Recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents

Students interpret percentages as parts per hundred, represent relative size with grids and number lines, and connect common percentages such as 10%, 25%, 50% and 75% to fractions and decimals.

A percentage compares a part with a whole scaled to 100 equal parts.

The whole must be identified. Thirty-five shaded cells out of 100 represent 35%, but the actual quantity depends on what one whole represents.

Use equivalent forms to compare relative sizes and solve simple contextual questions. Percentage does not state the actual amount until the whole is known.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Represent the concept accurately
• Explain the place-value or number relationship
• Select an efficient strategy
• Apply it to a new context
• Verify and justify the result

Content description: recognise that 100% represents the complete whole and use percentages to describe, represent and compare relative size; connect familiar percentages to their decimal and fraction equivalents.

• E1: recognising applications of percentages used in everyday contexts; for example, the bar model used for charging devices indicating the percentage of power remaining; advertising in retail contexts relating to discounts or sales
• E2: creating a model by subdividing a whole; for example, using 10 x 10 grids to represent various percentage amounts and recognising complementary percentages, such as 30% and 70% combine to make 100%
• E3: creating a model by subdividing a collection of materials, such as blocks or money, to connect decimals and percentage equivalents of tenths and commonly used fractions \frac12, \frac14 and \frac34; for example, one-tenth or 0.1 represents 10% and one half or 0.5 represents 50%; recognising that 60% is 10% more than 50%
• E4: using physical and virtual materials to represent the relationship between decimal notation and percentages; for example, 0.3 is 3 out of every 10, which is 30 out of every 100, which is 30%)

Core idea: A percentage compares a part with a whole scaled to 100 equal parts.

Remember

• Represent the concept accurately
• Explain the place-value or number relationship
• Select an efficient strategy
• Apply it to a new context
• Verify and justify the result

Important questions

• Represent 35%. Explain using the model or evidence above.
• Convert 50% to fraction and decimal. Explain using the model or evidence above.
• Compare 40% and 3/8. Explain using the model or evidence above.
• Explain 100%. Explain using the model or evidence above.
• Why does the whole matter? Explain using the model or evidence above.

• 100% means 100 objects — It means the complete whole, whatever its size.
• Percent and decimal copied without place-value change — 35% = 0.35, not 35.0.
• Percentages compared without the whole — Equal percentages of different wholes can be different amounts.
• 25% treated as 25/10 — Percent means denominator 100 before simplification.

Learn from the Topic Guide and fixed Teacher Slides, complete the Practice Sheet, use Practice for supported feedback, then take the Test when ready.

Students interpret percentages as parts per hundred, represent relative size with grids and number lines, and connect common percentages such as 10%, 25%, 50% and 75% to fractions and decimals.

A percentage compares a part with a whole scaled to 100 equal parts.

The whole must be identified. Thirty-five shaded cells out of 100 represent 35%, but the actual quantity depends on what one whole represents.

Use equivalent forms to compare relative sizes and solve simple contextual questions. Percentage does not state the actual amount until the whole is known.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Represent the concept accurately
• Explain the place-value or number relationship
• Select an efficient strategy
• Apply it to a new context
• Verify and justify the result

Australian Curriculum Version 9.0

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