NCERT Ganita Prakash, Class 7, textbook pages 136–163 (Part 2)

How to teach Class 7 Maths Part 2 Chapter 6, Constructions and Tilings, at home

Geometric constructions and tiling patterns, taught with things you already have at home: a 20-minute activity, a game for the week, a 5-day plan and the mistakes to watch for.

3 × 120° = 360°

NCERT Class 7 Maths Part 2 Chapter 6 Constructions and Tilings: what it teaches

Your child makes constructions with ruler and compass (perpendiculars, angle bisectors, special angles like 60° and 90°), and explores which regular polygons tile a floor and why.

Why it matters later. Constructions support geometry proofs; tiling links angles and patterns.

See it: this chapter in pictures

60°compass: equal arcs
Equal arcs give an equilateral triangle, so 60°.
perpendicular bisector
Cuts the segment in half at a right angle.
pentagon angle 108°3 × 108° = 324°gap → no tiling
Angles at a point must make 360°.

You need

  • compass, ruler, protractor
  • paper polygons: triangles, squares, hexagons, pentagons
  • scissors

Tonight’s 20 minutes

  1. Construct a 60° angle with a compass, then bisect it for 30°.
  2. Draw the perpendicular bisector of a line segment.
  3. Cut regular polygons and try to tile: which fit around a point?
  4. Check: angles meeting at a point must add to 360°.

Words to use

  • construct
  • bisect
  • perpendicular
  • regular polygon
  • tiling
  • 360°

Watch for

  • Compass width changing mid-construction. Tighten the compass and keep the width for both arcs.
  • Thinking regular pentagons tile. 108° × 3 = 324°: a gap remains.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouDo regular pentagons tile?

Your child108 × 3 = 324, so no.

A game for this week: Tile test

  1. Cut 6 copies each of 4 regular polygons.
  2. Try tiling each around a point.
  3. Record angle sums.
  4. Explain which work and why.

A 5-day plan, 20 minutes a day

  1. Day 160° and 30° constructions.
  2. Day 2Perpendicular bisector.
  3. Day 3Tiling with polygons.
  4. Day 4Angle sum at a point.
  5. Day 5Tile test.

Everyday moments to practise

  • Floor tiles.
  • Honeycombs.
  • Quilts.
  • Islamic geometric art.

Quick check

Ask these at the end of the week. Tap to see the answer.

Which regular polygons tile alone?

Triangles, squares and hexagons.

Angle of a regular hexagon?

120°.

How do you get 30° with a compass?

Construct 60° and bisect it.

Ready for the next chapter when your child…

  • Constructs basic angles and bisectors.
  • Explains which polygons tile.
  • Uses the 360° condition.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Prakash (Class 7). See the full Class 7 parent guide for every chapter.

Questions parents ask

Why do hexagons tile?

Three 120° angles make 360° exactly.

What is a perpendicular bisector?

A line cutting a segment in half at 90°.

Can pentagons ever tile?

Regular ones can’t; some irregular pentagons can.