Here is the final method we will use to check for equivalent ratios - finding a unit rate. I will present the essential question. Then, we will have a brief turn-and-talk about finding a unit rate as a review. We have been using unit rates in several lessons so this should be a quick review.
I will then present an example problem. We are expected to find a unit rate in terms of inches per hour. It is worth discussing that most unit rates involving time have time as the denominator. It is possible to think about the unit rate in reverse - hours per inch. We can discuss the distinction between these two points of view.
The first problem is similar to the example. I tried to set up the rates so that the other methods of checking for a proportional relationship are less convenient. The point of these different methods is to give students a variety of methods and then they can determine the best one to use based on the problem.
The second problem has students complete a table based on a linear relationship that is not proportional.
The first problem first requires students to test for a proportional relationship - there is none. Then students use this information to re-price one of the values.
The second problem also requires students to test for a proportional relationship - one exists here. Students then use the unit rate to solve another problem.
The final problem has a slightly more difficult layer of complexity. Students are not explicitly told to find a unit rate, but they need to figure out which values are equivalent to a given amount.
Then students have a problem where they are to decide where to buy 100 pounds of the fruit. There is not necessarily a correct answer here if the students are able to present an argument for their viewpoint (MP3). For example, some may choose the store with the cheapest unit price. Others may say they prefer shopping at another store or they know the quality is better so a higher price is worth it.
We will briefly summarize that rates that have the same unit rate are equivalent, thus they form a proportional relationship.
The exit ticket item has two parts. It is very similar to the problem already solved. I think a student should be able to answer both questions to feel that they mastered the lesson. However, they are probably on their way to success if they solve problem 1 but not problem 2.