GANITA PRAKASH · GRADE 8 · PART II · CHAPTER 1
UNMASK — What percentage means: per hundred
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with a prediction.
Three of four equal parts are painted. How many of 100 equal parts would represent the same share?
Sketch or write an independent attempt before reading on. Test your idea using the model.
Understand
A percentage expresses a share relative to a whole of 100 equal parts. Always identify what counts as the whole.
Key Ideas
Equal parts matter: counting unequal pieces does not measure their share of the whole.
Visualise
A hundred equal parts
Predict first. Change the controls, then compare your reasoning.
Fractions on a bar
Predict first. Change the controls, then compare your reasoning.
Decimal ≈ 0.75; percentage ≈ 75%. Display rounded to at most four decimal places. Each outlined piece is of a whole; 4 pieces make one whole.
Method
Name the whole. Write part ÷ whole. Scale the fraction to a denominator of 100 when possible, or multiply it by 100 to find the percentage.
Worked Example
Given
Three quarters of a paint mixture is red.
To Find
Percentage of the mixture that is red
Reasoning
Equivalent fractions describe the same share.
Solution
- = .
- 75 parts per hundred means 75%.
Result
75% of the mixture is red.
AIMS Method
- 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.
Focused Practice
15 of 25 counters are white. Predict whether the white share is above half, then find its percentage.
Check & Feedback
Name the whole, explain the method and give one check that would catch a wrong percentage base.
Textbook connection: Ganita Prakash · Grade 8 · Part II · Fractions in Disguise · printed page 1