Relate percentages to parts out of 100

What you will learn

• Relate percentages to parts out of 100

Models used: number sentences, stories, diagrams.

Before you start

• Multiply mixed numbers by whole numbers
• Convert measurements using decimals

Percent is a share of one hundred

This grid is one whole. It has 100 equal squares.

1. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   This grid is one whole. It has 100 equal squares.

   The same percentage can describe different quantities when the whole changes. In a change problem, identify the original whole.

   0/100 = 0 = 0%

2. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Shade 25 squares. We have shaded one quarter of the whole.

   25 out of 100 = 25%

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   25/100 = 0.25 = 25%

3. The full bar represents $80, which is 100%. The shaded share is 25%.

   Now the whole is $80. One quarter of $80 is $20.

   25% of $80 = $20

   Each section: 5% = $4

   0%100% = $80

   25% of $80 = $20

4. The complete bar is the whole. Each labelled section is one part of it.

   The fraction, decimal and percentage describe the same share.

   1/4 = 0.25 = 25%

   80

   20one quarter60three quarters

Worked example: A new example, together

25 of 100 equal squares are shaded. What percentage is shaded?

1. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Mark 100%, the percentage share and whether the question asks for that share or the final amount.

   Percentages, fractions and decimals can name the same part of a whole.

2. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Percent means out of 100.

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   25 of 100 equal squares are shaded. What percentage is shaded?

   25 %

3. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Percent means out of 100.

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   25/100 = 0.25 = 25%

4. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   25% = 25/100.

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   25/100 = 0.25 = 25%

5. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   This is 1/4 as a fraction, or 0.25 as a decimal.

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   25/100 = 0.25 = 25%

6. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Check the result against the question we started with.

   0.25 × 100 = 25%.

   We found 25 %. Percentages, fractions and decimals can name the same part of a whole.

   25/100 = 0.25 = 25%

Common mistakes to discuss

• Reading a percentage as a count. A percentage is a share of a whole, not a number of objects. 30% of 80 pencils is 24 pencils, not 30.

Check your understanding

• Relate percentages to parts out of 100
• 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.