Chapter 5 of 14
Chapter 5: Fun with Shapes
Edges, Corners, Flat & Curved Surfaces, 2D Patterns & Tangram Creations | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Identifying 2D shapes: rectangles, squares, triangles, and circles.
- Properties of shapes: counting straight sides, curved sides, and corners (vertices).
- Special properties: opposite sides equal in rectangles, all 4 sides equal in squares.
- Creating pictures with basic shapes and exploring tiling patterns.
All Textbook Exercises & In-Text Tasks (18 Questions)
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Q1
Textbook Exercise • Shape Attributes
Look at the following objects: A postcard, a round plate, a triangular birthday cap, and a chessboard. State the shape, number of edges, and number of corners for each.
[3 Marks]
✅ Step-by-Step Solution & Working
Shape Breakdown:
• Postcard: Rectangle → 4 straight edges, 4 corners.
• Round Plate: Circle → 1 curved edge, 0 corners.
• Birthday Cap face: Triangle → 3 straight edges, 3 corners.
• Chessboard: Square → 4 equal straight edges, 4 corners.
• Postcard: Rectangle → 4 straight edges, 4 corners.
• Round Plate: Circle → 1 curved edge, 0 corners.
• Birthday Cap face: Triangle → 3 straight edges, 3 corners.
• Chessboard: Square → 4 equal straight edges, 4 corners.
CBSE Step-by-Step Marking Scheme
Correct shape identification for all 4 items
1.5 M
Correct counts of edges and corners
1.5 M
Q2
Tangram Investigation • Problem Solving
How many pieces are in a 5-piece tangram? Which pieces are triangles, and can you combine two small triangles to make a square? Show the working.
[2 Marks]
✅ Step-by-Step Solution & Working
Explanation:
1. A 5-piece tangram has 5 pieces: 3 triangles, 1 square, and 1 parallelogram.
2. Making a square: Yes, by placing the longest sides (hypotenuses) of two identical small right-angled triangles together, their right angles become two opposite corners of a new square.
1. A 5-piece tangram has 5 pieces: 3 triangles, 1 square, and 1 parallelogram.
2. Making a square: Yes, by placing the longest sides (hypotenuses) of two identical small right-angled triangles together, their right angles become two opposite corners of a new square.
CBSE Step-by-Step Marking Scheme
Correct composition of 5-piece tangram
1.0 M
Accurate geometric explanation of forming a square
1.0 M
Q3
Practical Application • Tiling & Tessellation
Why can square and rectangular floor tiles cover a room completely without any gaps, but circular coins leave gaps when placed next to each other?
[3 Marks]
✅ Step-by-Step Solution & Working
Geometric Reason:
• Squares and rectangles have straight edges and 90° corner angles. When placed side by side, their edges align flush against each other, filling all 360° around every point with zero empty space.
• Circles have curved boundaries. When round items touch, circular arcs curve away from each other, leaving open gaps between them. Hence, circles cannot tessellate.
• Squares and rectangles have straight edges and 90° corner angles. When placed side by side, their edges align flush against each other, filling all 360° around every point with zero empty space.
• Circles have curved boundaries. When round items touch, circular arcs curve away from each other, leaving open gaps between them. Hence, circles cannot tessellate.
CBSE Step-by-Step Marking Scheme
Explanation of straight edges and corners fitting flush
1.5 M
Explanation of curved arc gaps in circles
1.5 M
Q4
Geometric Solids • Edges, Corners & Faces
Fill in the table for everyday objects:
(a) Brick (Cuboid): Number of faces, edges, and corners.
(b) Die (Cube): Number of faces, edges, and corners.
(c) Football (Sphere): Number of faces, edges, and corners.
(d) Can (Cylinder): Number of flat faces and curved surfaces.
[4 Marks]
(a) Brick (Cuboid): Number of faces, edges, and corners.
(b) Die (Cube): Number of faces, edges, and corners.
(c) Football (Sphere): Number of faces, edges, and corners.
(d) Can (Cylinder): Number of flat faces and curved surfaces.
