Unit Rates Lesson Plan

Warm-Up

With this problem, students may use different techniques to answer the questions. Once students have their answers, allow them to share their reasoning with a partner and check if their answers match.

Understanding unit rate

Let students know that situations with rates all have a unit rate. Stress the importance of the number of boxes being `1` because they want to know how many in “each box”. To help prepare students for the more complicated problems related to unit rate, consider having students write the situation as a fraction, such as `\frac{\text{120 donuts}}{\text{10 boxes}}`. It may be helpful to help students recognize that because the question is relating to “each box”, “boxes” needs to be in the denominator.

Introducing the double number line

To help introduce students to the double number line, ask them to explain what the number lines represent. This can help students become more acquainted with the context. Consider asking them how they could fill in the gray boxes with the information given. You can let students know that only one box should be left blank because it will represent the answer. 

Students should recognize that `$950` and `5` hours would correspond to the two boxes on the right. From there, you may need to bring focus to the phrase “pay per hour” in the question and ask students how many hours would be needed if it was “per hour” to help them recognize it should just be `1`.

Finding unit rate with a double number line

With the double number line filled in with those `3` values, ask students to look for a pattern to help them find the unit rate. You may need to help by drawing an arrow and saying, “how can we go from `5` to `1`?” Students will likely recognize that if they do `5 \div 5`, it will equal `1` for the hours. Then you can show how we would need to do `950 \div 5` to get the answer. You can draw another arrow on top to help students grasp the concept.

If students mention that they did not need to use the double number line, you can let them know that the values they are given do not always work out as nicely. To help transition, ask students how they would have approached the problem if the `5` had been a fraction instead. 

Finding unit rate with fractions

We want to now want to introduce unit rates with fractions. It is a good idea to scaffold their thinking. You will first ask them to fill in the information that is given in the problem. 

Ask them if they can figure out how many square feet will be covered using `1/5` of the bag. 

Students will talk about how you can get from `3/5` to `1/5` by dividing by `3`. Ask them how they know this (if you take `1/5` three times, you get `3/5`). Once you have established that you have to divide by `3`, ask then what they should do next. 

The next step is to go from `1/5` to `1`, which is by multiplying by `5`.

Some students might be comfortable with going directly from `3/5` to `1` and you should not stop them from doing it their way. However, even these students will find the unit-fraction strategy useful, especially when the numbers are not simple.

Comparing unit rates

With this problem, consider having students work with a partner. Then, one student can find the cost per pound of strawberries, and the other partner can find the cost per pound of pineapple.

By having students split up finding the unit rates with this problem, they can truly compare their answer with their partner’s. Although some students may have been able to logically recognize that the strawberries cost more per pound, they still are logically comparing the unit rates.