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* *Reflection: Discourse and Questioning
Making the Most of Rates and Unit Rates! - Section 1: DO NOW

I really liked this problem as students were able to think about it in different ways which then led to some really good discussion.

Students were able to say that the ratio of boys to students was 4:9. When it came to part b, however, they went back to the 4 to 5 ratio (boys to girls) when the question clearly asked them to find out how many students would there be if there were 120 boys.

Some students used a ratio table using the 4:5 ratio and they wanted to make 120 on the bottom for the boys. They forgot that students are both boys and girls and that they would need to add the two to get the total amount of students.

Another group used the 4 to 9 ratio which is an expert leap. They saw that the problem asked for boys to students ratio and they had already found that in part a. They knew there target number was 120 boys so they worked the table to find out that it would be 270 students altogether.

I really like using the terminology "expert leap". The students want to be considered experts and they try different things to achieve that status. I usually let them know if there is an expert leap invovled in the problem to help get them motivated.

*Possible solutions*

*Discourse and Questioning: Possible solutions*

# Making the Most of Rates and Unit Rates!

Lesson 11 of 25

## Objective: SWBAT find rates and unit rates using tools such as tables, tape diagrams and double number lines. Students will also be able to use rate language (each, to, per, for each)

#### DO NOW

*15 min*

I’m going to have students warm up with a problem from Illustrative Math called Boys and Girls. The problem is:

The ratio of the number of boys to the number of girls at school is 4:5.

a. What fraction of the students are boys?

b. If there are 120 boys, how many students are there altogether?

This problem has students looking at ratios as a fraction (so they will need to know that a fraction is a part to whole relationship) and also finding equivalent ratios. In order for students to fully understand their thinking, I’m going to have them explain their steps and say why they took the steps that they took. I’m also going to have them apply a tool from their tool box to use for this problem.

Give students time to interact with a partner to go over their answers. You can use the HUSUPU tool to get them into pairs.

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#### Introducing Rates

*10 min*

To begin the instruction for the day, I’m going to give the students a partial list of rates we use in our daily lives. I will be using the “special” words (per, each, in ) for rate as I discuss each of them. When I’m done, I’m going to have students work with their tablemates to come up with 3 more rates they have heard in daily lives. When students have completed their lists, add them to the board as a visual for today’s learning. You can also do an “I have that” to increase their list if needed. One student says a rate, if you have it, you say “I have that”. If you don’t, then you add it to your list.

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#### Vocabulary

*10 min*

There are two vocabulary words the students need to understand: rate and unit rate

Rate is a special kind of ratio that compares two types of measurements. This concept can be difficult for students so it may be a good idea to point out how the two quantities are different.

Unit Rate is a ratio of two measurements in which one of the measurements is a single unit. Ask the students what another word for single is? Next, ask students if all unit rates are rates? (Let them discuss with their partner), then ask them if all rates are unit rates? (Again, discuss with a partner) **(SMP 1)**

#### Resources

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#### Let's do some problems!

*35 min*

During this part of the instruction, I’m going to give the students a variety of rate problems to convert into unit rates. Students will be encouraged to use whatever strategy they are most comfortable with during the “your turn” part of the power point. While I’m modeling instruction I will be using different strategies so I will appeal to all members of the class. The strategies I will be using for this lesson are double number lines, tape diagrams and ratio tables. Also, during the modeling portion, I will be repeating the phrase “If I only had one _____ then…. **(SMP 6)** This will continually reinforce the vocabulary of unit rate. After working on the unit rate problems, students will be working a variety of problems that address rate and other ratio problems.

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#### Closure

*10 min*

I’m going to have students write about a time when finding a unit rate would be very important. If time permits, I will have them share with a partner to hear different opinions.

#### Resources

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- LESSON 1: Introducing Ratios!
- LESSON 2: Introducing Ratios - Stations
- LESSON 3: Writing Ratios the Right Way!
- LESSON 4: Writing Ratios the right way - Stations
- LESSON 5: Making Equivalent Ratios!
- LESSON 6: Equvalent Ratios Again!
- LESSON 7: Real-World Ratios Day 1
- LESSON 8: Real-World Ratios Day 2
- LESSON 9: Ratio Review for 6.RP.1, 6.RP.3a, 6.RP.3d
- LESSON 10: Ratio Assessment (6.RP.1,6.RP.3a,6.RP.3d)
- LESSON 11: Making the Most of Rates and Unit Rates!
- LESSON 12: Understanding Rates and Unit Rates Stations Activity
- LESSON 13: Using Rates
- LESSON 14: Are You a Good Consumer?
- LESSON 15: Using Rates Stations
- LESSON 16: Review of Rates and Unit Rates
- LESSON 17: Rates and Unit Rates Assessment
- LESSON 18: Scale Drawings
- LESSON 19: Constant Speed
- LESSON 20: Give me 100%.
- LESSON 21: Percents and double line diagrams and tape diagrams (Day 1)
- LESSON 22: Visually representing percent word problems (Day 2)
- LESSON 23: Solving Percent Problems (Day 1)
- LESSON 24: Solving Percent Problems (Day 2)
- LESSON 25: Performance Task (2 days)