NCERT Ganita Prakash, Class 8, textbook pages 55–69 (Part 2)

How to teach Class 8 Maths Part 2 Chapter 3, Proportional Reasoning-2, at home

Inverse proportion and sharing in a ratio, taught with things you already have at home: a 30-minute activity, a game for the week, a 5-day plan and the mistakes to watch for.

6 workers → 10 days4 workers → ? days6 × 10 = 4 × 15 → 15 days

NCERT Class 8 Maths Part 2 Chapter 3 Proportional Reasoning-2: what it teaches

More workers finish a job faster: that is inverse proportion. Your child tells direct from inverse proportion, solves time-and-work and speed problems, and divides amounts in a given ratio.

Why it matters later. Proportional reasoning appears in science (speed, density) and in Class 9–10 algebra.

See it: this chapter in pictures

more pens → more costdirectmore workers → less time: inverse
Ask: does one go up while the other goes down?
₹600 in 2 : 35 parts → ₹120 each₹240 and ₹360
Add the parts first.
180 km at 60 km/h = 3 hat 90 km/h= 2 h
Distance fixed: speed and time are inverse.

You need

  • a calculator
  • paper

Tonight’s 30 minutes

  1. Direct or inverse? More pens, more cost. More workers, less time.
  2. 6 workers take 10 days. How long for 4 workers? (15)
  3. Share ₹600 between two people in the ratio 2 : 3.
  4. At 60 km/h a trip takes 3 h. At 90 km/h?

Words to use

  • inverse proportion
  • direct proportion
  • ratio
  • share
  • constant product

Watch for

  • Treating inverse as direct: fewer workers, fewer days. In inverse proportion the product stays the same: 6 × 10 = 4 × 15.
  • Sharing in ratio by dividing by the ratio numbers directly. Add the parts first: 2 + 3 = 5 parts.

What it sounds like at home

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

You4 workers instead of 6. More or fewer days?

Your childMore: 6 × 10 = 60, so 15.

A game for this week: Direct or inverse?

  1. Read situation cards.
  2. Players shout direct or inverse.
  3. Then solve.
  4. Points for both.

A 5-day plan, 30 minutes a day

  1. Day 1Direct vs inverse.
  2. Day 2Work problems.
  3. Day 3Speed and time.
  4. Day 4Sharing in ratio.
  5. Day 5Direct or inverse? game.

Everyday moments to practise

  • Sharing costs.
  • Travel times.
  • Work shifts.
  • Cooking for more people.

Quick check

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

6 workers 10 days; 4 workers?

15 days.

₹600 in 2 : 3?

₹240 and ₹360.

60 km/h 3 h; 90 km/h?

2 hours.

Ready for the next chapter when your child…

  • Distinguishes direct and inverse proportion.
  • Solves work and speed problems.
  • Divides in a ratio.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Prakash (Class 8). See the full Class 8 parent guide for every chapter.

Questions parents ask

What is inverse proportion?

As one increases, the other decreases so their product stays constant.

How do I share in a ratio?

Add the ratio parts, find one part, then multiply.

Is speed and time inverse?

Yes, for a fixed distance.