✅ Step-by-Step Solution & Working
Step-by-Step Properties:
| Shape | Faces | Edges | Corners (Vertices) |
|---|---|---|---|
| Brick (Cuboid) | 6 flat faces | 12 straight edges | 8 corners |
| Die (Cube) | 6 flat square faces | 12 straight edges | 8 corners |
| Football (Sphere) | 1 curved surface | 0 edges | 0 corners |
| Can (Cylinder) | 2 flat circular faces + 1 curved surface | 2 circular curved edges | 0 corners |
CBSE Step-by-Step Marking Scheme
Correct properties for cuboid and cube
2.0 M
Correct properties for sphere and cylinder
2.0 M
Q5
7-Piece Tangram • Shape Assembly
In a standard 7-piece tangram puzzle:
(a) How many triangles are there in total?
(b) How many 4-sided shapes are there, and what are their names?
(c) Which two triangles are exactly identical in size?
[3 Marks]
(a) How many triangles are there in total?
(b) How many 4-sided shapes are there, and what are their names?
(c) Which two triangles are exactly identical in size?
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
(a) Triangles in 7-piece Tangram:
• There are 5 triangles in total (2 large triangles, 1 medium triangle, and 2 small triangles).
(b) 4-Sided Shapes:
• There are 2 four-sided shapes: 1 Square and 1 Parallelogram.
(c) Identical Triangles:
• The 2 large triangles are exactly identical to each other.
• The 2 small triangles are also exactly identical to each other.
(a) Triangles in 7-piece Tangram:
• There are 5 triangles in total (2 large triangles, 1 medium triangle, and 2 small triangles).
(b) 4-Sided Shapes:
• There are 2 four-sided shapes: 1 Square and 1 Parallelogram.
(c) Identical Triangles:
• The 2 large triangles are exactly identical to each other.
• The 2 small triangles are also exactly identical to each other.
CBSE Step-by-Step Marking Scheme
Correct count of 5 triangles
1.0 M
Correct identification of square and parallelogram
1.0 M
Correct identification of identical pairs
1.0 M
Q6
Tiling & Tessellation • Floor Patterns
Which of the following geometric shapes can cover a flat floor completely without leaving any gaps or overlaps?
(a) Squares
(b) Equilateral triangles
(c) Circles
Explain why circles cannot tile a flat surface.
[3 Marks]
(a) Squares
(b) Equilateral triangles
(c) Circles
Explain why circles cannot tile a flat surface.
✅ Step-by-Step Solution & Working
Step-by-Step Explanation:
• (a) Squares: Yes, squares tile a floor seamlessly (like bathroom tiles).
• (b) Equilateral Triangles: Yes, equilateral triangles fit together perfectly around a point without gaps.
• (c) Circles: No, circles cannot tile a plane.
Why Circles Cannot Tile: When identical circles are placed touching each other, curved spaces (interstitial gaps) are always left between them. Curved boundaries cannot fill straight plane vertices completely.
• (a) Squares: Yes, squares tile a floor seamlessly (like bathroom tiles).
• (b) Equilateral Triangles: Yes, equilateral triangles fit together perfectly around a point without gaps.
• (c) Circles: No, circles cannot tile a plane.
Why Circles Cannot Tile: When identical circles are placed touching each other, curved spaces (interstitial gaps) are always left between them. Curved boundaries cannot fill straight plane vertices completely.
CBSE Step-by-Step Marking Scheme
Correct identification of squares and triangles as tiling shapes
1.5 M
Clear mathematical reason why circles leave gaps
1.5 M
Q7
Paper Folding • Corners Exploration
Take a square sheet of paper. It has 4 corners.
(a) If you fold one corner diagonally, how many corners does the paper have now?
(b) Can you fold a piece of paper so that it has exactly 3 corners? What shape does it become?
[3 Marks]
(a) If you fold one corner diagonally, how many corners does the paper have now?
(b) Can you fold a piece of paper so that it has exactly 3 corners? What shape does it become?
✅ Step-by-Step Solution & Working
Step-by-Step Hands-on Geometry:
(a) Folding One Corner:
• By folding down one corner, a new straight edge is formed across that corner, creating 2 new corners in place of the 1 folded corner.
• Total corners = 4 - 1 + 2 = 5 corners (it becomes a pentagon).
(b) Folding to 3 Corners:
• Yes. If you fold a square sheet in half along its diagonal from corner to opposite corner, the folded paper forms a Triangle, which has exactly 3 corners.
(a) Folding One Corner:
• By folding down one corner, a new straight edge is formed across that corner, creating 2 new corners in place of the 1 folded corner.
