: 1/2 × ₹16 = ₹8.
• Potatoes: 3/4 × ₹20 = 3 × ₹5 = ₹15.
• Onions: 1/4 × ₹24 = ₹6.
• Total spent = ₹8 + ₹15 + ₹6 = ₹29.
CBSE Assessment Rubric: 1.5 Marks for itemized fractions; 1.5 Marks for total ₹29.
10
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 10: Play with Patterns
Tiling Patterns, Number Towers, Magic Squares & Secret Message Decryption
Chapter Highlights, Mathematical Ideas & Key Properties
- Tiling patterns (tessellations) on floors and historical monuments.
- Number towers: each box is the sum of the two boxes directly below it.
- Magic Squares (3×3 grid): where every row, column, and diagonal adds up to the exact same magic sum (e.g., 15 or 45).
- Secret message decoding using alphabet-number substitutions.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
In a number tower, the bottom row has the numbers 20, 30, and 50. Fill in the missing numbers for the middle row and the top box. State the rule used.
Number Tower Solving Rule
3 Marks
✅ Step-by-Step Model Answer & Solution:
Rule of the Number Tower:
The number in each higher box is the sum of the two boxes directly below it.
• Middle row left box: 20 + 30 = 50.
• Middle row right box: 30 + 50 = 80.
• Top box: Sum of middle row = 50 + 80 = 130.
Completed Tower:
[ 130 ]
[ 50 ] [ 80 ]
[ 20 ] [ 30 ] [ 50 ]
The number in each higher box is the sum of the two boxes directly below it.
• Middle row left box: 20 + 30 = 50.
• Middle row right box: 30 + 50 = 80.
• Top box: Sum of middle row = 50 + 80 = 130.
Completed Tower:
[ 130 ]
[ 50 ] [ 80 ]
[ 20 ] [ 30 ] [ 50 ]
CBSE Step-by-Step Marking Scheme
States addition rule of number tower
1.0 M
Correct values: middle row 50, 80; top box 130
2.0 M
Q2
Complete a 3×3 magic square using numbers from 1 to 9 so that every row, column, and diagonal adds up to 15.
Magic Square Construction
3 Marks
✅ Step-by-Step Model Answer & Solution:
The standard 3×3 magic square with sum 15 is:
• Rows: 8+1+6 = 15; 3+5+7 = 15; 4+9+2 = 15.
• Columns: 8+3+4 = 15; 1+5+9 = 15; 6+7+2 = 15.
• Diagonals: 8+5+2 = 15; 6+5+4 = 15. All equal 15!
| 8 | 1 | 6 |
| 3 | 5 | 7 |
| 4 | 9 | 2 |
• Columns: 8+3+4 = 15; 1+5+9 = 15; 6+7+2 = 15.
• Diagonals: 8+5+2 = 15; 6+5+4 = 15. All equal 15!
CBSE Step-by-Step Marking Scheme
Correct 3x3 grid layout with numbers 1 to 9
2.0 M
Verification of rows, columns, and diagonals = 15
1.0 M
Q3
In a 3×3 magic square using numbers 1 to 9, the sum of numbers along every row, column, and diagonal is 15. If the central cell is 5, explain why 5 must be in the centre.
Magic Squares • 3x3 Grid Puzzle
3 Marks
✅ Step-by-Step Model Answer & Solution:
Magic Square Mathematical Logic:
1. Sum of all numbers 1 to 9:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.
Dividing by 3 rows gives the magic constant: 45 ÷ 3 = 15.
2. Why 5 must be in the Centre:
The central cell belongs to 4 lines (1 horizontal row, 1 vertical column, and 2 diagonals). Therefore, it must be the exact median (average) of all 9 numbers. Pairing numbers that sum to 10 (1+9=10, 2+8=10, 3+7=10, 4+6=10) with 5 in the centre always yields: 10 + 5 = 15.
1. Sum of all numbers 1 to 9:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45.
Dividing by 3 rows gives the magic constant: 45 ÷ 3 = 15.
2. Why 5 must be in the Centre:
The central cell belongs to 4 lines (1 horizontal row, 1 vertical column, and 2 diagonals). Therefore, it must be the exact median (average) of all 9 numbers. Pairing numbers that sum to 10 (1+9=10, 2+8=10, 3+7=10, 4+6=10) with 5 in the centre always yields: 10 + 5 = 15.
CBSE Step-by-Step Marking Scheme
Calculating total sum 45 and magic constant 15
1.5 M
Explaining central cell median alignment with 4 intersecting lines
1.5 M
Q4
In a number tower, the bottom row has numbers 10, 20, 30. The rule is that adding two adjacent lower numbers gives the number above them. Find the top number of the tower.
Number Pyramids • Addition Rules
2 Marks
✅ Step-by-Step Model Answer & Solution:
Tower Addition Steps:
• Bottom Row (Row 1): [ 10 ] [ 20 ] [ 30 ]
• Middle Row (Row 2):
Left box = 10 + 20 = 30.
