21st Century Lessons

Real –World Practice with Rates and Unit Rates

Primary Lesson Designer(s):

Stephanie Conklin

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This project is funded by the American Federation of Teachers.

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21st Century Lessons – Teacher Preparation

• Spend AT LEAST 30 minutes studying the Lesson Overview, Teacher Notes on each slide, and accompanying worksheets.

• Set up your projector and test this PowerPoint file to make sure all animations, media, etc. work properly.

Please do the following as you prepare to deliver this lesson:

• Feel free to customize this file to match the language and routines in your classroom.

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Lesson Objective OBJECTIVE: Students will use unit rates to compare quantities in real-life situations.Language Objective: Students will use vocabulary relating to rates like per and for every.

Lesson Description This lesson will begin with a review of finding unit rate in a real-world situation. Then, students will be introduced to finding unit rates using decimals, like Usain Bolt’s time. We will then ask students to use unit rates to compare costs and also to make choices based on unit rates. For example, students will decide when we want to have a higher unit rate (i.e. earnings per hour) or a low unit rate (i.e. cost per package of buttons).

We will finish the lesson with scaffolded class work and a summary and assessment.

Lesson Overview (1 of 3)

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Lesson Vocabulary A unit rate is a comparison of 2 different quantities where one measurement only has 1 unit.

Materials Teachers will need -Set of class notes for students to follow-Calculators or students have strong knowledge of dividing decimals-Set of class work and homework hand-outs

Scaffolding This lesson provides steps to solve, guided practice and also review of key definitions for this lesson.

Enrichment Students will use unit rates to solve questions that ask students to show further understanding of unit rates. They will use unit rates to calculate costs and rates of larger quantities.

Online Resources for Absent Students

http://www.math.com/school/subject1/lessons/S1U2L3GL.htmlhttp://www.khanacademy.org/math/arithmetic/basic-ratios-proportions/v/finding-unit-rates

Lesson Overview (2 of 3)

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Lesson Overview (3 of 3)

Common Core State Standard

6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1

Before and After Before this lesson, students will learn how to calculate a rate and a unit rate. Calculators can be used for this lesson or if not, students should have strong knowledge of dividing decimals. In this lesson, we will extend this to calculate rates that are not whole #s. Further, students will compare rates. We will then use this in our next lesson to calculate desired quantities. For example, if we pay $75 for 15 hamburgers, how much is 25 hamburgers?

Topic Background This lesson asks students to use unit rates to solve problems with distance and time as well as price per hour and salary. We will teach students how to answer real-world situations like “what’s the better value?” or “which job should he take?”

Warm UpOBJECTIVE: Students will use unit rates to compare quantities in real-life situations.Language Objective: Students will use vocabulary relating to rates like per and for every.

Agenda7

Kyle can mow 3 lawns in 2 hours. If Kyle takes the same time to mow each lawn, how long does it take him to mow 1 lawn? Write a sentence!

Hint: Convert the time from

hours to minutes.

We’ll use a unit rate to solve this question:

2 hours 2 (60 minutes) = 120 minutes

120 minutes 3 lawns

40 minutes 1 lawn=

This means that Kyle can mow 1 lawn in 40 mins.

Agenda:

1) Warm Up (Individual)2) Launch – Fastest Man in World (Whole Class and Partner)

3) Explore – Mini Lesson and Practice (Whole Class and Partner)

4) Summary (Whole Class)5) Practice (Partner and Whole Class)

6) Assessment (Individual)

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OBJECTIVE: Students will use unit rates to compare quantities in real-life situations.Language OBJECTIVE: Students will use vocabulary relating to rates like per and for every.

What are some real-

world examples of

rate?

Launch

Agenda9

http://vimeo.com/46634479

Please watch the following video on Usain Bolt, the Olympic Gold Medalist in the Men’s 100-meter spring. Answer the questions below!

1) How fast does Usain run the 100 meter sprint?

2) Does he run this race in seconds, minutes or hours?

3) After how many meters can Usain tell if he will win a race?

4) What country is Usain from?

9.58

9.58 seconds

After 60-70 meters

Jamaica

Launch

Agenda10

Let’s find the Usain’s speed using rates and unit rates! We will compare distance (meter) to time (seconds).Step 1: Write a rate in fraction form

Step 2: Simplify to write as a unit rate

Let’s learn a trick to convert a rate to a unit rate!

100 meters 9.58 seconds

Hold up! How can we simplify

this rate?

