Chapter 5 of 14
Chapter 5: Shapes and Designs
2D Geometrical Shapes, Corners, Edges, Floor Patterns, Weaving & Tangrams | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- Comparing edges: straight edges vs curved edges.
- Corners (vertices) in 2D shapes: triangles (3), quadrilaterals (4), circles (0).
- Floor tiling patterns: tessellations that tile without gaps.
- Traditional Indian textile weaving patterns and borders.
All Textbook Exercises & In-Text Tasks (17 Questions)
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Q1
Corner & Edge Classification
Look at these objects: (1) A sheet of paper, (2) A wheel, (3) A blackboard, (4) An egg. State whether each object has straight edges or curved edges, and how many corners it has.
[2 Marks]
✅ Step-by-Step Solution & Working
Classification:
• 1. Sheet of paper: Straight edges (4) → 4 corners.
• 2. Wheel: Curved edge (1 continuous circular boundary) → 0 corners.
• 3. Blackboard: Straight edges (4) → 4 corners.
• 4. Egg: Curved surface → 0 corners.
• 1. Sheet of paper: Straight edges (4) → 4 corners.
• 2. Wheel: Curved edge (1 continuous circular boundary) → 0 corners.
• 3. Blackboard: Straight edges (4) → 4 corners.
• 4. Egg: Curved surface → 0 corners.
CBSE Step-by-Step Marking Scheme
Correct straight/curved edge identification
1.0 M
Correct corner counts for all 4 items
1.0 M
Q2
Tangram Dissection • 7-Piece Tangram
In a standard 7-piece Tangram puzzle: (a) How many triangles are there? (b) Are all triangles of the same size? (c) Name the two other shapes in the puzzle.
[3 Marks]
✅ Step-by-Step Solution & Working
Tangram Composition:
• (a) Triangles: There are 5 triangles.
• (b) Sizes: No, they are of different sizes: 2 large triangles, 1 medium triangle, and 2 small triangles.
• (c) Other shapes: 1 Square and 1 Parallelogram.
• (a) Triangles: There are 5 triangles.
• (b) Sizes: No, they are of different sizes: 2 large triangles, 1 medium triangle, and 2 small triangles.
• (c) Other shapes: 1 Square and 1 Parallelogram.
CBSE Step-by-Step Marking Scheme
Correct count of triangles (5)
1.0 M
Distinction between large, medium, small triangles
1.0 M
Naming square and parallelogram
1.0 M
Q3
Tessellation & Floor Patterns
Explain what a tessellation is. Draw or describe how a combination of triangles can tile a floor completely without leaving any gaps.
[2 Marks]
✅ Step-by-Step Solution & Working
Explanation:
• A tessellation is a pattern made of repeating geometric shapes that covers a flat surface completely without any gaps or overlaps.
• Triangle Tiling: Two identical triangles can be placed together along their diagonal to form a rectangle. These rectangles can then be arranged in neat rows and columns to cover any floor seamlessly.
• A tessellation is a pattern made of repeating geometric shapes that covers a flat surface completely without any gaps or overlaps.
• Triangle Tiling: Two identical triangles can be placed together along their diagonal to form a rectangle. These rectangles can then be arranged in neat rows and columns to cover any floor seamlessly.
CBSE Step-by-Step Marking Scheme
Definition of tessellation (no gaps, no overlaps)
1.0 M
Explanation of triangle pairing to form rectangles
1.0 M
Q4
Counting Shapes • Star and Geometrical Figures
Look at a standard 6-pointed star figure made of overlapping triangles:
(a) How many small triangles can you count?
(b) How many corners (vertices) does the 6-pointed star have?
(c) Does a circle have any corners?
[3 Marks]
(a) How many small triangles can you count?
(b) How many corners (vertices) does the 6-pointed star have?
(c) Does a circle have any corners?
✅ Step-by-Step Solution & Working
Shape Analysis:
• (a) Small Triangles: There are 6 outer pointed triangles, plus 2 large central overlapping triangles = 8 triangles in total.
• (b) Corners: The 6 outward points form 6 corners (or 12 vertices counting inner corners).
• (c) Circle Corners: No, a circle is a continuous smooth curve with 0 corners.
• (a) Small Triangles: There are 6 outer pointed triangles, plus 2 large central overlapping triangles = 8 triangles in total.
• (b) Corners: The 6 outward points form 6 corners (or 12 vertices counting inner corners).
• (c) Circle Corners: No, a circle is a continuous smooth curve with 0 corners.
CBSE Step-by-Step Marking Scheme
Correct triangle count with explanation
1.0 M
Correct corner identification
1.0 M
Correct circle property (0 corners)
1.0 M
Q5
Weaver's Borders • Repeating Patterns
Identify the repeating rule (unit of pattern) in each border design:
(a) ▲ ▼ ▲ ▼ ▲ ▼ ___ ___
(b) 🔲 ⚪ 🔲 ⚪ 🔲 ⚪ ___ ___
(c) Draw the next two figures for each pattern.
[3 Marks]
(a) ▲ ▼ ▲ ▼ ▲ ▼ ___ ___
(b) 🔲 ⚪ 🔲 ⚪ 🔲 ⚪ ___ ___
(c) Draw the next two figures for each pattern.