Right box = 20 + 30 = 50.
Row 2: [ 30 ] [ 50 ]
• Top Row (Row 3):
Top box = 30 + 50 = 80.
The number in the top box is 80.
• Bottom Row (Row 1): [ 10 ] [ 20 ] [ 30 ]
• Middle Row (Row 2):
Left box = 10 + 20 = 30.
Right box = 20 + 30 = 50.
Row 2: [ 30 ] [ 50 ]
• Top Row (Row 3):
Top box = 30 + 50 = 80.
The number in the top box is 80.
CBSE Step-by-Step Marking Scheme
Middle row calculation (30 and 50)
1.0 M
Top number = 80
1.0 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Coded Message for Class Picnic
Real-World Math Context: Teenu writes a secret note using numbers for letters: A=1, B=2, C=3, ... Z=26. Her note reads: '13-5-5-20 13-5 1-20 14-15-15-14'.
Analytical Task: Decrypt Teenu's secret note.
Decoded Note: 'MEET ME AT NOON'.
• 13=M, 5=E, 5=E, 20=T (MEET)
• 13=M, 5=E (ME)
• 1=A, 20=T (AT)
• 14=N, 15=O, 15=O, 14=N (NOON)
• 13=M, 5=E, 5=E, 20=T (MEET)
• 13=M, 5=E (ME)
• 1=A, 20=T (AT)
• 14=N, 15=O, 15=O, 14=N (NOON)
CBSE Assessment Rubric: 1 Mark for letter substitution method; 1 Mark for 'MEET ME AT NOON'.
11
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 11: Tables and Shares
Counting Legs of Animals, Division as Equal Shelving & Group Distribution
Chapter Highlights, Mathematical Ideas & Key Properties
- Multiplying by grouping: counting legs of cats (4 legs each), spiders (8 legs each), and frogs.
- Arranging pots, almirah shelves, and plants in arrays (rows × columns).
- Division strategies: jumping backwards on a number line and repeated subtraction.
- Distributing items among people with equal shares and determining leftovers.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
(a) Gayatri saw 28 cat legs peeping out from under a wooden cupboard. How many cats were there inside? (b) Some ducks and cows are standing in a field. Together they have 20 legs. If there are 3 cows, how many ducks are there?
Leg Counting & Grouping
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Cats under the cupboard:
• 1 cat has 4 legs.
• Number of cats = Total legs ÷ 4
• Number of cats = 28 ÷ 4 = 7 cats.
(b) Ducks and Cows leg puzzle:
• 1 cow has 4 legs. 3 cows have 3 × 4 = 12 legs.
• Remaining legs = Total legs - Cow legs = 20 - 12 = 8 legs.
• 1 duck has 2 legs.
• Number of ducks = 8 ÷ 2 = 4 ducks.
Check: (3 cows × 4 legs) + (4 ducks × 2 legs) = 12 + 8 = 20 legs. Correct!
• 1 cat has 4 legs.
• Number of cats = Total legs ÷ 4
• Number of cats = 28 ÷ 4 = 7 cats.
(b) Ducks and Cows leg puzzle:
• 1 cow has 4 legs. 3 cows have 3 × 4 = 12 legs.
• Remaining legs = Total legs - Cow legs = 20 - 12 = 8 legs.
• 1 duck has 2 legs.
• Number of ducks = 8 ÷ 2 = 4 ducks.
Check: (3 cows × 4 legs) + (4 ducks × 2 legs) = 12 + 8 = 20 legs. Correct!
CBSE Step-by-Step Marking Scheme
Correct calculation for cats (7 cats)
1.5 M
Correct two-step deduction for ducks (4 ducks)
1.5 M
Q2
Shyama wants to plant 18 rose saplings in rectangular flowerbeds. In how many different rectangular array arrangements (rows × plants in each row) can she plant them? List all pairs.
Array Multiplication • Shyama's Garden
3 Marks
✅ Step-by-Step Model Answer & Solution:
Factor Pairs of 18:
We find all pairs of whole numbers whose product is 18:
1. 1 row of 18 plants: 1 × 18 = 18
2. 2 rows of 9 plants each: 2 × 9 = 18
3. 3 rows of 6 plants each: 3 × 6 = 18
4. 6 rows of 3 plants each: 6 × 3 = 18
5. 9 rows of 2 plants each: 9 × 2 = 18
6. 18 rows of 1 plant each: 18 × 1 = 18
She can arrange them in 6 different rectangular arrays.
We find all pairs of whole numbers whose product is 18:
1. 1 row of 18 plants: 1 × 18 = 18
2. 2 rows of 9 plants each: 2 × 9 = 18
3. 3 rows of 6 plants each: 3 × 6 = 18
4. 6 rows of 3 plants each: 6 × 3 = 18
5. 9 rows of 2 plants each: 9 × 2 = 18
6. 18 rows of 1 plant each: 18 × 1 = 18
She can arrange them in 6 different rectangular arrays.
