Shapes and Patterns – Class 5 Maths Chapter 7 Notes & NCERT PDF

Class 5MathematicsChapter 7NCERT book: Maths Mela - Mathematics Class 5

Notes and a simple summary of Chapter 7 of the NCERT Class 5 Mathematics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

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Chapter 7: Shapes and Patterns

Introduction

This chapter begins with weaving mats from paper strips, just like woven baskets we see at home. From weaving we move to tiling (tessellation), special triangles and quadrilaterals, the tangram, kites, circle designs, cube puzzles and two amazing solid shapes — the icosahedron and the dodecahedron. Most of the learning happens with hands: folding, cutting and fitting shapes.

Key Ideas

1. Weaving Patterns

A paper mat (30 cm × 20 cm) is folded, slits are cut, and 3 cm wide strips are woven in.

Row 1 — 1 under, 1 over, 1 under, 1 over … (repeat)

Row 2 — 1 over, 1 under, 1 over, 1 under … (repeat)

Changing the rule (for example 2 over, 1 under) gives a new design. A pattern is a rule that repeats.

2. Tiling and Tessellation

When shapes cover a flat surface with no gaps and no overlaps, we say they tessellate.

Regular shapes have all sides equal.

Equilateral triangles tessellate — 6 fit around a point.

Squares tessellate — 4 fit around a point (5 squares cannot fit).

Regular hexagons tessellate — 3 fit around a point.

Regular pentagons do not tessellate — 3 fit around a point but leave a gap.

Regular octagons do not tessellate on their own.

Some patterns mix shapes, such as squares with triangles.

3. Types of Triangles (from the rhombus pieces)

A rhombus (all sides equal) is cut into 4 triangles. By fitting pieces together we discover:

Isosceles triangle — 2 equal sides and 2 equal angles

Equilateral triangle — 3 equal sides and 3 equal angles

Scalene triangle — no equal sides

4. Quadrilaterals (4-sided shapes)

Kite — two pairs of equal adjacent sides (Side 1 = Side 2, Side 3 = Side 4)

Parallelogram — opposite sides equal, opposite angles equal

Rectangle — a special parallelogram where all angles are right angles

Rhombus — all sides equal, opposite angles equal

Square — all sides equal and all angles right angles

5. Tangram

Seven pieces (triangles, a square and a parallelogram) are cut out and joined to make many shapes. We compare their sides and angles.

6. Circles, Cubes and Solids

Join the ends of two diameters of a circle → you always get a rectangle (a square if the diameters are perpendicular).

Circle designs — joining points around a circle in a rule (1 to 11, 11 to 2, 2 to 12 …) makes star-like thread art.

Painted cube puzzle — 27 small cubes make a big cube painted red.

Icosahedron has 20 triangle faces; dodecahedron has 12 pentagon faces.

Worked Examples

Example 1 — How many shapes fit at a point?

Squares: each corner is a right angle. 4 right angles make a full turn, so 4 squares fit with no gap.

Example 2 — The painted cube (Nisha's 3 × 3 × 3 cube):

3 faces painted: the 8 corner cubes

2 faces painted: 12 edge cubes (one on each of the 12 edges)

1 face painted: 6 centre cubes (one per face)

0 faces painted: 1 hidden cube in the middle

Check: 8 + 12 + 6 + 1 = 27 ✔

Example 3 — Which shape am I? "All my sides are equal, but all my angles are not equal." → Rhombus.

"All my angles are right angles, but all my sides are not equal." → Rectangle.

Example 4 — Tanu's puzzle uses clues about position (between, next to, left of) to arrange 7 shapes in a line — good practice in logical thinking.

Maths Words

Pattern (प्रतिरूप / पैटर्न), Weave (बुनना)

Tessellation / Tiling (टाइलिंग, बिना खाली जगह के ढकना)

Regular shape (सम आकृति)

Equilateral triangle (समबाहु त्रिभुज), Isosceles (समद्विबाहु), Scalene (विषमबाहु)

Quadrilateral (चतुर्भुज), Parallelogram (समांतर चतुर्भुज), Rhombus (समचतुर्भुज)

Kite (पतंग आकार), Diameter (व्यास)

Face, Edge, Vertex (फलक, किनारा, शीर्ष)

Maths in Daily Life

Floor tiles, bathroom walls, honeycombs (hexagons), baskets and mats, rangoli, kites and footballs all use these shapes and patterns.

Common Mistakes

Thinking every regular shape tessellates — pentagons and octagons do not.

Confusing a kite (adjacent sides equal) with a parallelogram (opposite sides equal).

Forgetting that a rectangle and a square are also parallelograms.

Counting edges of a solid twice — count carefully, one face at a time.

Practice Tips

Always cut and try: fit paper shapes around a point to test tessellation.

Measure sides with a ruler and fold to compare angles.

Draw kites and parallelograms on grid paper.

Make the icosahedron and dodecahedron from the nets at the back of the book and count faces, edges and vertices.

💡 Key Learning Points

✓A pattern is a rule that repeats, as in weaving mats (1 under, 1 over …).
✓Shapes tessellate when they cover a surface with no gaps or overlaps; equilateral triangles, squares and regular hexagons do, regular pentagons and octagons do not.
✓Triangles can be isosceles (2 equal sides and angles), equilateral (3 equal) or scalene (none equal).
✓A kite has pairs of equal adjacent sides; a parallelogram has equal opposite sides; a rectangle is a parallelogram with right angles.
✓Solid shapes have faces, edges and vertices: an icosahedron has 20 triangular faces, a dodecahedron 12 pentagonal faces.

👨‍🏫 Teaching Tips

→Let every child weave the 30 cm × 20 cm paper mat and then invent and write their own weaving rule.
→Give cut-outs of triangles, squares, pentagons, hexagons and octagons; children test which ones fit around a point without gaps.
→Use the rhombus cut-out from the back of the book to build triangles and quadrilaterals in pairs; record findings in a table.
→Play 'Which Shape Am I?' as a guessing game where one child reads a property and others hold up the matching shape.
→Fold the paper kite in class and ask children to find the shapes inside it.
→Build a 3 × 3 × 3 cube from small blocks (or use a Rubik's cube) to explore the painted-faces puzzle.
→Make thread-art circle designs on card as a display activity.

📋 Assessment Questions

Can the child explain why regular pentagons do not tessellate while regular hexagons do?
Can the child identify and draw an isosceles, equilateral and scalene triangle?
Can the child tell a kite from a parallelogram by looking at which sides are equal?
Can the child solve the painted-cube puzzle and check that the four answers add up to 27?
Can the child continue a given weaving or tiling pattern correctly?

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