Recap/Everyday examples of direct proportion (individual/class) (20 minutes)
- Review of the homework task from last lesson where students thought about where rates/direct proportion are used in their everyday lives. Get students to share the ideas that they came up with
- Using computers, students conduct online research on common everyday examples of rates/direct proportion, or where rates/direct proportion appear in their everyday lives. Teacher may provide students with some resources such as: 1. , 2. , 3.
- Using mini whiteboards, Google classroom or other ways students can share their ideas. Students to write down the everyday examples of direct proportion that they have researched online ( e.g. working salary)
- Teacher chooses some ideas and asks the student to explain it, getting students to use vocabulary such as, as the number of hours working increases, earnings also increase (see additional resources for literacy activity) (literacy) (AFL)
Teacher questioning/prompts
- Is the graph you have drawn appropriate for representing the example of direct proportion?
- How did you determine the shape of your graph?
Application of direct proportion/rates in solving an issue (group) (25 minutes)
- This problem provides a real-life context for working with proportionality, speed, rates, and units of measurement. The final answer may be surprising and leads to interesting questions about the validity of the model suggested (problem-solving)
- Split the class into groups of 4, and give each group a copy of this worksheet. Students will work on the worksheet using whiteboards (AFL)
- "Your task is to work out which athlete burned the most calories in a triathlon. Before you do any calculations, discuss which athlete you think it might be, together with your reasons why, and make a note of it."
- As they are working, circulate and listen to the conversations that students are having, to identify anyone with particular insights that it would be useful to share.
- students work on the worksheet
- Towards the end of the lesson, bring the class together and invite different groups to explain how they worked out the number of calories burned for each stage of the triathlon. Allow some time for discussion of the perhaps surprising answer to the question "Who burned the most calories?". (reasoning, communication) (AFL)
Teacher questioning/prompts
- What do you need to know to work out each athlete's speed?
- How can you work out the speed in kilometres per hour?
- If his (swimming) speed is slower than (4.5)km/h, would you expect him to burn more or less than (600) kcal per hour?
- Once you know the rate at which he burns calories, how will you work out how many calories he burns in (19 minutes and 12 seconds)?
Lesson conclusion: Exit slip (5 minutes)
- Students receive an exit slip which they complete and hand in to the teacher before leaving the class (AFL)
- Instructions: In preparation for the research task next lesson. Think about some problems that can be solved using direct proportion/rates OR think about a concept that utilises direct proportion/rates (e.g. space travel)