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CBSE Class 3 Mathematics★ 4–5 marks · CBSE Class 3 Mathematics (Math-Magic) Chapter 5

Shapes and Designs

Explore 2D shapes — circle, square, rectangle, triangle. Learn about edges and corners. Have fun with tangrams and creating designs with shapes. CBSE Class 3 Mathematics (Math-Magic) Chapter 5.

⏱ 8 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Identify and describe 2D shapes: circle, square, rectangle, triangle — by number of sides and corners
2Understand edges (straight sides) and corners (where edges meet) — count them for each shape
3Create designs and patterns using combinations of basic shapes (rangoli, tile patterns)
4Use tangram pieces to form different shapes — a square, a triangle, a house, a cat
5Recognize shapes embedded in everyday objects and art

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Why this chapter matters

Shapes are everywhere — in rangoli, tiles, buildings, and art. This chapter deepens children's understanding of 2D shapes (circle, square, rectangle, triangle) by teaching edges and corners, and introduces tangrams — the ancient Chinese puzzle of 7 pieces that can form hundreds of shapes. Tangrams develop spatial reasoning, creativity, and problem-solving in a playful, hands-on way.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Class 3 Mathematics Chapter 1: Where to Look From

Builds on 2D and 3D shapes — now exploring 2D shapes more deeply with edges, corners, and tangrams.

Shapes and Designs

What are 2D Shapes?

2D stands for TWO-DIMENSIONAL. These shapes are FLAT. They have LENGTH and BREADTH but NO thickness.

Think of a SHEET OF PAPER — it is flat. Shapes drawn on paper are 2D shapes.

Basic 2D Shapes

Circle

Sides: 0 (one CURVED line)
Corners: 0
Examples: Bangle, coin, wheel, chapati

A circle has NO straight sides. It is perfectly ROUND.

Square

Sides: 4 (ALL sides EQUAL)
Corners: 4
Examples: Chess board square, tile, napkin, Rubik's cube face

All four sides of a square have the SAME length.

Rectangle

Sides: 4 (OPPOSITE sides equal)
Corners: 4
Examples: Book, door, mobile phone, table top

A rectangle has 2 LONG sides and 2 SHORT sides.

Triangle

Sides: 3
Corners: 3
Examples: Sandwich piece, roof shape, pizza slice, ruler set square

A triangle ALWAYS has 3 sides and 3 corners.

Comparing Shapes

Shape	Number of Sides	Number of Corners	Special Property
Circle	0 (curved)	0	Perfectly round
Semi-circle	1 straight + 1 curved	2	Half of a circle
Square	4 equal sides	4	All sides same
Rectangle	4 sides (opposite equal)	4	Two long, two short
Triangle	3 sides	3	Three sides, three corners
Pentagon	5 sides	5	Five sides shape
Hexagon	6 sides	6	Six sides shape
Octagon	8 sides	8	Eight sides shape

Edges and Corners

What is an Edge?

An EDGE is a STRAIGHT line where two sides MEET.

A triangle has 3 edges
A square has 4 edges
A rectangle has 4 edges
A circle has NO edges (it has a CURVED boundary)

What is a Corner?

A CORNER (also called a VERTEX) is where two edges MEET.

A triangle has 3 corners
A square has 4 corners
A rectangle has 4 corners
A circle has NO corners

Key Rule: The number of CORNERS is the SAME as the number of EDGES for most shapes.

Making Shapes with Other Shapes

Two Triangles Make a Square

Take two IDENTICAL right-angled triangles. Place them together along the LONG side. What do you get? A SQUARE!

Two Squares Make a Rectangle

Take two IDENTICAL squares. Place them side by side. What do you get? A RECTANGLE!

Four Triangles Make a Bigger Triangle

Take four small EQUILATERAL triangles. Arrange them. You get a BIGGER triangle!

Tangrams

What is a Tangram?

