Chapter 2 of 11
⬅️ Ch 1: A Day at the Beach Ch 3: Fun with Numbers ➡️
NCERT Class 2 Mathematics • New NEP 2020 / NCF-FS

Chapter 2: Shapes Around Us

2D & 3D Shapes, Rolling, Sliding & Surface Properties | CBSE Session 2026–27

Core Pedagogical Competencies & Concepts
  • Distinguishing flat (2D) shapes: circle, square, rectangle, triangle.
  • Exploring solid (3D) shapes: sphere (ball), cylinder (can), cube (dice), cone (party hat).
  • Identifying which objects roll, which slide, and which can both roll and slide.
Circle (Rolls) • Square (Slides) • Triangle (Slides) • Cylinder (Rolls & Slides)

All Textbook Exercises & In-Text Tasks (18 Questions)

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Q1 Shape Identification • 2D vs 3D
Classify the following items into 'Rolls', 'Slides', or 'Both Rolls and Slides': (a) Cricket Ball, (b) Eraser, (c) Coin, (d) Pencil.
[3 Marks]
✅ Step-by-Step Solution & Working
Classification:
• (a) Cricket Ball: Rolls (it has only a curved round surface).
• (b) Eraser: Slides (it has flat faces).
• (c) Coin: Both rolls and slides (rolls on circular edge, slides on flat faces).
• (d) Round Pencil: Both rolls (along cylindrical body) and slides (on flat ends).
CBSE Step-by-Step Marking Scheme
Correct classification for all 4 items 3 M
Q2 Corner & Edge Counting
How many corners and straight edges does a rectangular postcard have? Does a circle have any corners?
[2 Marks]
✅ Step-by-Step Solution & Working
Answer:
1. A rectangular postcard has 4 straight edges and 4 corners (vertices).
2. A circle has 0 corners and 0 straight edges (it is formed by 1 continuous curved line).
CBSE Step-by-Step Marking Scheme
Postcard: 4 edges, 4 corners 1 M
Circle: 0 corners, curved line 1 M
Q3 Creative Construction • Towers
Can you stack footballs on top of each other to make a tall tower? Why or why not? What shapes make stable towers?
[3 Marks]
✅ Step-by-Step Solution & Working
Answer:
• No, we cannot stack round footballs because they have curved surfaces and roll off.
• Objects with flat surfaces like books, square wooden blocks, and shoe boxes make stable towers because flat faces sit securely on each other.
CBSE Step-by-Step Marking Scheme
Reason why round balls cannot stack 1.5 M
Identification of flat surface objects for stacking 1.5 M
Q4 Let Us Do • Flat vs Curved Faces
Fill in the blanks with 'Flat' or 'Curved':
(a) A blackboard has a ______ surface.
(b) A globe has a ______ surface.
(c) A party hat has both a ______ base and a ______ side surface.
[3 Marks]
✅ Step-by-Step Solution & Working
Answers:
(a) Flat
(b) Curved
(c) Flat base and a Curved side surface.
CBSE Step-by-Step Marking Scheme
Correct fills (1 M each) 3 M
Q5 Tracing Shapes • Imprints
What 2D shape will you get if you trace the outline of:
(a) The base of a tea cup?
(b) A matchbox?
(c) A dice?
(d) A ruler?
[2 Marks]
✅ Step-by-Step Solution & Working
Answers:
(a) Base of tea cup: Circle
(b) Matchbox: Rectangle
(c) Dice: Square
(d) Ruler: Long Rectangle.
CBSE Step-by-Step Marking Scheme
All 4 shapes identified correctly (0.5 M each) 2 M
Q6 Let Us Think • Wheels of Vehicles
Why are the wheels of cars, buses, and bicycles made round (circular) and not square or triangular?
[2 Marks]
✅ Step-by-Step Solution & Working
Answer:
• Round wheels have a smooth curved surface with no sharp corners, allowing them to roll effortlessly with minimal friction.
• Square or triangular wheels have corners that would get stuck on the ground and bump violently, making vehicles unable to roll smoothly.
CBSE Step-by-Step Marking Scheme
Rolling property of curved surfaces 1 M
Obstacle of sharp corners explained 1 M
Q7 Shape Properties • Triangles
How many corners and straight sides does a samosa or a road sign triangle have? Can a triangle have a curved side?
[2 Marks]
✅ Step-by-Step Solution & Working
Answer:
1. A triangle has 3 straight sides and 3 corners.
2. No, a standard geometric triangle cannot have a curved side; all three sides must be straight lines.
CBSE Step-by-Step Marking Scheme
3 sides and 3 corners 1 M
Sides must be straight 1 M
Q8 Comparing 2D Shapes • Square vs Rectangle
State one similarity and one difference between a square and a rectangle.
[2 Marks]
✅ Step-by-Step Solution & Working
Answer:
• Similarity: Both have 4 straight sides and 4 square corners (vertices).
• Difference: In a square, all 4 sides are equal in length, whereas in a rectangle, only opposite sides are equal.
CBSE Step-by-Step Marking Scheme
Similarity: 4 sides & 4 corners 1 M
Difference: Equal sides vs opposite sides 1 M
Q9 Rolling and Sliding Game
In a carrom game, what happens when you slide the striker on its flat face? What happens if you stand the striker on its round edge and push it?
