Year 6 Mathematics · AC9M6N07

Fractions, Decimals and Percentages of Quantities

Find familiar parts, discounts and remaining amounts efficiently

Ready to project and teach

Learning goalsSay it simply

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
Curriculum focus: 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
Key conceptTeach from the board

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.

partstrategyamount25% = 1/4240 ÷ 4$6040% = 4/10240 ÷ 10 × 4$9675% = 3/4240 ÷ 4 × 3$180

Use a familiar equivalent form that makes the quantity easy to partition. A 25% discount is $60; the sale price is $180.

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.

20% discount on $85discount $17; pay $68
10% of 36036
0.5 of 7437
3/5 of 9054
digital toolcompare many prices after formula is set

Always identify whether the question asks for the part, the remaining amount or the new total.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6N07 - Fractions, Decimals and Percentages of Quantities
Example 1

part strategy amount 25% = 1/4 240 ÷ 4 $60 40% = 4/10 240 ÷ 10 × 4 $96 75% = 3/4 240 ÷ 4 × 3 $180

Example 2

20% discount on $85 discount $17; pay $68

Example 3

: 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

Example 4

: 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

Curriculum examplesCopied content

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.

Questions and answersWith answers

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.

Practice and reviewReady for practice
Discount amount reported as final priceSubtract the discount from the original.
Percent converted to whole number multiplier20% = 0.20, not 20.
Quantity divided by percentage number onlyUse a fraction, decimal or benchmark strategy.
Whole not identifiedState the original total before finding a part.
Curriculum alignmentStart here

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
Curriculum focus: 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
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