The lesson will begin with a discussion of what we know so far about proportional relationships. I will ask the essential question and ask students to discuss it. In order to provide a reference for their thinking I will present a simple problem or ratio. This is to bring out the idea that equivalent ratios can be seen as multiples of each others.
I will then show the example problem. The idea of multiples is here. I will draw them in from column to column as we discuss. This will help us identify the column of values that is not proportional to the others.
For part ii, I will show at least two ways to solve this problem. One will be using a bar model and the other will be using multiplication.
The first guided practice problem shows a proportional relationship. Part ii of the problem asks students to find out how much the company will contribute based on an employee contribution of $20. Students may struggle a bit in finding the common scale factor. As a hint I may say "How many times greater is 16 than 8? What operation tells me this?". This can then be applied to this problem. I will allow my students to use calculators so that they can spend time focus on proportional relationships and not arithmetic.
The second problem asks students to create two tables based on different pay rates. I will be on the look out for people who think Abe's earnings should be $23 for 1 hour, $46 for 2 hours, $69 for 3 hours, etc.. They will need to be reminded to read the description very carefully.
Now students work in pairs or independently while solving 3 more problems. Students should be encouraged to use a model to solve. For problem 1, this can be as simple as drawing the multiplier used between columns. A double number line may be especially helpful for problems 2 and 3. I will just need to be making sure students are using these models correctly.
Part i of problem 3 looks tricky but hopefully students will quickly see that Quantity C is the culprit.
Each problem will be worth 2 points: 1 for a correct answer and 1 for a valid explanation. A score of 3 out of 4 will be considered a success. Before beginning we will summarize/review what we know about equivalent ratios. Up to this point, we have only discussed the relationship of a common multiple between the ratios. I will accept a student answer that identifies the proportional relationship by using any other valid method.