✅ Step-by-Step Solution & Working
Patterns & Next Terms:
• (a) Up and Down Triangles:
- Repeating unit: [▲, ▼]
- Next two figures: ▲, ▼.
• (b) Square and Circle:
- Repeating unit: [🔲, ⚪]
- Next two figures: 🔲, ⚪.
• (a) Up and Down Triangles:
- Repeating unit: [▲, ▼]
- Next two figures: ▲, ▼.
• (b) Square and Circle:
- Repeating unit: [🔲, ⚪]
- Next two figures: 🔲, ⚪.
CBSE Step-by-Step Marking Scheme
Identification of repeating core unit for both patterns
1.5 M
Accurate continuation with next two shapes
1.5 M
Q6
Clapper Activity • Paper Craft Geometry
In the 'Paper Clapper' activity described in the textbook:
(a) What shape of paper is used to begin with?
(b) How many times is the paper folded along its edges?
(c) What causes the loud 'pop' or clapping sound when swung down sharply?
[3 Marks]
(a) What shape of paper is used to begin with?
(b) How many times is the paper folded along its edges?
(c) What causes the loud 'pop' or clapping sound when swung down sharply?
✅ Step-by-Step Solution & Working
Paper Clapper Mechanics:
• (a) Paper Shape: A standard rectangular sheet of paper (like newspaper or scrap notebook paper).
• (b) Folds: It is folded lengthwise in half, then folded down several times into a thick band, and finally folded in half across the middle.
• (c) The Clapping Sound: When swung sharply downward, the sudden rush of air opens the inner folded pocket violently, snapping the paper open to produce the loud clapping sound.
• (a) Paper Shape: A standard rectangular sheet of paper (like newspaper or scrap notebook paper).
• (b) Folds: It is folded lengthwise in half, then folded down several times into a thick band, and finally folded in half across the middle.
• (c) The Clapping Sound: When swung sharply downward, the sudden rush of air opens the inner folded pocket violently, snapping the paper open to produce the loud clapping sound.
CBSE Step-by-Step Marking Scheme
Correct initial paper shape (rectangular)
1.0 M
Clear description of folding sequence
1.0 M
Physical explanation of air pressure opening paper pocket
1.0 M
Q7
Straight Edges vs Curved Edges
Classify the following 6 objects into 'Straight Edges Only' and 'Curved Edges / Both':
Postcard, Coin, Blackboard, CD/DVD, Book, Bottle cap.
[3 Marks]
Postcard, Coin, Blackboard, CD/DVD, Book, Bottle cap.
✅ Step-by-Step Solution & Working
Classification:
• Straight Edges Only:
1. Postcard
2. Blackboard
3. Book
• Curved Edges / Both:
1. Coin (Curved circular edge)
2. CD/DVD (Curved circular edge)
3. Bottle cap (Curved circular edge).
• Straight Edges Only:
1. Postcard
2. Blackboard
3. Book
• Curved Edges / Both:
1. Coin (Curved circular edge)
2. CD/DVD (Curved circular edge)
3. Bottle cap (Curved circular edge).
CBSE Step-by-Step Marking Scheme
Correct straight-edge objects classified (3 objects)
1.5 M
Correct curved-edge objects classified (3 objects)
1.5 M
Q8
Textbook Exercise • Real-Life Math
In Chapter 5 ('Shapes and Designs'), a student solves an NCERT word problem: If 1 kg of apples costs ₹60 and 1 kg of oranges costs ₹40, how much do 2 kg of apples and 3 kg of oranges cost altogether?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
1. Cost of 2 kg apples = 2 × ₹60 = ₹120.
2. Cost of 3 kg oranges = 3 × ₹40 = ₹120.
3. Total cost = ₹120 + ₹120 = ₹240.
CBSE Step-by-Step Marking Scheme
Apples = ₹120
1 M
Oranges = ₹120
1 M
Total = ₹240
1 M
Q9
In-Text Activity • Hands-on Investigation
In 'Shapes and Designs', how do you measure and compare quantities accurately? Explain with an example using standard units.
[3 Marks]
✅ Step-by-Step Solution & Working
Measurement Explanation:
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
• Standard units provide consistent and reliable measurements across the world.
• For length, we use metres (m) and centimetres (cm).
• For weight, we use kilograms (kg) and grams (g).
• For liquids, we use litres (L) and millilitres (mL).
• Unlike non-standard units (such as footsteps or handspans), standard units give the exact same measurement no matter who measures.
CBSE Step-by-Step Marking Scheme
Standard units defined
1.5 M
Examples for length, weight, liquid
1.5 M
Q10
Practice Time • Two-Step Word Problem
Suresh bought a school bag for ₹175 and a pencil box for ₹45. He gave a ₹500 note to the shopkeeper. How much change did he receive?
[3 Marks]
✅ Step-by-Step Solution & Working
Step-by-Step Solution:
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
1. Total money spent = ₹175 + ₹45 = ₹220.
2. Amount paid = ₹500.
3. Change returned = ₹500 - ₹220 = ₹280.
CBSE Step-by-Step Marking Scheme
Total spent = ₹220
1.5 M
Change = ₹280
1.5 M
Q11
Mental Math • Quick Calculations
Calculate mentally without writing long columns:
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ?