• Total corners = 4 - 1 + 2 = 5 corners (it becomes a pentagon).
(b) Folding to 3 Corners:
• Yes. If you fold a square sheet in half along its diagonal from corner to opposite corner, the folded paper forms a Triangle, which has exactly 3 corners.
CBSE Step-by-Step Marking Scheme
Correct deduction of 5 corners after folding one corner
1.5 M
Correct identification of diagonal fold creating a triangle with 3 corners
1.5 M
Q8
Textbook Exercise • Practical Problem Solving
In Chapter 5 ('Fun with Shapes'), a student solves an exercise problem: If 1 packet contains 12 items, how many items are in 4 such packets? Explain using repeated addition and multiplication.
[2 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
1. Repeated addition: 12 + 12 + 12 + 12 = 48 items.
2. Multiplication fact: 4 × 12 = 48 items.
3. Both methods yield the exact same answer. Multiplication is efficient repeated addition.
CBSE Step-by-Step Marking Scheme
Repeated addition 12+12+12+12 = 48
1 M
Multiplication 4 × 12 = 48
1 M
Q9
In-Text Activity • Concept Exploration
In 'Fun with Shapes', how do you verify your mathematical calculations? Give an example using two numbers that add up to 100.
[2 Marks]
✅ Step-by-Step Solution & Working
Verification Method:
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
• Take two numbers: 65 and 35. Sum = 65 + 35 = 100.
• Verification by inverse operation (subtraction): 100 - 35 = 65, and 100 - 65 = 35.
• Since subtraction brings back the original numbers, the addition is confirmed correct.
CBSE Step-by-Step Marking Scheme
Addition 65 + 35 = 100
1 M
Inverse check 100 - 35 = 65
1 M
Q10
Practice Time • Mental Math Drills
Solve mentally:
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ?
[2 Marks]
(a) 25 + 75 = ?
(b) 150 - 60 = ?
(c) Double of 45 = ?
(d) Half of 80 = ?
✅ Step-by-Step Solution & Working
Mental Calculations:
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
• (a) 25 + 75 = 100.
• (b) 150 - 60 = 90.
• (c) 45 × 2 = 90.
• (d) 80 ÷ 2 = 40.
CBSE Step-by-Step Marking Scheme
All 4 mental math facts correct
2 M
Q11
Word Problem • Real Life Application
A school library received 3 boxes of mathematics activity books. Each box contained 25 books. During the week, 38 books were distributed to Grade 3 children. How many books remain in the library?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
1. Total books received = 3 × 25 = 75 books.
2. Books distributed = 38 books.
3. Books remaining = 75 - 38 = 37 books.
CBSE Step-by-Step Marking Scheme
Total 3 × 25 = 75
1.5 M
Remainder 75 - 38 = 37
1.5 M
Q12
Critical Thinking • Finding the Pattern
Observe the sequence related to 'Fun with Shapes': 12, 24, 36, 48, ___, ___. Find the next two terms and state the mathematical rule.
[2 Marks]
✅ Step-by-Step Solution & Working
Pattern Analysis:
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
• 12 + 12 = 24
• 24 + 12 = 36
• 36 + 12 = 48
• Rule: Successive addition of 12 (Multiples of 12).
• Next terms: 48 + 12 = 60, 60 + 12 = 72.
CBSE Step-by-Step Marking Scheme
Next terms 60, 72
1 M
Rule: multiples of 12 / +12 step
1 M
Q13
Estimation & Measurement • Practical Judgment
Estimate whether each measurement is greater than or less than 1 metre:
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard.
[2 Marks]
(a) Length of your classroom pencil.
(b) Height of your classroom teacher.
(c) Width of your mathematics textbook.
(d) Length of the school blackboard.
✅ Step-by-Step Solution & Working
Estimation:
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
• (a) Pencil: Less than 1 metre (approx. 15 cm).
• (b) Teacher height: Greater than 1 metre (approx. 1.6 to 1.7 m).
• (c) Textbook width: Less than 1 metre (approx. 20 cm).
• (d) Blackboard length: Greater than 1 metre (approx. 2 to 3 m).
CBSE Step-by-Step Marking Scheme
Correct estimation for all 4 items
2 M
Q14
Data Interpretation • Reading Simple Tables
A table shows student preferences for fruit: Apple (15), Banana (22), Mango (35), Orange (18).
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed?