A TANGRAM is a Chinese puzzle made of SEVEN pieces called TANS:

Piece	Shape	Number
Large triangle	Triangle	2
Medium triangle	Triangle	1
Small triangle	Triangle	2
Square	Square	1
Parallelogram	Parallelogram	1

Total pieces: 7

Rules of Tangram

Use ALL 7 pieces
Pieces must NOT OVERLAP
Pieces must TOUCH each other
You can FLIP or ROTATE pieces

Things You Can Make with Tangrams

Animals: Cat, dog, rabbit, bird, fish
People: A dancing person, a runner, a family
Objects: House, boat, candle, rocket
Letters: T, L, A, K

Fun Fact: You can make OVER 6500 different shapes using the same 7 tangram pieces!

Patterns with Shapes

Repeating Shape Patterns

Circle, Square, Circle, Square, Circle, ___ (Square)
Triangle, Square, Triangle, Square, ___ (Triangle)

Shape Patterns with Colour

Red circle, Blue circle, Red circle, Blue circle, ___ (Red circle)

Growing Shape Patterns

One triangle, Two triangles, Three triangles, ___ (Four triangles)

Rotating Patterns

A shape can be ROTATED to make a pattern:

Square on its side → Diamond (a square ROTATED by 45 degrees)

Creating Designs with Shapes

Design 1: A House

SQUARE for the main house
TRIANGLE for the roof
RECTANGLE for the door
SMALL SQUARES for windows
CIRCLE for the sun

Design 2: A Flower

CIRCLE for the centre
TRIANGLE or OVAL shapes for petals
RECTANGLE for the stem
OVALS for leaves

Design 3: A Rocket

RECTANGLE for the body
TRIANGLE for the top
SMALL TRIANGLES for fins
CIRCLE for the window

Common Mistakes

'A circle has one side.' — A circle has NO straight sides. It has one CURVED boundary.
'A square and a rectangle are always different.' — A square IS a special type of rectangle where ALL sides are equal.
'A triangle can have 4 sides.' — No! A triangle ALWAYS has exactly 3 sides and 3 corners.
'All shapes with 4 sides are squares.' — No! A shape with 4 sides could be a RECTANGLE, a RHOMBUS, or a TRAPEZIUM.
'Corner and edge mean the same thing.' — No! An EDGE is the line where two sides meet. A CORNER is where two edges meet.

Quick Self-Test

Q1: How many sides does a triangle have? A1: 3 sides.

Q2: How many corners does a circle have? A2: 0 corners.

Q3: What shape has 4 equal sides? A3: A square.

Q4: How many pieces are there in a tangram? A4: 7 pieces.

Q5: Can you make a rectangle with two squares? A5: Yes, put two squares side by side.

Q6: How many edges does a pentagon have? A6: 5 edges.

Q7: What is the difference between a square and a rectangle? A7: A square has ALL 4 sides equal. A rectangle has OPPOSITE sides equal.

Q8: Use a tangram to make a cat. How many pieces do you use? A8: All 7 pieces (that is the rule of tangram!).

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Edges and corners of 2D shapes

Circle: 0 straight edges (curved), 0 corners · Square: 4 equal edges, 4 corners · Rectangle: 4 edges (opposite equal), 4 corners · Triangle: 3 edges, 3 corners

An EDGE is a straight side. A CORNER is where two edges meet. A circle has no edges or corners because it's curved.

What is a tangram?

A tangram is a square cut into 7 pieces: 2 large triangles, 1 medium triangle, 2 small triangles, 1 square, 1 parallelogram. These 7 pieces can be rearranged to form hundreds of different shapes — animals, people, objects, letters.

Tangrams teach spatial reasoning: how shapes fit together to form new shapes. It's like a puzzle with infinite possibilities.

Creating new shapes from basic shapes

2 triangles can make a square · 2 triangles can make a larger triangle · A square + a triangle on top = a house · 2 squares side by side = a rectangle · A rectangle cut diagonally = 2 triangles

Complex designs are made of simple shapes. Rangoli, tile patterns, and building designs all start with basic shapes.

