Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M10M05
Numeracy Progression: Proportional thinking: P7
At this level, students use a mathematical modelling approach in a range of contexts for problemsolving and modelling practical situations. These include drawing plans and elevations to scale, using ratio and proportion when making a prototype, and using estimation. Some of their enquiry may be investigated with handson materials and digital software programs.
Students are expected to be able to formulate questions to problems, identify and make comparisons between variables and elements to consider for a given context. Students brainstorm and consider a variety of approaches to find solutions efficiently and effectively. They must also be able to interpret their results and consider whether their model was successful. Refining and listening to feedback along the way is essential.
Importantly, students report and communicate their method, findings and conclusions, and identify limitations and those elements of their modelling that could be improved or refined.
Teaching and learning summary:
 Demonstrate how measurement with ratios, proportion and scaling is used in a range of realworld contexts taking a mathematicalmodelling approach.
 Make use of measurement skills when problemsolving.
 Encourage students to brainstorm, use creativity and listen to feedback when creating and using mathematical modelling to solve problems.
 Give students opportunities to communicate their findings to the class or small groups, or as an assessment task.
Students:
 use their knowledge of measurement in a range of realworld contexts
 can apply their knowledge of ratio, proportion and scaling when problemsolving
 use handson materials or digital technology when mathematically modelling their problem
 listen to feedback, make refinements and reevaluate findings in light of their model
 communicate, outlining the problem, variables and assumptions, and method and findings
 identify and suggest what revisions could be made in future investigations.
Some students may:
 undervalue feedback as part of the mathematicalmodelling process
 undervalue brainstorming ideas, questioning and using creative thinking to solve problems
 misunderstand that reevaluation and refinement is part of the process.
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 discover the realworld opportunities that employ mathematics in their everyday careers.
 We show that mathematics is not so boring after all.
Why are we learning about this?
When we think about careers in mathematics or that use mathematics, we usually think about mathematicians in universities, engineers, scientists or statisticians. However, mathematics is all around us and you would be surprised to learn about jobs that use mathematics to model a successful outcome.
What to do
Career interview: furniture design
Read this about Australian furniture designers. Most weren’t always designers.
Ask yourself these questions while you read.
 How do you become a furniture designer?
 Why would you use mathematics in furniture design?
 Do you really need a PhD?
 What other crosscurriculum subject areas use mathematics?
 Which part of mathematics that you've learnt could help you design a chair?
 Can you use software programs to help scale something small to something much bigger?
 What cool events and conferences can you attend if you’re a furniture designer?
Success criteria
 I can apply areas of mathematics, like geometry, to career paths I hadn’t thought about before, like furniture design.
 I understand ratios, proportion and scaling is very important in building things such as bridges, buildings and furniture.
 I can can keep an open mind when thinking about mathematics all around us.
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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.

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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Collaborative learning
For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.
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Mathematics investigation
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.
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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.

A piece of cake
In this lesson, students build on their skills in finding volumes and surface areas of prisms and cylinders to design a multilevel celebration cake for a party.
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Mathematical modelling: a guidebook
An excellent guide for teachers to learn about and employ mathematicalmodelling projects in the classroom. The guide discusses what mathematical modelling is, discusses a framework that students can follow, describes types of models and provides ageappropriate example problems.
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Teacher package: mathematical modelling
This site gives descriptions and approaches, and provides a number of links to realworld example problems to take inspiration from.
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Understanding compound interest
Students learn how compound interest works and why saving now can help you later.
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Different ways to pay
Students learn about the pros and cons of various payment options, what happens to their money, different consumer products and where to go for more information.
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Assessment
By the end of Year 10, students can use mathematical modelling to solve practical problems involving proportion and scaling, evaluating and modifying models, and reporting assumptions, methods and findings.

Constructions
A modelling activity that uses geometry and scaling, and applies this knowledge to a realworld Defence problem.
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Mathematical modelling: a guidebook
An excellent guide for teachers to learn and employ mathematical modelling projects into the classroom. The guide discusses what mathematical modelling is, discusses a framework that students can follow, describes types of models and provides ageappropriate example problems.
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Seaside
This video employs knowledge of geometry, similar triangles, scale drawing and loci. An effective short activity to use on the board in the classroom.
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