Fractions, Decimals and Percentages of Quantities

Learning goal

Students connect equivalent fractions, decimals and percentages, find benchmark parts by division and multiplication and distinguish discount amount from sale price.

Success criteria

• I can represent or identify the concept.
• I can explain the underlying relationship.
• I can select an appropriate strategy or feature.
• I can apply it in a new context.
• I can justify and verify the response.

Teaching routine

1. Represent
2. Reason
3. Calculate
4. Interpret
5. Verify

Find 25%, 40% and 75% of $240

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

Build discounts and percentage increase in context

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

AC9M6N07: solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies and using digital tools where appropriate

• E1: explaining how \frac13 of a quantity can be achieved by dividing by 3, and how knowledge of \frac13 of a quantity can be used to find \frac23 or \frac43 of the same quantity using situations involving money, length, duration, mass or capacity
• E2: investigating percentage discounts of 15%, 30% and 45% in an online toy sale, using their equivalent decimal representations of 0.15, 0.3 and 0.45 to calculate the amount of discount on sale items, with and without digital tools
• E3: linking percentages to their decimal equivalent of tenths and hundredths and using these to determine percentage discounts; for example, finding 30% discount by using its equivalence to 0.3, dividing by 10 and multiplying the result by 3 to give 30%
• E4: explaining the equivalence between percentages and fractions; for example, 33\frac13% and \frac13; keeping to percentages that are equivalent to fractions with small denominators such as 66\frac23% and 12.5%
• E5: representing a situation with a mathematical expression; for example, numbers and symbols such as \frac14\times24, that involve finding a familiar fraction or percentage of a quantity; using mental strategies or a calculator and explaining the result in terms of the situation in question

Use the central and application models above to connect each elaboration to the same underlying concept.

Check understanding

• Find 25% of 240.
• Find 3/5 of 90.
• Calculate a 20% discount.
• Distinguish discount/sale price.
• Choose a benchmark strategy.

Evidence of mastery

• Represent or identify the concept
• Explain the underlying relationship
• Select an appropriate strategy or feature
• Apply it in a new context
• Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Australian Curriculum v9.0

AC9M6N07: solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies and using digital tools where appropriate

The Australian Curriculum code and wording are exact. International teachers can use the underlying mathematical concept while matching the lesson to their local grade or year outcomes.

• Australian Curriculum Version 9.0
• NSW Curriculum
• Victorian Curriculum F–10