[2 Marks]
✅ Step-by-Step Solution & Working
Answer:
• When placed flat, the striker slides smoothly across the board.
• When stood on its circular edge and pushed, the striker rolls forward like a tiny wheel.
CBSE Step-by-Step Marking Scheme
Flat face slides 1 M
Circular edge rolls 1 M
Q10 Let Us Do • Count Shapes in a Picture
In a drawing of a toy truck made of shapes:
• The body is 1 rectangle.
• The cabin is 1 square.
• The wheels are 4 circles.
• The headlights are 2 triangles.
How many total geometric shapes were used?
[2 Marks]
✅ Step-by-Step Solution & Working
Calculation:
• Rectangle = 1
• Square = 1
• Circles = 4
• Triangles = 2
• Total shapes = 1 + 1 + 4 + 2 = 8 shapes.
CBSE Step-by-Step Marking Scheme
Shape breakdown 1 M
Total = 8 shapes 1 M
Q11 3D Solid Names • Everyday Match
Match each solid shape name to its real-world example:
1. Sphere — (A) Party hat
2. Cylinder — (B) Wooden playing dice
3. Cone — (C) Can of tomato soup
4. Cube — (D) Tennis ball
[2 Marks]
✅ Step-by-Step Solution & Working
Correct Matching:
1. Sphere ➔ (D) Tennis ball
2. Cylinder ➔ (C) Can of tomato soup
3. Cone ➔ (A) Party hat
4. Cube ➔ (B) Wooden playing dice.
CBSE Step-by-Step Marking Scheme
All 4 correctly matched (0.5 M each) 2 M
Q12 Let Us Think • Can You Stack?
Which of the following can be stacked to make a stable pile without falling?
(a) Matchboxes, (b) Marbles, (c) 5-rupee coins, (d) Oranges, (e) Exercise books.
[2 Marks]
✅ Step-by-Step Solution & Working
Answer:
• Can be stacked: (a) Matchboxes, (c) 5-rupee coins, and (e) Exercise books (all have flat faces).
• Cannot be stacked: (b) Marbles and (d) Oranges (round spherical objects roll off).
CBSE Step-by-Step Marking Scheme
Correct stacking list 1 M
Correct non-stacking list with reason 1 M
Q13 Creative Math • Tangram / Shape Art
Can you combine two identical triangles along their longest side to make a square or rectangle? Explain.
[2 Marks]
✅ Step-by-Step Solution & Working
Answer:
• Yes, joining two identical right-angled triangles along their longest side (hypotenuse) forms a complete square or rectangle.
CBSE Step-by-Step Marking Scheme
Affirmative answer (Yes) 1 M
Forms square or rectangle 1 M
Q14 Shape Riddle
I have 0 flat sides, 0 corners, and I look identical from every angle. I love rolling on the grass. What 3D shape am I?
[1 Marks]
✅ Step-by-Step Solution & Working
Answer:
I am a Sphere (like a ball or globe).
CBSE Step-by-Step Marking Scheme
Identified as Sphere 1 M
Q15 Shape Riddle
I have 1 circular flat base and 1 pointed corner at the top. You put me on your head at birthday parties. What shape am I?
[1 Marks]
✅ Step-by-Step Solution & Working
Answer:
I am a Cone (Party hat).
CBSE Step-by-Step Marking Scheme
Identified as Cone 1 M
Q16 Let Us Do • Edge Inspection
Run your finger along the rim of a coin. Is the edge straight or curved? Run your finger along a textbook page. Is the edge straight or curved?
[2 Marks]
✅ Step-by-Step Solution & Working
Answer:
• The rim of a coin is a curved edge.
• The edge of a textbook page is a straight edge.
CBSE Step-by-Step Marking Scheme
Coin edge: curved 1 M
Page edge: straight 1 M
Q17 True or False • Shape Knowledge
Write True or False:
(a) A cylinder has 2 flat circular faces and 1 curved surface.
(b) A cube has 6 flat square faces.
(c) A triangle has 4 corners.
[3 Marks]
✅ Step-by-Step Solution & Working
Answers:
(a) True
(b) True
(c) False (A triangle has exactly 3 corners).
CBSE Step-by-Step Marking Scheme
All 3 evaluated correctly (1 M each) 3 M
Q18 Visual Problem • Cut Corner
If you take a square sheet of paper and snip off one of its corners with scissors, how many corners does the paper now have?
[2 Marks]
✅ Step-by-Step Solution & Working
Answer:
• Cutting off 1 corner replaces that 1 corner with 2 new corners.
• Remaining corners = 3 original + 2 new = 5 corners (the paper becomes a pentagon!).
CBSE Step-by-Step Marking Scheme
Explanation of corner replacement 1 M
Final count: 5 corners 1 M
🌟 NEP 2020 Competency-Based Case Study

Playground Ramp Experiment

During lunch break, Ananya slides her lunchbox down a slide and rolls an apple down the same slide.

Analytical Task: Why does the apple roll while the lunchbox slides? Name one everyday item that can do both.
Evaluation & Model Answer:
1. The apple has a curved surface without flat edges, allowing it to roll smoothly.
2. The lunchbox has flat surfaces, so it slides along the slide.
3. A coin or a carrom coin or a water bottle can both roll (on its curved side) and slide (on its flat face).
Rubric: 1.5 M for surface explanation + 1.5 M for coin/bottle example
⬅️ Ch 1: A Day at the Beach Ch 3: Fun with Numbers ➡️