Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M7N09
Numeracy Progression: Additive strategies: P10, Interpreting fractions: P8, Multiplicative strategies: P9, Proportional thinking: P2, Understanding money: P8
At this level, students are required to have knowledge of the other topics in the Number strand, so that applying knowledge and skills can be used in the mathematicalmodelling process. This can be done in groups or as a whole class, as well as individually. Collaborative learning works well for practical problems.
Students are required to formulate problems, choose representations and efficient calculation strategies, using digital tools as appropriate.
Once identified, students are required to interpret and communicate solutions in terms of the situation, justifying choices made about the representation.
One practical example of the use of ratios is ‘best buy’ deals, using the unitary method to compare offers and evaluate which is better value. Students compare the cost of items to make financial decisions, both with and without technology. They make estimations to judge the reasonableness of results.
There are many realworld scenarios to pose to students that require students to draw on skills and knowledge of positive and negative quantities using all operations, proportion and reasoning to both financial and land area/perimeters. This is also an opportunity to create problems using crosscurriculum connections in Science, Design and Humanities subject areas.
This topic has many connections with other areas in the mathematics curriculum, for example, fractions, percentages, graphs and algebra.
Teaching and learning summary:
 Revise all other strands of Number: rational numbers, percentages, ratios.
 Ensure students can identify representations and use the correct calculation strategy as appropriate.
 Give opportunities for students to communicate their reasoning and justify their choices.
 Practical example: show how the unitary method can determine the ‘best buy’.
 Use other realworld problems and guide students with recognition, representation, expression, computation, reasoning, communication and justification.
Students:
 formulate problems, choose representations and use efficient calculation strategies
 use digital tools appropriately to help with their investigation
 use realworld scenarios, such as 'bestbuy deals' to make connections between what they are learning and their everyday lives
 bring together all knowledge and skills from the Number strand
 listen to feedback and work collaboratively to work efficiently and to refine their model.
Some students may:
 find it overwhelming to solve or investigate problems that are openended or could be tackled using different approaches.
 be tentative to brainstorm, express their creative thoughts and communicate their ideas for solving problems.
 find it difficult to work collaboratively.
 not realise that it is the attempt of a complex problem rather than the result that counts at this stage.
 attempt to use additive strategies for problems that require multiplicative thinking.
 assume that everything is out of 100 for per cent rather than per 100.
Percentages are relative – teach students that they should not assume the larger percentage will result in the larger number; for example, 50% of 60 is less than 25% of 130. It is dependent on both the value of percentage and the whole (100%).
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
 I am going to learn about 'bestbuy tickets' from my local supermarket.
 I am going to learn to make evidencebased decisions when deciding what products to buy.
Why do I need to know this?
Visiting a supermarket can be overwhelming. There are thousands of foods and products on the shelves and it can be difficult to know what to get. All sorts of questions arise when you look closely at the way a product or food is advertised. For example, you will be told the price, how much you will save if it is on sale and the unit price. But you can be tricked! You will now learn how to make sound decisions the next time you look at a ticket price at your local supermarket ... or any other shop for that matter!
What to do
Number  Product  Unit weight  Cost for product  Cost for 10 products  Best value 
1.  Orange cordial  500 mL  $2.50  $25.00  
2.  Orange cordial  1 L  $3.00 on sale  $30  This is the better value. 
 Choose 10 foods or products from your local supermarket. Perhaps pick foods or products you like.
 Then choose a competing brand and pair it with each of your 10 products. You should have 20 products altogether.
 You can find the products on the supermarket's website. Alternatively, you could go to the supermarket and check the ticket prices yourself beneath each product.
 In a table, like the one above, create 21 rows and six columns.
 The top row is for your headings and the remaining rows are for each of the products you have chosen.
 Record the prices and fill out your table.
 The final column is called 'best value'. This is where you decide which product of your pairs will give you the best value for the money you will spend. Remember, just because a product is on sale, doesn't mean it is the best value.
 In my example, I also have a column called 'Cost for 10 products'. This was one way I could figure out how to find the best value of my pairs. However, there are other ways you could make comparisons depending on what information is on the ticket price.
 Find an alternative way to make fair comparisons.
Success criteria
 I have learnt about 'bestbuy tickets' from my local supermarket.
 I understand that it is important to make evidencebased decisions when deciding what products to buy.
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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.

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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Concrete, Representational, Abstract (CRA model)
The CRA model is a threephased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.
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Worked examples
A worked example is not just a preworked question that is given to the students. There are several types of worked examples and ways of using them.
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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.

Estimating and rounding decimals
In this lesson, students draw on prior knowledge of rounding whole numbers.
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Graphs: formulas and variables
In this lesson, students use algebra and linear equations to model two realworld scenarios.
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Patterns, rules and graphs
In this lesson, students use games to learn about space and location on a Cartesian plane.
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Practical numbers: Part 2
In this lesson we use the context of an ancient bazaar to investigate measurement systems.
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Prime factorisation
This mathematical modelling investigation explores prime factorisation and how we can use number grids, prime factorisation, factors and multiples, HCM and LCM to solve problems.
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Real numbers: sum of squares
This mathematical investigation explores history, encourages the collection of evidence, working systematically to find patterns to solve problems using whole numbers, square roots and perfect squares.
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Mathematical modelling: a guidebook for teachers
Use this comprehensive guide to learn how to implement mathematical modelling to solve authentic problems into your teaching. Activities are included for all developmental levels.
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Friday 13th
This question encourages mathematical thinking by using realworld tools and working collaboratively to solve an interesting question around number.
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Assessment
By the end of Year 7, students use mathematical modelling to solve practical problems involving rational numbers and percentages and ratios. Students can formulate problems, choosing representations and efficient calculation strategies to interpret their solutions to financial and other contexts. Students communicate and justify their choices made about the representation.

Using proportional reasoning
This lesson will help you to assess students’ ability to use proportional reasoning. The activities allow them to demonstrate their ability to describe a ratio, express a ratio in different ways and answer contextual problems.
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Bestbuy tickets
This resource uses a contextualised problem to assess students’ ability to calculate a best buy.
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Alison’s quilt
This investigation asks students to use manipulatives to solve a problem involving prime factorisation. It is suitable as a collaborative task or assessment.
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