Maths Lab · Free lesson · 18 minutes
Percent of what? Find the base first
Connect fractions, decimals and percentages, find a percentage of a quantity and distinguish an increase from the final amount.
Primary 6 · percentages01 · Think first
Start with a question.
A notice says '15% extra'. Fifteen percent of a ₦200 price and fifteen percent of a ₦2,000 price cannot be the same cash amount. A percentage always refers to a base quantity.
What you already know
- Divide by 10 and 100
- Understand fractions of a whole
- Add and multiply decimals
02 · See it
A percentage is a scale factor
The same quantity has three consistent names. Each operation refers to the original 360-unit base.
- Rate
- 15% = 15/100 = 0.15
- 10% of 360
- 36
- 5% of 360
- 18
- 15% of 360
- 54
Use the justified worked steps below to explore this idea.
03 · Show steps · explain why
One justified step at a time.
- 1
0.75 = 75/100 = 3/4 = 75%
These are different representations of one number. Percent means 'per hundred', not an instruction to move digits without meaning.
04 · Mistake clinic
Find the first wrong idea.
15% of 360 = 15 × 360.
Compare the correction and its reason
15% of 360 = 0.15 × 360 = 54.
15% is less than one whole, so its amount must be less than 360. The missing division by 100 makes the wrong result far too large.
Check: Estimate first: 15% lies between 10% and 20%, so the amount lies between 36 and 72.
A mistake is evidence about the next idea to repair. It is not a label for the learner.
05 · Your turn
Try first. Then use a hint.
06 · Check & reflect → next step
Understanding includes explaining.
Name the base quantity in each problem. How did an estimate help you check the answer?
Distinguish a part-to-part ratio from a fraction of the whole, then revisit compound percentage changes later.
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JEM-P6-M03-007 · Phase 1 Primary6 Readiness and Core Mathematics · Lesson 7 · printed pp. 23–24
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