Chapter 2 of 14
Chapter 2: Hide and Seek
Top View, Front View, Side View, Grid Directions & Spatial Mapping | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- 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.
All Textbook Exercises & In-Text Tasks (15 Questions)
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Q1
Perspective Identification
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.
[4 Marks]
✅ Step-by-Step Solution & Working
(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
Grid Map & Navigation
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?
[3 Marks]
✅ Step-by-Step Solution & Working
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
Spatial Perspectives • 3D Block Towers
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)?
[2 Marks]
✅ Step-by-Step Solution & Working
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
Coordinate Grids • Route Mapping
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?
[2 Marks]
✅ Step-by-Step Solution & Working
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
Textbook Exercise • Real-World Context
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?
[3 Marks]
✅ Step-by-Step Solution & Working
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
Practice Time • Measurement & Conversions
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.
[3 Marks]
(a) 4 metres 65 centimetres into centimetres.
(b) 3500 millilitres into litres and millilitres.
(c) 2 kilograms 750 grams into grams.
✅ Step-by-Step Solution & Working
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
Try These • Geometry and Shapes
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?
[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?
✅ Step-by-Step Solution & Working
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
Money & Accounts • Rate List Calculation
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?
[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?
✅ Step-by-Step Solution & Working
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
Fractions Exploration • Parts of a Whole
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?
[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?
✅ Step-by-Step Solution & Working
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
Time & Clocks • Elapsed Time
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?
[3 Marks]
(a) Convert 1:15 PM into 24-hour railway clock time.
(b) How long did the cricket match last?
✅ Step-by-Step Solution & Working
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
Perimeter & Area • Fencing a Field
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.
[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.
✅ Step-by-Step Solution & Working
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
Mental Math • Division and Multiplication
Solve mentally using number breakdown:
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ?
[2 Marks]
(a) 72 ÷ 6 = ?
(b) 15 × 8 = ?
(c) 25 × 40 = ?
(d) 96 ÷ 8 = ?
✅ Step-by-Step Solution & Working
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
Patterns & Symmetries • Rotational Turns
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)?
[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)?
✅ Step-by-Step Solution & Working
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
Smart Charts • Data Interpretation
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.
[3 Marks]
(a) What fraction of children like Cricket?
(b) Draw a simple circular pie chart (Chapati Chart) representing this data.
✅ Step-by-Step Solution & Working
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
Chapter Review • True or False
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).
[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).
✅ Step-by-Step Solution & Working
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
Drone Photography of the School Sports Ground
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?
Evaluation & Model Answer:
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.
Rubric: 1 Mark for explaining line of sight; 1 Mark for vertical post alignment.