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 problem-solving 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 hands-on 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 real-world contexts taking a mathematical-modelling approach.
- Make use of measurement skills when problem-solving.
- 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.
- use their knowledge of measurement in a range of real-world contexts
- can apply their knowledge of ratio, proportion and scaling when problem-solving
- use hands-on materials or digital technology when mathematically modelling their problem
- listen to feedback, make refinements and re-evaluate 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 mathematical-modelling process
- undervalue brainstorming ideas, questioning and using creative thinking to solve problems
- misunderstand that re-evaluation 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.
- We discover the real-world 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 cross-curriculum 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?
- 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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A collection of evidence-based 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.
A worked example is not just a pre-worked question that is given to the students. There are several types of worked examples and ways of using them.Go to resource
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.Go to resource
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.Go to resource
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.
Mathematical modelling: a guidebook
An excellent guide for teachers to learn about and employ mathematical-modelling projects in the classroom. The guide discusses what mathematical modelling is, discusses a framework that students can follow, describes types of models and provides age-appropriate example problems.Resource details
Teacher package: mathematical modelling
This site gives descriptions and approaches, and provides a number of links to real-world example problems to take inspiration from.Resource details
Understanding compound interest
Students learn how compound interest works and why saving now can help you later.Resource details
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.Resource details
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.
A modelling activity that uses geometry and scaling, and applies this knowledge to a real-world Defence problem.Resource details
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 age-appropriate example problems.Resource details
This video employs knowledge of geometry, similar triangles, scale drawing and loci. An effective short activity to use on the board in the classroom.Resource details