##
* *Reflection: Exit Tickets
Calculating Unit Rates - Section 4: Closure and Ticket to Go

I collected the tickets to go to see what students understood about calculating unit rates and what gaps in understanding they had. I corrected the tickets to go and grouped them in the following way:

**Novice:** These students struggled to use the information in the problem to calculate unit rates and in turn had difficulty comparing the rates. Some students were able to set up rates from the problem, but had problems with division. A few students were able to set up the rates from the problem, but instead of dividing, they multiplied to calculate a unit rate. This student understands that a unit rate must show the amount of money saved in one week, but does not understand how to move from a rate for 3 weeks to a rate for 1 week.

**Approaching Mastery:** These students were able to create and label a rate with the information in problem 2. These students made one division error. For part (a) this particular student created a rate of $45/4 weeks, but to create the unit rate he divided $45 by 3 to get $15/week, rather than dividing $45 by 4. He understand the concept of finding unit rates, but the careless mistakes are holding him back.

**Proficient:** These students were able to correctly calculate the unit rates and compare them. They struggled to create a clear and coherent sentence for part (c) that explained *why *Sam was saving at a faster rate.

**Advanced: **These students were able to correctly calculate the unit rates and compare them. What set them apart from the proficient students was their explanation in part (c). Advanced students were able identify that Sam was saving at a faster rate since he was saving more money *each week. *

Most students were able to correctly calculate unit rates, but struggled to create an explanation that explained *why *Sam is saving at a faster rate. The most common mistakes were division mistakes, which tells me I need to spiral in some division work.

# Calculating Unit Rates

Lesson 14 of 21

## Objective: • Use data to calculate and compare unit rates.

## Big Idea: How long does it take each student to make one bracelet? How many bracelets can each student make in an hour? Students practice finding and using unit rates to answer questions.

*50 minutes*

#### Do Now

*7 min*

See my **Do Now** in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want to see what strategies students will use to fill in the table and find the unit rate. Some students may create a rate of 150 miles/ 5 gallons and divide to find that the car travels 30 miles/1 gallon. Other students may work with the two distances to find the other distances. For instance, if the car travels 150 miles using 5 gallons of gas, then for 10 gallons they would multiply 150 by 2. They could also divide 180 by two to find the distance the car can travel using 3 gallons of gas. I am interested to see what kind of strategies students use to find the unit rate.

Students participate in a **Think Pair Share. **I call on students to share their different ways of filling out the table and finding the miles per gallon. I ask students, “What do we call it when one of the measurements in a rate is 1?” I want students to understand the difference between a rate and a unit rate.

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#### Miles Per Gallon

*10 min*

Notes:

- Students will work in partners. Before the class, I use the data from the 2 previous lessons to create partner pairs.
- I
**Post a Key**around the room.

We work through problem 2 together. I ask, “How can we use the data in the table to fill in the blanks?” Similar to the do now, students will use different methods to calculate the missing data and this is great. I give partners a couple minutes to do their calculations and then we share out. I ask, “How can we use this data to know how many miles per gallon Car B gets?” Students may use different data points to find the unit rate. I show students how we can use the unit rate to find out how far the car can travel with 17 gallons of gas. I stress to students that it will help them keep track of units and measurements if they create equivalent rates that are labeled. A common mistake is for students to set up the rates with different units in the numerator or denominator. Another common mistake is for students to take one piece of the rate to multiply it without understanding what they are doing. Some students may also struggle with unit rates that include a decimal. Most students can use their division and multiplication skills to work through the problems. If students are still struggling to multiply and divide with decimals, I let them use a calculator. Even if a student uses a calculator they must first set up and label the equivalent rates.

For part d, the important question is “What data can we compare?” In order to compare rates, we needs to compare rates that share a common measurement. For instance we can compare the distance both cars can travel with 1 gallon, but we can’t compare the distance Car A travels using 3 gallons and the distance Car B travels using 5 gallons. I make a connection to comparing fractions. One way we compare fractions is by creating a common denominator. To compare rates, each rate must have a common measurement.

#### Resources

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#### Work Time

*20 min*

I explain that students are going to apply these strategies to more problems. I ask students to review their strategies if they get stuck from the previous lesson (Comparing Rates).

As students work, I walk around to monitor student progress and behavior. Students are engaging in **MP1: Make sense of problems and persevere in solving them, MP2: Reason abstractly and quantitatively, **and** MP6: Attend to precision. ** If a partner pair completes a problem, I briefly look over it to check for glaring mistakes. If the students are on track, I send them to check their work with the key.

If students are struggling, I may ask one or more of the following questions:

- What specifically is your question?
- What is a unit rate?
- How can you calculate a unit rate?
- What are you trying to find out?
- What do you know?
- What can you compare?
- What strategies did you use in questions 1 and 2 in this packet?
- What do you notice about the graph?

If students successfully answer questions 3-5, they can work on the extra practice problems.

#### Resources

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#### Closure and Ticket to Go

*13 min*

I ask students, “What is the difference between a rate and a unit rate?” and “When is it helpful to use a unit rate?” I want students to recognize that if they can calculate a unit rate, they can find other calculations easily.

Then I tell students to turn to the strawberry graph on page 6. I ask them, “What can you tell about the prices of strawberries at store A, B, C, and D just by looking at the graph?” Students participate in a **Think Pair Share. **I want students to recognize that Store D has the cheapest strawberries because it has the flattest graph and that Store A has the most expensive strawberries because it has the steepest graph. Other students may share the cost per pound of strawberries of each store. The important part is that students are able to justify their ideas using data from the graph.

With about 6 minutes left, I pass out the **Ticket to Go **and the **HW Calculating Unit Rates.**

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##### Similar Lessons

Environment: Urban

###### Finding Equivalent Ratios

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*Resources(11)*

Environment: Urban

Environment: Urban

- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: Nana's Chocolate Milk
- LESSON 2: Introduction to Ratios
- LESSON 3: Extending and Comparing Ratios
- LESSON 4: Ratios with Thinking Blocks
- LESSON 5: Working with Percents
- LESSON 6: Converting Measurements Using Ratios
- LESSON 7: Converting Measurements Using Ratios Day 2
- LESSON 8: Show What you Know About Ratios
- LESSON 9: Introduction to Rates
- LESSON 10: Heart Rate
- LESSON 11: Calculating Speed Day 1
- LESSON 12: Calculating Speed Day 2
- LESSON 13: Comparing Rates
- LESSON 14: Calculating Unit Rates
- LESSON 15: The State Fair
- LESSON 16: Better Deal Stations
- LESSON 17: Show what you know about rates
- LESSON 18: Finals Week Day 1
- LESSON 19: Finals Week Day 2
- LESSON 20: Unit 5 Review Stations
- LESSON 21: Unit 5 Test