[3 Marks]
(a) Which fruit is preferred by the maximum number of students?
(b) How many more students prefer Mango over Banana?
(c) What is the total number of students surveyed?
✅ Step-by-Step Solution & Working
Table Interpretation:
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
• (a) Maximum preference: Mango with 35 students.
• (b) Difference: 35 - 22 = 13 more students prefer Mango.
• (c) Total students: 15 + 22 + 35 + 18 = 90 students.
CBSE Step-by-Step Marking Scheme
Mango identified
1 M
Difference = 13
1 M
Total = 90
1 M
Q15
Let us Do • Shapes and Symmetry
Draw a line of symmetry through each shape:
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have?
[3 Marks]
(a) A rectangle
(b) An equilateral triangle
(c) A circle.
How many lines of symmetry does a circle have?
✅ Step-by-Step Solution & Working
Symmetry Properties:
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
• (a) A rectangle has 2 lines of symmetry (horizontal and vertical through centers of opposite sides).
• (b) An equilateral triangle has 3 lines of symmetry (from each vertex to opposite midpoint).
• (c) A circle has infinite lines of symmetry (any diameter passing through the center).
CBSE Step-by-Step Marking Scheme
Rectangle = 2 lines
1 M
Triangle = 3 lines
1 M
Circle = infinite lines
1 M
Q16
Puzzle Time • Missing Number Grid
In a 3x3 magic square, the sum of each row, column, and diagonal is 15. The center number is 5. What numbers go in the opposite corners if one corner is 2?
[2 Marks]
✅ Step-by-Step Solution & Working
Magic Square Logic:
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
• In a 3x3 magic square with sum 15 and center 5, opposite corners must sum to 10 (since 2 + 5 + x = 15 → x = 8).
• If one corner is 2, the diagonally opposite corner must be 8.
• Other corner pairs: 4 and 6.
CBSE Step-by-Step Marking Scheme
Opposite corner = 8 with reasoning
2 M
Q17
Money & Shopping • Cash Memo Bill
Rani visits a stationery shop and buys: 2 Pencils at ₹5 each, 1 Eraser for ₹3, and 1 Notebook for ₹25. Prepare a simple cash memo showing total bill and change returned from a ₹50 note.
[3 Marks]
✅ Step-by-Step Solution & Working
Cash Memo Preparation:
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
• 2 Pencils @ ₹5 = ₹10
• 1 Eraser @ ₹3 = ₹3
• 1 Notebook @ ₹25 = ₹25
• Total Bill Amount = ₹10 + ₹3 + ₹25 = ₹38.
• Amount paid = ₹50.
• Change returned = ₹50 - ₹38 = ₹12.
CBSE Step-by-Step Marking Scheme
Correct item breakdown and total ₹38
2 M
Change = ₹12
1 M
Q18
Chapter Review • Comprehensive Concept Check
True or False:
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners.
[3 Marks]
(a) 1 kilometre is equal to 1000 metres.
(b) 500 millilitres is equal to half a litre.
(c) A square has 4 equal straight edges and 4 right-angled corners.
✅ Step-by-Step Solution & Working
Review Answers:
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
• (a) True: 1 km = 1000 m.
• (b) True: 1 Litre = 1000 mL, so half a litre = 500 mL.
• (c) True: A square has 4 equal sides and 4 right angles.
CBSE Step-by-Step Marking Scheme
All 3 statements correctly evaluated as True
3 M
🌟 NEP 2020 Competency-Based Case Study
Classroom Floor Tiling Project
The school is laying square tiles of side 1 metre in an activity hall that is 6 metres long and 4 metres wide.
Analytical Task: How many 1-metre square tiles are needed to pave the entire floor? If each tile costs ₹50, find the total cost of tiles.
Evaluation & Model Answer:
1. Area of floor = Length × Width = 6 m × 4 m = 24 square metres.
2. Area of 1 tile = 1 m × 1 m = 1 square metre.
3. Number of tiles needed = 24 ÷ 1 = 24 tiles.
4. Total cost = 24 × ₹50 = ₹1,200.
2. Area of 1 tile = 1 m × 1 m = 1 square metre.
3. Number of tiles needed = 24 ÷ 1 = 24 tiles.
4. Total cost = 24 × ₹50 = ₹1,200.
Rubric: 1.5M tile count calculation + 1.5M total cost multiplication.