CBSE Step-by-Step Marking Scheme
Listing factor pairs of 18
1.5 M
Stating all distinct row-column configurations
1.5 M
Q3
Explain how you can easily construct the multiplication table of 7 using the tables of 2 and 5.
Distributive Property • Splitting Tables
3 Marks
✅ Step-by-Step Model Answer & Solution:
Using the Distributive Property: 7 = 2 + 5
To find any multiple of 7, add the corresponding multiple of 2 and multiple of 5:
• 7 × 1 = (2 × 1) + (5 × 1) = 2 + 5 = 7
• 7 × 2 = (2 × 2) + (5 × 2) = 4 + 10 = 14
• 7 × 3 = (2 × 3) + (5 × 3) = 6 + 15 = 21
• 7 × 4 = (2 × 4) + (5 × 4) = 8 + 20 = 28
• 7 × 8 = (2 × 8) + (5 × 8) = 16 + 40 = 56
• 7 × 10 = (2 × 10) + (5 × 10) = 20 + 50 = 70.
This demonstrates that large multiplication tables can be constructed by combining smaller, easy tables.
To find any multiple of 7, add the corresponding multiple of 2 and multiple of 5:
• 7 × 1 = (2 × 1) + (5 × 1) = 2 + 5 = 7
• 7 × 2 = (2 × 2) + (5 × 2) = 4 + 10 = 14
• 7 × 3 = (2 × 3) + (5 × 3) = 6 + 15 = 21
• 7 × 4 = (2 × 4) + (5 × 4) = 8 + 20 = 28
• 7 × 8 = (2 × 8) + (5 × 8) = 16 + 40 = 56
• 7 × 10 = (2 × 10) + (5 × 10) = 20 + 50 = 70.
This demonstrates that large multiplication tables can be constructed by combining smaller, easy tables.
CBSE Step-by-Step Marking Scheme
Stating 7 = 2 + 5 principle
1.5 M
Demonstrating at least 3 correct row additions
1.5 M
Q4
A carpenter has 84 wooden books. If he puts 7 books on each shelf, how many shelves will be completely filled?
Division as Grouping • Shelving Books
2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
84 ÷ 7
• 70 ÷ 7 = 10
• 14 ÷ 7 = 2
• 10 + 2 = 12
Exactly 12 shelves will be completely filled.
84 ÷ 7
• 70 ÷ 7 = 10
• 14 ÷ 7 = 2
• 10 + 2 = 12
Exactly 12 shelves will be completely filled.
CBSE Step-by-Step Marking Scheme
Correct division yielding 12 shelves
2.0 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Flower Garland Distribution
Real-World Math Context: A gardener has 84 marigold flowers. She needs 8 flowers to weave 1 garland.
Analytical Task: How many complete garlands can she make, and how many flowers will be left over?
84 ÷ 8 = 10 garlands with 4 flowers left over.
Working: 10 × 8 = 80 flowers used; 84 - 80 = 4 remaining.
Working: 10 × 8 = 80 flowers used; 84 - 80 = 4 remaining.
CBSE Assessment Rubric: 1 Mark for 10 garlands; 1 Mark for 4 leftover flowers.
12
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 12: How Heavy? How Light?
Pan Balance Weighing, Grams & Kilograms, Postal Tariffs & Weight Estimation
Chapter Highlights, Mathematical Ideas & Key Properties
- Comparing weights using a beam balance scale.
- 1 Kilogram (kg) = 1,000 Grams (g); 1/2 kg = 500 g; 1/4 kg = 250 g.
- Indian Post Office parcel and letter tariff rates based on weight increments.
- Estimating weights of heavy objects (elephant, tractor, sack of wheat) vs light objects (pencil, feather).
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Look at the postal rates: A parcel weighing 50 grams or less costs ₹5. For every additional 50 grams or part thereof, it costs ₹3. Radha wants to send a book parcel weighing 225 grams to her friend. How much postal stamp value must she affix on the parcel?
Postal Tariff Calculation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step 1: Break down the weight of 225 grams into 50 g slabs:
• First 50 grams = 50 g (remaining = 225 - 50 = 175 g).
• Next 50 grams = 50 g (remaining = 125 g).
• Next 50 grams = 50 g (remaining = 75 g).
• Next 50 grams = 50 g (remaining = 25 g).
• Final 25 grams counts as an additional 50 g slab.
Total slabs = 1 basic slab + 4 additional slabs.
Step 2: Calculate cost:
• First 50 g = ₹5.
• 4 additional slabs of 50 g = 4 × ₹3 = ₹12.
• Total postal stamp value = ₹5 + ₹12 = ₹17.
• First 50 grams = 50 g (remaining = 225 - 50 = 175 g).
• Next 50 grams = 50 g (remaining = 125 g).
• Next 50 grams = 50 g (remaining = 75 g).
• Next 50 grams = 50 g (remaining = 25 g).
• Final 25 grams counts as an additional 50 g slab.
Total slabs = 1 basic slab + 4 additional slabs.