Yahhh! Tricks make math

easier!

Launch

Agenda11

Step 2: Simplify to write as a unit rate

Let’s learn a trick to convert a rate to a unit rate!

100 meters 9.58 seconds

What operation does the

fraction bar represent in the

ratio?

Divide is right!! Let’s divide 100 meters by 9.69 to find a unit

rate!

REVIEW:

We can write this as division problem:

This unit rate means Usain runs 10.32 meters per second. This unit rate also means that in 1 second Usain Bolt runs 10.32 meters.

Explore: Mini-Lesson

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Agenda

Let’s find the unit rate of each real-world situation!

(ex 1) Kenny goes to the grocery store and buys 5 pounds of Apples for $8.40.

Step 1: Write a rate in fraction form.

Step 2: Divide to find the unit rate. .

$8.40_ 5 pounds

$8.40 ÷ 5 pounds = $1.68 per pound

Kenny paid $____ per ______ of apples..

What does this unit rate mean?

Kenny paid $1.68 per pound of apples..

Explore: Try with a Partner

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Agenda

Let’s find the unit rate of each real-world situation!

(ex 2) Michelle is computer programmer who designs video games. She works 30 hours each week and makes $2,535.

Step 1: Write a rate in fraction form.

Step 2: Divide to find the unit rate. .

$2,535_ 30 hours

$2,535 ÷ 30 hours = $84.50 per hour

Michelle makes $84.50 per hour

Write a sentence to explain this

situation.

Explore: A New Challenge

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Agenda

(ex 3) Cameron has 2 jobs offers as a camp counselor. At the YMCA, he will be paid $90 for working 8 hours. At the school’s day camp, he will be paid $78 for working 6.5 hours.

Brainstorm with your partner: Which job should Cameron take?

Use your note’s from today to help

you!

Explore: A New Challenge

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Agenda

(ex 3) Cameron has 2 jobs offers as a camp counselor. At the YMCA, he will be paid $90 for every 8 hours of work. At a school day camp, he will be paid $78 for every 6.5 hours of work. Brainstorm with your partner: How can we decide which job pays Cameron the most per hour?

YMCA Job School Job$90 ÷ 8 hours = $11.25 per hour $78 ÷ 6.5 hours = $12 per hourCreate a table to

organize your work!

Write a sentence to answer question.

Cameron should choose the school job because he will make $12 per hour which is $0.75 more than at the YMCA.

Explore: Practice with a Partner

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Agenda

(ex 4) Maria is a clothing designer and needs to buy a lot of buttons to make her clothes! The following shows button advertisements from 2 different stores:

Button R’ Us Button-Up!

Answer the following questions: a)What is the unit rate for buttons at Button R’ Us?b)What is the unit rate for buttons at Button-Up?c)Which store do you think Maria should buys buttons from?

55 Buttons for $5.50

140 Buttons for $12.60

Explore: Practice with a Partner

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Agenda

Button R’ Us Button-Up!

Answer the following questions: a)What is the unit rate for buttons at Button R’ Us?

b)What is the unit rate for buttons at Button-Up?

c)Which store do you think Maria should buys buttons from? Explain your answer!

55 Buttons for $5.50

140 Buttons for $12.60

$5.50 ÷ 55 buttons = $0.10 per button

$12.60 ÷ 140 buttons = $0.09 per button

Button-Up is cheaper than Button R’Us by 2 cents.

Challenge: Practice with a Partner

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Agenda

Button-Up!

Maria has decided to use the Button-Up! Company! Remember, she found a unit price of $0.09 per button. How much would it cost her to buy 500 buttons?

140 Buttons for $12.60

500 buttons x $0.09 per button = $45.00

Practice

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Agenda

Practice

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Agenda

Summary – Partner Work

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Agenda

1) Today, we learned that to compare rates, we can first find the ______ ______ .

2)A unit rate is a comparison of 2 different quantities where one measurement has only _____ unit.

3)We can use unit rates to find things like how much a job pays per hour. What other real-world examples are there for using unit rates?

unit rate

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Assessment

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Agenda

Try on your own:Martina drives 360 miles in 6 hours and Carlos drives 248 miles in 4 hours. Who drives the fastest?

Martina: 360 miles ÷ 6 hours = 60 miles per hourCarlos: 248 miles ÷ 4 hours = 62 miles per hour

Carlos has a faster rate at 62 miles per hour!

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