Primary 5 maths · Ratio, rate & percentage · About 12 minutes

Find a percentage of a quantity

Predict, build a model, explain what changed, then use the relationship in a new situation.

What you will learn

Models used: number sentences, stories, tables.

A box holds 80 pencils. Thirty per cent are blue. Does 30% mean thirty pencils?

The full bar represents 80, which is 100%. The shaded share is 0%.
The entire bar is all 80 pencils. Its ten equal sections each represent ten per cent of that whole.
100% = 80 pencils
Each section: 10% = 8
0% of 80 = 0
The full bar represents 80, which is 100%. The shaded share is 10%.
Divide 80 into ten equal shares. One section, or ten per cent, contains eight pencils.
10% = 80 ÷ 10 = 8 pencils
Each section: 10% = 8
10% of 80 = 8
The full bar represents 80, which is 100%. The shaded share is 30%.
Three sections represent thirty per cent. Three groups of eight contain twenty-four pencils.
30% = 3 × 8 = 24 pencils
Each section: 10% = 8
30% of 80 = 24
The full bar represents 80, which is 100%. The shaded share is 30%.
The coloured part is less than half the bar. Twenty-four is less than half of eighty, so its size makes sense.
24 ÷ 80 = 0.30 = 30%
Each section: 10% = 8
30% of 80 = 24

A different box has 60 pencils. Thirty per cent are blue. How many blue pencils are there?

Each section: 10% = 6

30% of 60 = 18

The full bar represents 60, which is 100%. The shaded share is 30%.
The share is still 30%, but the whole is now 60 pencils. Each equal section must be smaller.
Each section: 10% = 6
30% of 60 = 18
The full bar represents 60, which is 100%. The shaded share is 10%.
Start with one of the ten equal sections.
Each section: 10%
How many pencils is 10% of 60?
6
The full bar represents 60, which is 100%. The shaded share is 30%.
Thirty per cent needs three sections, each containing six pencils.
Each section: 10%
A different box has 60 pencils. Thirty per cent are blue. How many blue pencils are there?
18
The full bar represents 60, which is 100%. The shaded share is 30%.
Eighteen pencils is 30% of sixty. The percentage stayed the same; the smaller whole made a smaller share.
60 ÷ 10 × 3 = 18
Each section: 10% = 6
30% of 60 = 18

Treating the percentage as the answer. Find one part of a hundred first. 30% of 90 is 27, because one per cent is 0.9.

Find a percentage by identifying the whole and building the requested share from equal parts.
connect a percentage, its reference whole and the requested quantity
check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.

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