21st Century Lessons

Ratio Tables and Graphing

Primary Lesson Designer(s):

Stephanie Conklin

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Warm Up

Agenda

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 Complete these problems:1) Label the x-axis, y-axis and origin. 2) Plot the point (2,4) 3) Plot the point (-2, -4)  4)  How are the two points related?  

x-axis

y-axis

The origin is the point (0,0)The origin is the point (0,0)

The points are the same distance from    the origin.

Objective: Students will use tables to graph real-world rate examples. Language Objective: Students will review vocabulary relating to graphs like origin, x-axis, y-axis and positive slope.

Agenda:

1) Warm Up (Individual) 2) Launch - Chocolate Chip Cookies (Whole Class and Partner Work)

3) Explore – Tour de France Example (Partner Work) 

4) Summary  (Whole Class)

5) Practice (Partner Work and Whole Class)

6) Assessment (Individual)

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Objective: Students will use tables to graph real-world rate examples. Language Objective: Students will review vocabulary relating to graphs like origin, x-axis, y-axis and positive slope.

Launch

Agenda

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Chocolate Chips Cookies Recipe1 cup butter, softened1 cup white sugar1 cup packed brown sugar2 eggs2 teaspoons vanilla extract3 cups all-purpose flour1 teaspoon baking soda2 teaspoons hot water1/2 teaspoon salt2 cups chocolate chips

Sarah and Tyreak are planning a bake sale to raise money for their local food shelter. They want to make A LOT of chocolate chip cookies! Here is the recipe for chocolate chip cookies:

Launch – Partner Work

Agenda

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Sara and Tyreak decide that they will need more than 1 batch of cookies of their sale. Answer the questions below to help Sara and Tyreak!1) In 1 batch of cookies, how many cups of white sugar will be needed?  2)  In 4 batches of cookies, how many cups of white sugar will be needed?  3)  How did you get your answer in #2?  Be ready to explain!   4)  How many eggs do Sara and Tyreak need to make 3 batches of cookies?   5) What do you think is the most important ingredient to making chocolate chip cookies?

Launch – Partner Work

Agenda

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Sara and Tyreak decide that they will need more than 1 batch of cookies of their sale. Answer the questions below to help Sara and Tyreak!1) In 1 batch of cookies, how many cups of white sugar will be needed?  2)  In 4 batches of cookies, how many cups of white sugar will be needed?  3)  How did you get your answer in #2?  Be ready to explain!   4)  How many eggs do Sara and Tyreak need to make 3 batches of cookies?   5) What do you think is the most important ingredient to making chocolate chip cookies?

1 cup of white sugar

4 cups of white sugar

6 eggs for 3 batches of cookies

Launch – Whole Class

Agenda

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Sara and Tyreak decide they will make as many batches of cookies as they can! However, they only have 12 cups of chocolate chips! How many batches can they make?

Let’s use one of our tools to help us! A TABLE!!!

Hey, wait! Have you used a table before? If so when?  Mmmm            cookies!

Hey, wait! Have you used a table before? If so when?  Mmmm            cookies!

Launch – Whole Class

Agenda

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We can use a table to help use organize information, especially when we need a lot of information! Create a table that compares # of batches to cups of chocolate chips.

What always goes in the first row of a         table? 

What always goes in the first row of a         table? 

# of batches Cups of chocolate chips

What do we already know about 1 batch    of cookies and cups of chocolate chips?

What do we already know about 1 batch    of cookies and cups of chocolate chips?

1 2

Let’s fill in the rest of the chart, and follow the pattern!

Let’s fill in the rest of the chart, and follow the pattern!

2 43 64 85 106 12

0 0

Launch – Whole Class

Agenda

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Let’s answer our question! How many batches of chocolate chip cookies can Sara and Tyreak make with 12 cups of chocolate chips?

0 0 # of batches Cups of chocolate chips

1 22 43 64 85 106 12

Sara and Tyreak can make 6 batches of cookies!

Launch – Whole Class

Agenda

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Let’s go one step further and GRAPH our table!

# of batches

Cups of choc. chips

0 0

1 2

2 4

3 6

4 8

5 10

6 12

What 3 things do we need to label on our graph?

What 3 things do we need to label on our graph?

# of batches

Cups

of

choc

. chi

ps

Batches of Choc. Chip Cookies

Launch – Whole Class

Agenda

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Let’s go one step further and GRAPH our table!

