# 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.

### Task 1: Ratios in the class

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

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

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.

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 studentsâ€™ 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.

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.