Step 2: Calculate cost:
• First 50 g = ₹5.
• 4 additional slabs of 50 g = 4 × ₹3 = ₹12.
• Total postal stamp value = ₹5 + ₹12 = ₹17.
CBSE Step-by-Step Marking Scheme
Correct breakdown of 225 g into 5 slabs
1.5 M
Accurate calculation giving ₹17 stamp cost
1.5 M
Q2
Look at the postal rates:
• Single letter (up to 20 g): ₹5.00
• For every additional 20 g: ₹2.00
Calculate the postage stamps required to send a heavy official letter weighing 75 grams. Postal Mathematics • Calculating Postage 3 Marks
• Single letter (up to 20 g): ₹5.00
• For every additional 20 g: ₹2.00
Calculate the postage stamps required to send a heavy official letter weighing 75 grams. Postal Mathematics • Calculating Postage 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Postal Calculation:
Total weight = 75 grams.
1. First 20 grams: Cost = ₹5.00.
2. Remaining weight: 75 g - 20 g = 55 grams.
• Next 20 g (21–40 g): + ₹2.00
• Next 20 g (41–60 g): + ₹2.00
• Remaining 15 g (part of next 20 g, 61–75 g): + ₹2.00
Total additional 20 g units = 3 units.
Additional cost = 3 × ₹2.00 = ₹6.00.
Total Postage Required:
₹5.00 + ₹6.00 = ₹11.00.
Total weight = 75 grams.
1. First 20 grams: Cost = ₹5.00.
2. Remaining weight: 75 g - 20 g = 55 grams.
• Next 20 g (21–40 g): + ₹2.00
• Next 20 g (41–60 g): + ₹2.00
• Remaining 15 g (part of next 20 g, 61–75 g): + ₹2.00
Total additional 20 g units = 3 units.
Additional cost = 3 × ₹2.00 = ₹6.00.
Total Postage Required:
₹5.00 + ₹6.00 = ₹11.00.
CBSE Step-by-Step Marking Scheme
Base charge for first 20 g (₹5.00)
1.0 M
Identifying 3 additional units (₹6.00)
1.0 M
Total postage: ₹11.00
1.0 M
Q3
State whether the following objects should be measured in 'grams' or 'kilograms':
(a) A tube of toothpaste
(b) A sack of rice
(c) A golden ring
(d) A newborn baby Weight Estimation • Grams vs. Kilograms 2 Marks
(a) A tube of toothpaste
(b) A sack of rice
(c) A golden ring
(d) A newborn baby Weight Estimation • Grams vs. Kilograms 2 Marks
✅ Step-by-Step Model Answer & Solution:
Units of Weight:
• (a) A tube of toothpaste: Grams (g) (approx. 100 g - 150 g)
• (b) A sack of rice: Kilograms (kg) (approx. 25 kg - 50 kg)
• (c) A golden ring: Grams (g) (approx. 4 g - 8 g)
• (d) A newborn baby: Kilograms (kg) (approx. 2.5 kg - 3.5 kg).
• (a) A tube of toothpaste: Grams (g) (approx. 100 g - 150 g)
• (b) A sack of rice: Kilograms (kg) (approx. 25 kg - 50 kg)
• (c) A golden ring: Grams (g) (approx. 4 g - 8 g)
• (d) A newborn baby: Kilograms (kg) (approx. 2.5 kg - 3.5 kg).
CBSE Step-by-Step Marking Scheme
All four units correctly identified
2.0 M
Q4
How many 250-gram packets of tea make 1 1/2 kilograms?
Weight Conversion • Balancing Scales
2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculation:
1. Convert 1 1/2 kg into grams:
1 kg = 1,000 g
1/2 kg = 500 g
Total weight = 1,000 g + 500 g = 1,500 grams.
2. Number of 250 g packets:
1,500 ÷ 250 = 6 packets.
Exactly 6 packets of tea make 1 1/2 kg.
1. Convert 1 1/2 kg into grams:
1 kg = 1,000 g
1/2 kg = 500 g
Total weight = 1,000 g + 500 g = 1,500 grams.
2. Number of 250 g packets:
1,500 ÷ 250 = 6 packets.
Exactly 6 packets of tea make 1 1/2 kg.
CBSE Step-by-Step Marking Scheme
Conversion to 1,500 g
1.0 M
Division: 1500 ÷ 250 = 6 packets
1.0 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Balancing Scales with Broken Stone Weights
Real-World Math Context: A vendor had a single 4 kg stone weight. It broke into two pieces of 1 kg and 3 kg.
Analytical Task: How can the vendor weigh out exactly 2 kg of firewood using these two pieces on a two-pan balance?
Procedure:
• Place the 3 kg piece on the left pan.
• Place the 1 kg piece on the right pan.
• Add firewood to the right pan until both pans balance in equilibrium.
• Since Left Pan (3 kg) = Right Pan (1 kg + Firewood), the weight of firewood is 3 kg - 1 kg = 2 kg.
• Place the 3 kg piece on the left pan.
