GANITA PRAKASH · GRADE 8 · PART II · CHAPTER 1

ESTIMATE — Mental strategies and reverse percentage

Think first. Use AI purposefully. Verify always.

DISCOVER

Begin with a prediction.

40% of a journey is 92 km. Is the whole journey more or less than 184 km?

Sketch or write an independent attempt before reading on. Test your idea using the model.

Known percentages can be combined when they refer to the same whole. Reverse percentage recovers the whole from a known part and its percentage.

Whole = part \div \frac{percentage}{100}

Reverse percentage is not the same as finding that percentage of the part. A zero percentage cannot determine the whole.

Predict first. Change the controls, then compare your reasoning.

Percentage: 25Whole quantity: 120

Percentage of the whole: 25

Bar scale: 0% to 200%. The midpoint marks 100%, which corresponds to 120 units.

Predict first. Change the controls, then compare your reasoning.

Known percentage: 40Known part: 92

40% corresponds to 92 units: 40

Build 15% as 10% + 5%, or 75% as three quarters. For a reverse problem, find 1% or divide the part by its decimal share.

40% of a journey is 92 km.

Total journey length and remaining distance

40% corresponds to 92 km.

The whole journey is 230 km; 138 km remain.

A — Attempt independently
Estimate and predict first.
I — Investigate the idea
Identify the whole and the percentage base.
M — Make connections
Connect fractions, decimals, bars and multipliers.
S — Scrutinise your reasoning
Check units, bases and the reasonableness of the result.

Think first. Use AI purposefully. Verify always.

Find 15% of 80 mentally in two ways.

Your reasoning

Name the whole, explain the method and give one check that would catch a wrong percentage base.

Explain your conclusion

Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 10