Introducing the constant of proportionality (teacher conducted) (15 minutes)
- Recap on the idea that was taught in the other lesson, looking at the worksheet question. The question said that Jim walks 4km/hr and the gradient of the graph the students calculated was 4. Last lesson linear direct proportion was also defined and students could see that y is directly proportional to x.
- Students also formulated an equation representing the line graph. y = mx where m=4
- From this the teacher introduces the new term, that m, which is the gradient is called the constant of proportionality. (literacy)
- In groups of 4, students reflect on their prior knowledge from linear relationships to come up with an equation that represents a linear proportional graph (aim is to get students to identify that the equation y = kx represents a linearly proportional graph)
- Teacher asks students what 'k' represents and then introduces the term 'constant of proportionality' instead of gradient
Teacher questioning/prompts
- From linear relationships, what is the basic equation of a line graph
- What would happen to the graph if the constant of proportionality was 10? Can you draw what the graph would look like?
Activity 2 (individual): Introducing linear direct proportion (30 minutes)
- Students work on the worksheet on creating equations, finding the constant of proportionality and finding variables (fluency)
- Students will have the prior knowledge to do this from linear relationships. The teacher can model some answers for students.
- After students complete the worksheet, as a class go over the questions in the worksheet and ask students to do questions on the board or explain their answers (AFL)
Lesson conclusion: Exit slip (5 minutes)
- Individually, students receive an exit slip which they complete and hand to the teacher before leaving the class (AFL)
- Students answer/complete the following question
Instructions: Think of examples where rates/direct proportion are used/appear in your everyday lives. Draw a linear direct proportional graph to represent the rate that you have chosen and describe why it is appropriate.