• Place the 1 kg piece on the right pan.
• Add firewood to the right pan until both pans balance in equilibrium.
• Since Left Pan (3 kg) = Right Pan (1 kg + Firewood), the weight of firewood is 3 kg - 1 kg = 2 kg.
CBSE Assessment Rubric: 1.5 Marks for correct pan placement; 1.5 Marks for mathematical balance proof.
13
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 13: Fields and Fences
Perimeter of Irregular Polygons, Wire Fencing Calculations & Grid Square Area Counting
Chapter Highlights, Mathematical Ideas & Key Properties
- Perimeter is the total continuous length of the outer boundary of a closed planar shape.
- Calculating perimeter by adding lengths of all straight boundary edges.
- Fencing fields with wire: single round vs. multiple rounds (e.g., 3-wire barbed fence).
- Counting whole and half squares on a square centimetre grid to estimate surface area.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
Rahmat is a farmer. He has a field with sides measuring 9 m, 15 m, 21 m, and 9 m. (a) What is the length of the boundary of Rahmat's field? (b) Rahmat bought a roll of 70 metres of barbed wire to fence his field. How much wire will be left over after putting one complete round of fence?
Boundary Length & Wire Requirement
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Length of boundary (Perimeter):
Sum of all sides = 9 m + 15 m + 21 m + 9 m = 54 metres.
(b) Wire remaining:
• Total wire in roll = 70 metres.
• Wire used for 1 round = 54 metres.
• Wire left over = 70 m - 54 m = 16 metres.
Sum of all sides = 9 m + 15 m + 21 m + 9 m = 54 metres.
(b) Wire remaining:
• Total wire in roll = 70 metres.
• Wire used for 1 round = 54 metres.
• Wire left over = 70 m - 54 m = 16 metres.
CBSE Step-by-Step Marking Scheme
Correct boundary sum 54 metres
1.5 M
Correct remaining wire 16 metres
1.5 M
Q2
A square has a side of 6 cm. (a) What is its perimeter? (b) If four 1 cm squares are cut out from its four corners, what is the perimeter of the new shape? Explain why the perimeter changes or stays the same.
Square Grid Area & Perimeter
3 Marks
✅ Step-by-Step Model Answer & Solution:
(a) Perimeter of original square:
Perimeter = 4 × side = 4 × 6 cm = 24 cm.
(b) Perimeter after cutting 1 cm squares from each corner:
• When a 1 cm square is removed from a corner, the two outer 1 cm edges that are removed are replaced by two inner 1 cm edges that form the new stepped corner.
• Therefore, the total boundary length remains exactly 24 cm!
• Conclusion: The perimeter stays the same (24 cm), even though the area has decreased by 4 sq cm.
Perimeter = 4 × side = 4 × 6 cm = 24 cm.
(b) Perimeter after cutting 1 cm squares from each corner:
• When a 1 cm square is removed from a corner, the two outer 1 cm edges that are removed are replaced by two inner 1 cm edges that form the new stepped corner.
• Therefore, the total boundary length remains exactly 24 cm!
• Conclusion: The perimeter stays the same (24 cm), even though the area has decreased by 4 sq cm.
CBSE Step-by-Step Marking Scheme
Original perimeter 24 cm
1.0 M
Explains corner cut effect and confirms perimeter remains 24 cm
2.0 M
Q3
A shape is drawn on a 1 cm square grid. It covers 12 complete squares and 6 half squares. (a) What is the area of this shape in square centimetres? (b) If each square has side 1 cm, what is the area of 1 unit square?
Area & Perimeter • Grid Squares
3 Marks
✅ Step-by-Step Model Answer & Solution:
Grid Area Calculation:
• Area of 1 unit square with side 1 cm = 1 cm × 1 cm = 1 sq cm.
1. 12 complete squares = 12 × 1 sq cm = 12 sq cm.
2. 6 half squares = 6 × (1/2 sq cm) = 3 sq cm.
Total Area of the Shape:
12 + 3 = 15 sq cm.
• Area of 1 unit square with side 1 cm = 1 cm × 1 cm = 1 sq cm.
1. 12 complete squares = 12 × 1 sq cm = 12 sq cm.
2. 6 half squares = 6 × (1/2 sq cm) = 3 sq cm.
Total Area of the Shape:
12 + 3 = 15 sq cm.
CBSE Step-by-Step Marking Scheme
Area of 1 unit square = 1 sq cm
1.0 M
Combining complete and half squares accurately (12 + 3)
1.0 M
Total area: 15 sq cm
1.0 M
Q4
Ganpat has a field with sides 15 m, 20 m, 18 m, and 27 m. He bought a 100-metre roll of barbed wire to fence the boundary once. (a) What is the perimeter of his field? (b) How much wire will be left over after fencing?
Field Fencing • Barbed Wire Math
3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
1. Perimeter of the Field:
Perimeter = Sum of all 4 sides
= 15 m + 20 m + 18 m + 27 m = 80 metres.