[2 Marks]
(a) 250 + 150 = ?
(b) 500 - 180 = ?
(c) 4 × 25 = ?
(d) 100 ÷ 4 = ?
✅ Step-by-Step Solution & Working
Mental Calculations:
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
• (a) 250 + 150 = 400.
• (b) 500 - 180 = 320.
• (c) 4 × 25 = 100.
• (d) 100 ÷ 4 = 25.
CBSE Step-by-Step Marking Scheme
All 4 mental results correct
2 M
Q12
Geometry & Shapes • Edge and Corner Counting
Name a 3D solid shape that has:
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners.
[3 Marks]
(a) 6 flat square faces, 12 straight edges, and 8 corners.
(b) 1 curved surface and 2 flat circular faces.
(c) Only 1 curved surface and 0 corners.
✅ Step-by-Step Solution & Working
Solid Shapes:
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
• (a) 6 square faces, 12 edges, 8 corners: Cube.
• (b) 1 curved and 2 circular faces: Cylinder.
• (c) Only 1 curved surface, 0 corners: Sphere.
CBSE Step-by-Step Marking Scheme
Cube
1 M
Cylinder
1 M
Sphere
1 M
Q13
Pattern Time • Sequences and Rules
Identify the rule and find the next two terms: 5, 10, 20, 40, ___, ___.
[2 Marks]
✅ Step-by-Step Solution & Working
Rule: Each term is multiplied by 2 (doubled).
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
• 40 × 2 = 80
• 80 × 2 = 160.
Next terms are 80, 160.
CBSE Step-by-Step Marking Scheme
Next terms 80, 160
1 M
Rule: multiplying by 2
1 M
Q14
Time & Calendar • Date Calculation
Rohan's summer vacation starts on 15th May and ends on 30th June. How many total days of vacation does Rohan get? (Remember: May has 31 days).
[3 Marks]
✅ Step-by-Step Solution & Working
Days Count:
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
• Days in May: From 15th to 31st = (31 - 15) + 1 = 17 days.
• Days in June: Full 30 days = 30 days.
• Total vacation days = 17 + 30 = 47 days.
CBSE Step-by-Step Marking Scheme
May days = 17
1.5 M
June days = 30; Total = 47 days
1.5 M
Q15
Equal Sharing • Division Problem
Mother bakes 36 cookies and wants to distribute them equally among 4 children. How many cookies does each child receive? Write the division sentence.
[2 Marks]
✅ Step-by-Step Solution & Working
Equal Sharing:
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
• Total cookies = 36.
• Number of children = 4.
• Cookies per child = 36 ÷ 4 = 9 cookies.
• Division sentence: 36 ÷ 4 = 9.
CBSE Step-by-Step Marking Scheme
36 ÷ 4 = 9 cookies
2 M
Q16
Data Handling • Reading a Bar Chart
A survey of pets owned by children: Dog (14), Cat (10), Parrot (6), Fish (8).
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots?
[3 Marks]
(a) Which pet is owned by the least number of children?
(b) How many total pets are there?
(c) How many more dogs are there than parrots?
✅ Step-by-Step Solution & Working
Survey Analysis:
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
• (a) Least owned pet: Parrot (only 6).
• (b) Total pets: 14 + 10 + 6 + 8 = 38 pets.
• (c) Difference: 14 Dogs - 6 Parrots = 8 more dogs.
CBSE Step-by-Step Marking Scheme
Parrot least
1 M
Total = 38
1 M
Difference = 8
1 M
Q17
Money • Making a Change
A toy train costs ₹85. You pay with a ₹100 note. The shopkeeper gives you change in 5-rupee coins only. How many 5-rupee coins do you receive?
[2 Marks]
✅ Step-by-Step Solution & Working
Calculations:
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
• Change due = ₹100 - ₹85 = ₹15.
• Number of 5-rupee coins = ₹15 ÷ ₹5 = 3 coins.
CBSE Step-by-Step Marking Scheme
Change = ₹15
1 M
3 coins of ₹5
1 M
🌟 NEP 2020 Competency-Based Case Study
Handloom Saree Border Design
A master weaver from Varanasi designs a border pattern using alternating red squares and yellow triangles. Every 10 cm repeat of the pattern uses 2 squares and 4 triangles.
Analytical Task: How many squares and how many triangles will be woven along a 1-metre (100 cm) saree border?
Evaluation & Model Answer:
1. Total border length = 1 metre = 100 cm.
2. Number of 10 cm pattern repeats = 100 ÷ 10 = 10 repeats.
3. Squares needed = 10 × 2 = 20 squares.
4. Triangles needed = 10 × 4 = 40 triangles.
2. Number of 10 cm pattern repeats = 100 ÷ 10 = 10 repeats.
3. Squares needed = 10 × 2 = 20 squares.
4. Triangles needed = 10 × 4 = 40 triangles.
Rubric: 1M meter to cm conversion + 1M pattern repeats + 1M shape counts.