Symmetry in shapes (introductory)

If you fold a shape and both halves match exactly, the shape is SYMMETRICAL. A square has 4 lines of symmetry. A rectangle has 2. An equilateral triangle has 3. A circle has infinite lines of symmetry.

At Class 3 level, focus on identifying symmetry by folding paper shapes. Full symmetry study comes in later classes.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Calling every 4-sided shape a 'square'

✓ A square has 4 EQUAL sides AND 4 corners. A rectangle has 4 sides but only opposite sides are equal. If all sides are not equal, it's a rectangle, not a square.

WATCH OUT

✗ Saying a circle has 1 curved 'side' and therefore 1 edge

✓ In geometry, an 'edge' is a straight line. A circle has a curved boundary — not an edge. So we say: 0 straight edges, 0 corners. The curved line is called the circumference.

WATCH OUT

✗ Thinking tangrams are just for fun — not 'real math'

✓ Tangrams develop critical spatial reasoning skills — understanding how shapes combine, rotate, and relate to each other. This is the foundation of geometry, engineering, and design thinking.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Shape identification and counting

Count edges and corners of shapes; identify shapes in rangoli and tile patterns

Questions

Tangram and design activities

Make shapes using tangram pieces; create your own designs using basic shapes; folding and symmetry

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Identify

How many edges and corners does a triangle have?

▶ Show solution

A triangle has 3 straight edges and 3 corners.

Q2EASY· Compare

How is a square different from a rectangle?

▶ Show solution

A square has ALL 4 sides equal. A rectangle has only OPPOSITE sides equal — adjacent sides may be different. Both have 4 edges and 4 corners.

Q3EASY· Create

Using 2 triangles of the same size, what 2D shape can you make?

▶ Show solution

Two triangles of the same size can form a SQUARE (if right-angled triangles joined at the long side) or a LARGER TRIANGLE (if joined along one equal side). It depends on how you arrange them.

Q4EASY· Count

Look at a picture of a house made of shapes. Count how many squares, rectangles, and triangles you see.

▶ Show solution

(Answer depends on picture. Typical house: 1 square for the main body, 1 triangle for the roof, 1 rectangle for the door, 1-2 squares for windows.)

Q5MEDIUM· Tangram

How many pieces are there in a tangram? Name the shapes of the pieces.

▶ Show solution

A tangram has 7 pieces (called 'tans'): 2 large triangles, 1 medium triangle, 2 small triangles, 1 square, and 1 parallelogram. All 7 pieces together form a large square.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•2D shapes are flat — drawn on paper. 3D shapes are solid — you can hold them
•Edges = straight sides. Corners = where edges meet. Circle has 0 edges, 0 corners (all curved)
•Square: 4 equal edges, 4 corners. Rectangle: 4 edges (opposite equal), 4 corners. Triangle: 3 edges, 3 corners
•A tangram is a 7-piece puzzle (5 triangles, 1 square, 1 parallelogram) that forms hundreds of shapes
•Complex designs (rangoli, tiles, buildings) are made by combining simple shapes
•Shapes are everywhere — in art, architecture, nature, and everyday objects

CBSE marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 4–5 marks in Class 3 Mathematics assessment

Question type	Marks each	Typical count	What it tests
Fill in the blanks / MCQ (1 mark)	1	2	Naming shapes; counting edges and corners; identifying shapes in a given design
Short answer / Drawing (2 marks)	2	1–2	Drawing specified shapes; creating a design using basic shapes; tangram-based questions

Prep strategy

Make a paper tangram set: draw a square, cut along the lines — 7 pieces. Let your child explore freely
Go on a 'Shape Hunt' at home: find circles (clock, plate), squares (tiles, window), rectangles (door, book), triangles (samosa, hanger)
Create rangoli designs using basic shapes — draw with chalk on the floor or on paper
Fold paper shapes to explore symmetry: fold a square in half, then unfold — the crease is a line of symmetry
Ask: 'What shapes can you see in that building/car/painting?' — train shape recognition everywhere

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