2. Wire Left Over:
Wire roll length = 100 m
Wire used = 80 m
Leftover wire = 100 m - 80 m = 20 metres.
1. Perimeter of the Field:
Perimeter = Sum of all 4 sides
= 15 m + 20 m + 18 m + 27 m = 80 metres.
2. Wire Left Over:
Wire roll length = 100 m
Wire used = 80 m
Leftover wire = 100 m - 80 m = 20 metres.
CBSE Step-by-Step Marking Scheme
Correct sum of sides = 80 m
1.5 M
Subtraction 100 - 80 = 20 m left
1.5 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Three-Strand Wire Fence Budget
Real-World Math Context: A farmer wants to put a 3-strand barbed wire fence around a rectangular field that is 40 metres long and 25 metres wide. Fencing wire costs ₹15 per metre.
Analytical Task: Calculate the total length of wire needed and the total cost.
Step 1: Perimeter:
2 × (40 + 25) = 2 × 65 = 130 metres.
Step 2: 3 strands:
130 m × 3 = 390 metres of wire.
Step 3: Total cost:
390 m × ₹15/m = ₹5,850.
2 × (40 + 25) = 2 × 65 = 130 metres.
Step 2: 3 strands:
130 m × 3 = 390 metres of wire.
Step 3: Total cost:
390 m × ₹15/m = ₹5,850.
CBSE Assessment Rubric: 1 Mark for perimeter (130 m); 1 Mark for 3 strands (390 m); 1 Mark for ₹5,850.
14
Classic Track: Math-Magic • Class 4 Mathematics (Classic CBSE)
Chapter 14: Smart Charts
Chapati Charts (Pie Charts), Road Traffic Tally Marks, Family Trees & Attendance Charts
Chapter Highlights, Mathematical Ideas & Key Properties
- Using tally marks for traffic flow observations: bicycles, cars, auto-rickshaws, buses, trucks.
- Chapati charts (circle graphs / pie charts): interpreting 1/2, 1/4, and 3/4 fractional shares.
- Reading family generation charts and student school absence records.
- Drawing conclusions and converting data tables into visual bar graphs.
📖 NCERT Textbook Exercise Solutions & Step-by-Step Working (15 Solved Questions)
Q1
In a class of 36 students, a Chapati Chart shows their favorite seasons: 1/2 of the students like Winter, 1/4 like Rainy season, and 1/4 like Summer. (a) How many students like Winter? (b) How many students like Summer? (c) How many more students like Winter than Summer?
Chapati Chart Interpretation
3 Marks
✅ Step-by-Step Model Answer & Solution:
Total students in class = 36.
• (a) Students who like Winter:
1/2 of 36 = 36 ÷ 2 = 18 students.
• (b) Students who like Summer:
1/4 of 36 = 36 ÷ 4 = 9 students.
• (c) Difference:
18 - 9 = 9 more students like Winter than Summer.
• (a) Students who like Winter:
1/2 of 36 = 36 ÷ 2 = 18 students.
• (b) Students who like Summer:
1/4 of 36 = 36 ÷ 4 = 9 students.
• (c) Difference:
18 - 9 = 9 more students like Winter than Summer.
CBSE Step-by-Step Marking Scheme
Winter = 18 students
1.0 M
Summer = 9 students
1.0 M
Difference = 9 students
1.0 M
Q2
Look at the primary school attendance record for a rainy day:
• Class 1: Total 30, Absent 4
• Class 2: Total 28, Absent 3
• Class 3: Total 32, Absent 5
• Class 4: Total 35, Absent 2
• Class 5: Total 25, Absent 1
(a) What was the total number of students enrolled in the school? (b) How many total students were present on that day? Smart Charts • Attendance Analysis 3 Marks
• Class 1: Total 30, Absent 4
• Class 2: Total 28, Absent 3
• Class 3: Total 32, Absent 5
• Class 4: Total 35, Absent 2
• Class 5: Total 25, Absent 1
(a) What was the total number of students enrolled in the school? (b) How many total students were present on that day? Smart Charts • Attendance Analysis 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Data Analysis:
1. (a) Total Students Enrolled:
30 + 28 + 32 + 35 + 25 = 150 students.
2. Total Students Absent:
4 + 3 + 5 + 2 + 1 = 15 students.
3. (b) Total Students Present:
150 (Total) - 15 (Absent) = 135 students.
In total, 135 students were present on that rainy day.
1. (a) Total Students Enrolled:
30 + 28 + 32 + 35 + 25 = 150 students.
2. Total Students Absent:
4 + 3 + 5 + 2 + 1 = 15 students.
3. (b) Total Students Present:
150 (Total) - 15 (Absent) = 135 students.
In total, 135 students were present on that rainy day.
CBSE Step-by-Step Marking Scheme
Total enrolled = 150
1.0 M
Total absent = 15
1.0 M
Total present = 135
1.0 M
Q3
A bar graph shows favourite fruits of Class 4 children. The bar for Mango has height 18 units, Apple 12 units, Banana 8 units, and Orange 6 units. (a) Which fruit is most popular? (b) How many more children prefer Mango over Banana?