# of batches

Cups of choc. chips

0 0

1 2

2 4

3 6

4 8

5 10

6 12

# of batches

Cups

of

choc

. chi

ps

Batches of Choc. Chip Cookies

Explore – Partner Work

Agenda

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In the Tour de France, athletes from all over the world compete to be the fastest cyclist by riding everyday for up to 8 hours! In last year’s race, American cyclists averaged a rate of 75 miles in 3 hours. Using this information, fill in the chart below and create a graph! Then answer the questions on your hand-out!.

Hours Total Miles Biked

0

1

2

3

4

5

6

7

8

Explore

Agenda

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In the Tour de France, athletes from all over the world compete to be the fastest cyclist by riding everyday for up to 8 hours! In last year’s race, American cyclists averaged a rate of 75 miles in 3 hours.

Hours Total Miles Biked

0 0

1 25

2 50

3 75

4 100

5 125

6 150

7 175

8 200 Hours

Mile

s pe

r ho

ur

Tour de France Race

Explore – Partner Work

Agenda

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Use the Tour de France graph and table to answer the following questions!1)  In 2 hours, how far will the cyclists have gone?  2)  If a cyclist traveled 125 miles, how many hours has he been biking?  3) In questions #1 and #2, did you use the graph or the table?  Why? 

4) Estimate, to the nearest hour, how long it would take a cyclist to go 170 miles? 

5)  Estimate how many miles a cyclist would bike after 2 hours and 30 minutes?  Explain how you got your answer.

  6)  What does the first point (0,0) on the graph represent?  

Explore – Check your answers!

Agenda

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Summary – Partner and Whole Class

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Agenda

Answer the following question with a partner, and be prepared to share your opinion with the class.

What is a better way to represent a rate, a table or graph? Explain your choice!

Practice – Partner Work

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Agenda

Practice Answers – Whole Class

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Agenda

Assessment (Individual)

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Agenda

Minutes Total Miles

0 0

10

20 14

30

40

50

60

In 20 minutes, Jacob drove 14 miles. Fill in the table to answer this question:

How many miles did Jacob drive in 1 hour? Minutes Total Miles

0 0

10 7

20 14

30 21

40 28

50 35

60 42

Jacob drove 42 miles in 1 hour.

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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 tables to graph real-world rate examples. Language Objective: Students will review vocabulary relating to graphs like origin, x-axis, y-axis and positive slope.

Lesson Description This lesson will first review students knowledge of applying ratio tools to solve real world problems. We will first look at a recipe and ask students to answer questions about making multiple batches of cookies. Then from this question, we will launch in a review of creating ratio tables, and then finally will graph this information to show a linear relationship. We will complete 1 example on cookies and graphing as a whole class, and then students will work in pairs to try a different problems on speed. Lastly, students will work on a challenge problem (negative slope) to graph their problems and answer follow-up questions. A summary and assessment, along with class work will be provided as a means to assess student learning.

Lesson Overview (1 of 3)

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Lesson Vocabulary Ratio Table – a table that include two quantities being comparedCoordinate Plane – the x-y axis where we can graph points (x,y)X-axis: horizontal line on a coordinate planeY-axis: vertical line on a coordinate plane

Materials - Class set of notes- Rulers

Scaffolding We will use frequent partner talk and pair-shares to review ratio tables. We will then use practice from the Warm-Up to help students practice graphing coordinate points. The class notes can be provided to students with or without answers as an accommodation.

Enrichment Students will identify positive and negative slopes when graphing ratio tables. - Teachers can provide alternative examples for students to practice this higher skill, examples can be found on websites.

Online Resources for Absent Students

http://www.indiana.edu/~atmat/units/ratio/ratio_t3.htmhttp://www.webmath.com/gpoints.htmlhttp://www.khanacademy.org/math/algebra/algebra-functions/e/graphing_points

Lesson Overview (2 of 3)

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Lesson Overview (3 of 3)

Common Core State Standard

6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Before and After Before this lesson, students have used tables to help identify equivalent ratios and also practiced finding ratios using a variety of tools. This is one of the more difficult skills in this unit, and after this students will continue their study of lines and proportionality in 7th grade standards.

Topic Background Today’s lesson relates to the real-world in many ways; we will use recipes and speed as two major real-world examples. Further, we will focus on how to find total distance traveled using graphs.