Proportional thinking - Ratios

This resource has been developed in partnership with the NSW Mathematics Strategy Professional Learning team, Curriculum Early Years and Primary Learners, and Literacy and Numeracy.

Using the resource

This resource is the third section of a four-part resource supporting proportional thinking. Use this resource in conjunction with the other resources in this series in order to support a connected network of critical mathematical concepts, skills and understanding.

Supporting tasks

Full instructions on how to use each of these tasks- including materials, related tasks and learning intentions - are included in the resource, available for download on this page.

Task 1: Ratios in the class

Core learning: Initial understanding of ratios and the importance of thinking multiplicatively rather than additively.

Task 2: Incorrect ratios

Core learning: Identifying errors in ratios and ways to correct them.

Task 3: Recipe alterations

Core learning: Using ratios to increase or decrease quantities to maintain a given proportion.

  • Variation: Decrease an amount of an ingredient in a recipe and calculate the required amounts of the other ingredients.

Task 4: Comparing lengths

Core learning: Determining equivalence between ratios of length by expressing them in their simplest form.

  • Variation 1: Add in the heights of buildings, local landmarks or well-known features such as the Sydney Tower (height of 320m).

  • Variation 2: Compare the lengths/heights of the big things around Australia, for example, The Big Banana, The Big Pineapple, The Big Merino, or heights of local buildings and objects.

Task 5: Ratios with cordial

Core learning: Expressing ratios in their simplest form using a real-life context, including the use of questioning to develop students’ understanding.

  • Variation 1: Students use different sized jugs to calculate the required quantity of cordial concentrate and water when given the ratio.

  • Variation 2: Give a simplified ratio and make up a 250 mL cup of cordial.

  • Variation 3: Students compare different ratios of red to white paint to create their preferred colour pink. Similar questions to those listed about can still be asked.

Task 6: Map scale

Core learning: Calculating ratio and scale factors to interpret a scale on a map and determine real distances.

  • Variation 1: Use a map of the school or local area to create a scale and measure the distances.

  • Variation 2: Using house plans as a base, find the scale and calculate the length of walls, windows or rooms.

  • Variation 3: Students create a scale drawing of their bedroom or a room in their house. Objects and furniture are drawn to scale.

Download part 3 of the proportional thinking series


  • Numeracy

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  • Educational Standards
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