Expected level of development
Australian Curriculum Mathematics V9: AC9M7N08
Numeracy Progression: Multiplicative strategies: P9, Interpreting fractions: P8, Proportional thinking: P3
At this level, ratios are introduced as a method of comparing quantities. Students learn how to recognise and represent these comparisons to solve problems. The concept of dividing a quantity by a given ratio is also introduced.
Showing students multiple examples of practical situations where students may meet ratios will support them in developing their understanding. Use visual or digital aids to show the quantitative relationship between two or more groups, for example, following a cake recipe.
There are many connections between ratios and fractions, such as simplifying and equivalence, but students should be aware that ratios can have more than two parts. Ensure students are competent with using fractions and use part-part and part-whole models to visualise ratios, for example, a cherry diagram or bar model.
Make connections to real-world examples to bolster understanding referring to sharing and dividing quantities (for instance, money or lollies) between two or more people. Use questioning to uncover recognition of part in a worded problem and relate it with diagrams and represent ratio notation. Solve problems further with the addition or subtraction of fractions.
This topic has many connections with other areas in the mathematics curriculum, for example, fractions, percentages, graphs and algebra.
Teaching and learning summary:
- Introduce the concept of ratio as a comparison of quantities. Use part-part and part-whole explanations as a visual aid.
- Discuss how a ratio is displayed – whole numbers, same units.
- Show how to ‘share’ and divide a given quantity by a ratio.
- Use diagrams and virtual material to represent ratios.
- Enable recognition, representation of parts and wholes to solve numerical and real-life problems.
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Teaching strategies
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.
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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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Concrete, Representational, Abstract (CRA model)
The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.
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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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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.
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Proportional reasoning: Video and teaching guide
Use this video as a springboard to explore scaling or proportional thinking, and to apply that thinking to a food-related context, drawing on reasoning and mathematical modelling.
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Practical numbers: Part 1
In this lesson, students explore standardised measuring systems.
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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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Patterns, rules and graphs
In this lesson, students use games to learn about space and location on a Cartesian plane.
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Recognise and solve problems involving simple ratios
This is a teacher-facing resource that provides guidance, worked examples and activities about comparing quantities using ratios as well as making meaning between different formats of the same ratio.
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Proportional relationships and percentages
This series of lesson plans, materials and assessments gives detailed step-by-step advice on proportion and scaling. The various resources for this topic allows for differentiation in the classroom.
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Ratio or proportion?
This article is perfect for teachers, giving lengthy guidance on teaching the concepts of ratio and proportion and the difference between them.
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First steps into proportions: comparing ratios
Students use this practical interactive to visually connect fractions, ratios and proportion.
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Assessment
By the end of Year 7, students can recognise, represent and solve problems involving ratios. Students understand that ratios express the quantitative relationship between 2 or more groups.
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Using proportional reasoning
This lesson assesses students’ ability to use proportional reasoning. Students demonstrate their ability to describe a ratio, to express a ratio in different ways, and to answer contextual problems.
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Mixing lemonade
In this interactive activity, students use the concepts of ratio and proportion to mix lemonade to a given strength. Teacher notes and extension suggestions are also included.
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Defining equivalent ratios
This interactive activity assesses students' ability to understand visual representations and numerical representations of ratio, proportions and fractions.
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