Data Visualization • Bar Charts
2 Marks
✅ Step-by-Step Model Answer & Solution:
Bar Graph Reading:
• Mango = 18
• Apple = 12
• Banana = 8
• Orange = 6
1. (a) Most Popular Fruit: Mango (tallest bar with 18 votes).
2. (b) Difference between Mango and Banana:
18 - 8 = 10 more children.
• Mango = 18
• Apple = 12
• Banana = 8
• Orange = 6
1. (a) Most Popular Fruit: Mango (tallest bar with 18 votes).
2. (b) Difference between Mango and Banana:
18 - 8 = 10 more children.
CBSE Step-by-Step Marking Scheme
Most popular fruit identified as Mango
1.0 M
Correct difference: 18 - 8 = 10
1.0 M
Q4
A student counts vehicles passing her gate in 15 minutes: 14 bicycles, 9 cars, and 6 auto-rickshaws. Represent each vehicle count using 5-bar tally marks.
Tally Tables • Traffic Survey
2 Marks
✅ Step-by-Step Model Answer & Solution:
Tally Marks Representation:
• Bicycles (14):|||| |||| |||| (Two groups of five + four)
• Cars (9):|||| |||| (One group of five + four)
• Auto-rickshaws (6):|||| | (One group of five + one).
• Bicycles (14):
• Cars (9):
• Auto-rickshaws (6):
CBSE Step-by-Step Marking Scheme
Accurate 5-bar grouping for 14, 9, and 6
2.0 M
Q5
A standard brick has length 20 cm, breadth 10 cm, and height 7 cm.
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
(a) What is the shape of a brick?
(b) What is the area of its largest face?
(c) How many bricks of 20 cm length placed end-to-end make a line 1 metre (100 cm) long? Building with Bricks • Brick Geometry & Measurement 3 Marks
✅ Step-by-Step Model Answer & Solution:
Brick Mathematics:
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
• (a) Shape: A standard brick is a cuboid.
• (b) Area of largest face: Length × Breadth = 20 cm × 10 cm = 200 square centimetres (cm²).
• (c) Number of bricks in 1 m: 1 m = 100 cm. Number of bricks = 100 ÷ 20 = 5 bricks.
CBSE Step-by-Step Marking Scheme
Cuboid shape
1 M
Area = 200 cm²
1 M
5 bricks
1 M
Q6
During a school trip to Bhopal, 4 buses stop at a petrol pump to fill diesel. Each bus takes 50 litres of diesel. If 1 litre of diesel costs ₹70:
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
(a) How many litres of diesel are filled in total?
(b) What is the total bill amount the school must pay? A Trip to Bhopal • Diesel Fuel Budget 3 Marks
✅ Step-by-Step Model Answer & Solution:
Step-by-Step Solution:
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
• (a) Total diesel: 4 buses × 50 L = 200 litres.
• (b) Total bill amount: 200 L × ₹70/L = ₹14,000.
CBSE Step-by-Step Marking Scheme
200 litres
1.5 M
₹14,000 bill
1.5 M
Q7
The world record for Men's High Jump is 245 cm and the Long Jump world record is 895 cm.
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
(a) Express the High Jump record in metres and centimetres.
(b) How many more centimetres are needed for the high jump record to reach exactly 2.5 metres (250 cm)? Long and Short • Height Comparisons 2 Marks
✅ Step-by-Step Model Answer & Solution:
Calculations:
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
• (a) High Jump: 245 cm = 2 metres 45 centimetres.
• (b) Difference: 250 cm - 245 cm = 5 centimetres.
CBSE Step-by-Step Marking Scheme
2 m 45 cm
1 M
5 cm difference
1 M
Q8
A packet of butter shows 'Manufactured: 15/01/26' and 'Best before 180 days from manufacture'. Can it be consumed safely on 15th April 2026? Explain.
Tick-Tick-Tick • Expiry Dates on Food
2 Marks
✅ Step-by-Step Model Answer & Solution:
Date Verification:
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
• From 15th Jan to 15th April is exactly 3 months (approx. 90 days).
• Since 90 days is well within the 180-day shelf life, the butter is completely safe to consume on 15th April 2026.
CBSE Step-by-Step Marking Scheme
Time elapsed is ~90 days
1 M
Safe to consume within 180 days
1 M
Q9
Kiran took a loan of ₹300 from a bank to set up her scrap shop. She pays back ₹51 every month for six months.
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
(a) How much money does she pay back in total?
(b) How much extra money (interest) did she pay to the bank? The Junk Seller • Loan and Interest 3 Marks
✅ Step-by-Step Model Answer & Solution:
Loan Repayment:
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
• (a) Total paid: 6 months × ₹51/month = ₹306.
• (b) Extra money (interest): ₹306 - ₹300 = ₹6.
