GANITA PRAKASH · GRADE 8 · PART II · CHAPTER 1

COMPARE — Compare proportions using percentages

Think first. Use AI purposefully. Verify always.

DISCOVER

Begin with a prediction.

Which is the higher test performance: 42 out of 50 or 70 out of 80? Explain why raw marks are insufficient.

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

Normalising to a common whole of 100 compares proportions with different denominators. It does not make the actual totals equal.

Percentage = \frac{part}{whole} \times 100

Percentage-only graphs cannot reveal absolute population counts. Different groups have different bases.

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

First score: 42First maximum: 50

42 out of 50 (%): 84

70 out of 80 (%): 87.5

Identify each denominator separately. Convert each share to a percentage. State whether the question asks about proportion or absolute quantity.

Test scores are $\frac{42}{50}$ and $\frac{70}{80}$ .

Which score is the higher percentage

Compare proportions on a common scale.

70 out of 80 is the higher percentage.

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.

A 150 g product has 9 g chemicals; a 400 g product has 24 g. Which has the smaller chemical proportion?

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 14