Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M6N07, AC9M6N08
Numeracy Progression: Interpreting fractions: P7, Multiplicative strategies: P9, Understanding money: P8, Proportional thinking: P2
At this level, students use their knowledge of percentage and decimal equivalents to calculate percentage discounts. Example problem: a 30% discount on a $75 item can be found by converting 30% to its equivalent decimal fraction (0.3) and multiplying it by $75 to see that a 30% discount will be $22.50.
Encourage the development of a range of flexible strategies when solving problems related to finding the fraction, decimal fraction or percentage of quantity. To support this aim, ask students to find two or more ways to solve the problem. For example, a second way to solve the 30% discount on a $75 item would be to find 10% ($7.50) and multiply it by 3. This form of thinking, where students find the unit, can be used in the context of fractions – a students can find 56 of 30 kg by finding 16 (5 kg) and multiplying it by 5 (25 kg).
Use questioning to develop students’ ability to approximate numerical solutions. Questions like, ‘What is an estimate that is too high? What is an estimate that is too low?’ Ask the students to make sense of the problem, which ensures that they are doing more than applying computation methods without understanding. Look for opportunities to highlight and model efficient approximation strategies, for example,
52% is about 12 , 0.263 is about 14 .
Use dynamic software that uses region models (such as the GeoGebra percent visualisation tool) to help students link equivalent representations of fractions, decimal fractions and percentages.
Continue to model correct place value language when describing decimal fractions. Describe 12.8 as ‘twelve and eight tenths’ as opposed to ‘twelve point eight’ to help students understand its quantity and make connections to its fractional equivalent.
Teaching and learning summary:
 Make connections between fractions, decimal fractions and percentages.
 Model ways to use flexible strategies to calculate percentage discounts.
 Help students develop mental approximation strategies to encourage sensemaking of quantities and operations involving fractions, decimal fractions and percentages.
Students:
 demonstrate their understanding of equivalent fractions, decimal fractions and percentages
 use flexible strategies to calculate percentage discounts
 approximate and justify reasonable answers.
Some students may:
 use wholenumber thinking and believe that the fraction 15 is smaller than 110 because it has a smaller denominator.
 see 34 and 56 as equivalent as they are both one number away from being a whole number. Model residual thinking where students compare the size of the fraction that is needed to get to 1 ( 14 and 16 in the case above) to help them determine that there is a size difference between the two fractions.
 use the operation rules from whole numbers to compute with fractions, that is, mistakenly adding the denominators when performing addition, 34 + 34 = 68.
 confuse wholenumber language and decimal fraction language, for example, tens (10), and tenths (0.1).
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
Learning intention
 We are learning to recognise equivalent fractions, decimal fractions and percentages.
Why are we learning about this?
 We can further our understanding of some of the different ways that rational numbers can be represented.
What to do
1. Write 45 as a decimal and percentage.
2. Use this hundredths grid to represent 45.
3. Use this bead string grid to represent 45.
4. Explain the connection between fractions, decimals and percentage using an example.
Success criteria
I can:
 interpret rational numbers shown as fractions, decimal fractions and percentages, and connect equivalent quantities.
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Teaching strategies
A collection of evidencebased teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.

Explicit teaching
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.
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Questioning
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.
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Classroom talks
Classroom talks enable students to develop language, build mathematical thinking skills and create mathematical meaning through collaborative conversations.
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Teaching resources
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.

Percent visualisation
Use this resource to quickly and easily demonstrate the connection between fractions and percentage by showing different examples of parts of a whole.
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Converting between fractions and decimals
A fluencybuilding, openended task where students must use the digits 0 to 9, at most one time each, to fill in the boxes so that the fraction and the decimal are equivalent.
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Open middle: percentages
A fluencybuilding openended task where students must use the digits 0 to 9 at most one time each, to fill in the boxes to make a true equation involving percentages.
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reSolve: Reconciliation data
This task interprets data of significance for Australian society and provides an opportunity to develop and use mathematical skills in a humanities and civics context.
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Operating with decimals
This learning sequence aims to develop student proficiency when adding, subtracting, multiplying and dividing with decimals.
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