CBSE Step-by-Step Marking Scheme
Total repayment = ₹306
1.5 M
Interest = ₹6
1.5 M
Q10
A doctor prescribes a cough syrup bottle of 150 mL for a child. The child takes a 5 mL dose three times a day.
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
(a) How much cough syrup does the child take in one day?
(b) For how many days will the 150 mL bottle last? Jugs and Mugs • Measuring Medicine Dose 3 Marks
✅ Step-by-Step Model Answer & Solution:
Dosage Calculations:
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
• (a) Daily intake: 3 doses × 5 mL = 15 mL per day.
• (b) Days bottle lasts: 150 mL ÷ 15 mL/day = 10 days.
CBSE Step-by-Step Marking Scheme
15 mL daily
1.5 M
Bottle lasts 10 days
1.5 M
Q11
A cyclist has a bicycle wheel with a radius of 35 cm.
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
(a) What is the diameter of the wheel?
(b) What is the relationship between the radius and diameter of any circle? Carts and Wheels • Circle Geometry 2 Marks
✅ Step-by-Step Model Answer & Solution:
Circle Properties:
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
• (a) Diameter: Diameter = 2 × Radius = 2 × 35 cm = 70 cm.
• (b) Relationship: The diameter is always twice the length of the radius (D = 2r), passing straight through the circle's center.
CBSE Step-by-Step Marking Scheme
Diameter = 70 cm
1 M
Formula D = 2r stated
1 M
Q12
Raju has ₹100. He spends 1/2 of his money on a book, and 1/4 of his total money on a pen.
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
(a) How much does the book cost?
(b) How much does the pen cost?
(c) How much money does Raju have left? Halves and Quarters • Fraction Sharing 3 Marks
✅ Step-by-Step Model Answer & Solution:
Fractional Expenditure:
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
• (a) Book (1/2): ₹100 ÷ 2 = ₹50.
• (b) Pen (1/4): ₹100 ÷ 4 = ₹25.
• (c) Money Left: ₹100 - (₹50 + ₹25) = ₹100 - ₹75 = ₹25.
CBSE Step-by-Step Marking Scheme
Book = ₹50
1 M
Pen = ₹25
1 M
Remaining = ₹25
1 M
Q13
In a secret code, each letter is replaced by its position in the alphabet (A=1, B=2, C=3, ... Z=26).
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
Decode the secret message: '13 - 1 - 20 - 8 - 19'. What word does it spell? Play with Patterns • Secret Message Cipher 2 Marks
✅ Step-by-Step Model Answer & Solution:
Decoding Cipher:
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
• 13 = M
• 1 = A
• 20 = T
• 8 = H
• 19 = S
The secret message spells MATHS.
CBSE Step-by-Step Marking Scheme
Correct decoding to spell MATHS
2 M
Q14
A florist has 58 roses. She wants to make bouquets containing 6 roses each.
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
(a) How many complete bouquets can she make?
(b) How many roses will be left over? Tables and Shares • Division with Remainder 2 Marks
✅ Step-by-Step Model Answer & Solution:
Division:
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
• 58 ÷ 6 = 9 with a remainder of 4.
• (a) Complete bouquets: 9 bouquets (9 × 6 = 54 roses).
• (b) Leftover roses: 58 - 54 = 4 roses left over.
CBSE Step-by-Step Marking Scheme
9 bouquets
1 M
4 leftover roses
1 M
Q15
State True or False:
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
(a) A square has 4 equal sides and its perimeter is 4 × side.
(b) 1 kilometre equals 100 metres.
(c) Half past 4 in the afternoon is written as 16:30 in 24-hour time. Review Questions • True or False 3 Marks
✅ Step-by-Step Model Answer & Solution:
Answers:
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
• (a) True: Perimeter = 4 × side.
• (b) False: 1 km = 1000 metres.
• (c) True: 4:30 PM = 12:00 + 4:30 = 16:30 hours.
CBSE Step-by-Step Marking Scheme
True, False, True with explanations
3 M
🌟 NEP 2020 Competency-Based Case Study (CBQ)
Road Safety Tally Observation
Real-World Math Context: Anita stood near a junction for 30 minutes and counted vehicles using tally marks: Cycle-rickshaws: '卌 卌 卌', Bicycles: '卌 卌 卌 卌 卌', Buses: '卌 ||', Cars: '卌 卌 ||'.
Analytical Task: Which vehicle was seen the most, and what is the total count of all vehicles observed by Anita?
Counts:
• Cycle-rickshaws: 15
• Bicycles: 25
• Buses: 7
• Cars: 12
• Most seen vehicle: Bicycles (25).
• Total vehicles: 15 + 25 + 7 + 12 = 59 vehicles.
• Cycle-rickshaws: 15
• Bicycles: 25
• Buses: 7
• Cars: 12
• Most seen vehicle: Bicycles (25).
• Total vehicles: 15 + 25 + 7 + 12 = 59 vehicles.
CBSE Assessment Rubric: 1.5 Marks for vehicle breakdown and most frequent; 1.5 Marks for total 59.