# Proportional thinking - Rates

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 final 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.

Core learning: Evaluating additive and multiplicative strategies to identify the most efficient method to solve problems involving rates.

• Variation: Repeat the activity using other examples of rates to justify multiplicative thinking as the most efficient strategy. Possible alternatives are typing speed per minute, heart rate, number of steps for every 100m.

### Task 2: Making rates simple

Core learning: Comparing 2 different units by expressing the relationship between them as a rate in its simplest form.

• Variation 1: Use different examples of rates such as wages earned per shift or time taken to fill a jug with water.

• Variation 2: Students find examples of rates at a grocery store. Possible findings: Cost of items per 100g, per 100mL, per L. Discuss if rates measured in per 100 units of quantity are in their simplest form. Ask them to explain why they are not expressed as per one gram or per one mL?

### Task 3: Which one is cheaper?

Core learning: Different quantities can be compared by determining a common unit of measure.

• Variation: Compare the cost of items that include 100 mL or 1 mL as a common measure to compare costs for all 3 sizes

### Task 4: Is it too crowded?

Core learning: Rates coordinate pairs of numbers and can be expressed in 2 ways to compare the relationships between the same 2 quantities.

• Variation 1: Model using students in a particular area in the classroom/space around school.

• Variation 2: Compare population density of different countries.

• Variation 3: Comparing by Finding Rates (NZ Maths)

### Task 5: How quickly can I type?

Core learning: Making rate comparisons by calculating the multiplicative relationship between the number pairs.

• Variation: Students use different scenarios to examine rate relationships, for example, conduct an experiment on the flow rate of water using 2 different taps to fill a glass or jug in 10 seconds, compare 2 babies with different starting weights and determine the rate of growth after 12 months or compare the improvement rates of 2 students who received different marks in a test, and in the follow up test they both received higher marks.

### Task 6: Comparing speed of moving objects

Core learning: Calculate and compare rates of speed.

• Variation: Use other types of travel like walking, running, or swimming to discuss and compare speed