Explaining lesson goals (teacher directed) (5 minutes)
- Teacher recaps that students have been learning about direct proportion and that in the next few lessons they will be exploring the idea of inverse proportion
- Introduce the goal of this lesson to be identifying what inverse proportion means and how we represent it
Activity 1 (individual/students can help each other(pair work)): Introducing inverse proportion (30 minutes)
- Students work on the worksheet which aims to get student to compare direct and indirect proportional graphs. Students also analyse inversely proportional graphs to create their own definition (i.e. when one quantity increases at the same rate, the other quantity decreases). Using the example students identify what as speed increases, the time taken to travel a particular distance decreases (reasoning, fluency, problem solving, literacy) (AFL)
- After worksheet completion, teacher goes through the worksheet problems as a class
- Teacher introduces the definition of inverse/indirection proportion (see vocabulary list) (literacy)
Teacher questioning/prompts
- How did you assign the axis for this graph?
- How did you know that this was the correct way to assign them? Why not the other way around?
Activity 2 (teacher demonstration) (10 minutes)
- Teacher uses this Interactive demonstration to show students the nature of inverse proportion and reaffirm the definition of inverse proportion and the relationship they have identified in the activity. Relate the tool with the worksheet, drawing similarities such as As height decrease, base increase and vise versa. And the distance the cars need to travel are all kept the same, similarly to the area of the rectangle always being the same.
- Teacher will ask students questions to gauge their understanding of the concept (assessment strategy) (communication, reasoning) (AFL)
- Interactive tool to show students how inverse proportion graphs look like and how they are affected by manipulating variables. (Good for showing the different shapes of inversely proportional graphs, there is no need to go into detain able how variables affect the graph as it is not covered in this topic)
Teacher questioning/prompts
- What do you notice about the shape of the graph that the rectangles create?
- Is this an inversely proportional graph? How can you tell?
- Describe what is being represented by the graph in terms of the height and base of the rectangle, using vocabulary that we just learnt (e.g as base increases, height decreases)
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)
- Students answer/complete the following question
Instructions: Think of examples where rates/indirect proportion are used/appear in your everyday lives. Draw a indirect proportional graph to represent the rate that you have chosen and describe why it is appropriate.