21 st Century Lessons Introduction to Tape Diagrams Primary Lesson Designer: Lisa Schad 1.

21st Century Lessons

Introduction to Tape Diagrams

Primary Lesson Designer:

Lisa Schad

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This project is funded by the American Federation of Teachers.

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*1st Time Users of 21st Century Lesson:Click HERE for a detailed description of our project.

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 Content Objective: SWBAT solve ratio problems by using a tape diagram. Language Objective: SWBAT discuss ratio problem solving with a partner and in groups.

Lesson Description The lesson begins with a review of what a ratio is and has students identify various ratios for a given situation. They will also watch a short video that showcases ratios in use in everyday life. There is an overarching question that is introduced before the mini-lesson that can be solved using the tool they learn today: tape diagrams. Students will be shown how tape diagrams are created based on information in a problem. They will practice in a heavily-scaffolded worksheet to fill in and later create tape diagrams. At the end of the lesson, for the exit ticket, students revisit the problem introduced before the mini-lesson and solve it using the tape diagram tool.

Lesson Overview (1 of 3)

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Lesson Vocabulary

Ratio – a relationship between two or more amounts

Tape diagram – a drawing that looks like a segment of tape, used to illustratenumber relationships. It is also known as a strip diagram, bar model, fractionstrip, or length model. These models work particularly well to showcomparisons between part-to-part or part-to-whole ratios.

Materials Required: All students have a notebook and pen or pencil. Teacher has board space for student work. Optional: Teacher can use large student whiteboards to put up student work for sharing with the class.

Scaffolding Opportunities to discuss and to write about the math content give ELL students the chance to practice the language of mathematics. The Thinking Blocks video provides a visual aid to any struggling students.

Enrichment Students who finish work quickly can work on additional tape diagram problems at the Thinking Blocks site given below.

Online Resources for Absent Students

How different professionals use ratios to solve problems at work http://www.bbc.co.uk/skillswise/video/ratio-and-proportion

Thinking Blocks website for a video demo of how to use tape diagrams to solveratio problems and practice problems with feedback. http://www.thinkingblocks.com/tb_ratios/ratios.html

Lesson Overview (2 of 3)

http://www.bbc.co.uk/skillswise/video/ratio-and-proportion


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Lesson Overview (3 of 3)Common Core State Standard

6RP3 Use ratio reasoning to solve real-world problems 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.http://www.corestandards.org/

Before and After This lesson builds off of previous lessons that introduced students to the idea of a ratio and the language of ratio by introducing them to problem solving with ratios. The tool, tape diagrams, will be helpful for solving many ratio problems involving two or more similar parts. (For more, see slide notes below.)

Topic Background Ratios have a real and practical purpose in the lives of adults. Many use ratios in their work lives, but also any home cook has had to increase or decrease a recipe. Even mixing juice from concentrate requires the use of ratios. The tape diagram model is heavily used in high performing Asian and European curricula, but rarely seen in current American curricula. This lesson and those that follow in this unit will help to bridge that gap.

Warm UpOBJECTIVE: SWBAT solve ratio problems by using a tape diagram.Language Objective: SWBAT discuss ratio problem solving with a partner and in groups.

Agenda

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Write each ratio as a fraction in lowest terms.

What is the ratio of…1. Girls to boys?2. People wearing pants to

people who are not?3. People wearing white to

people who are in jeans?4. Write a sentence about what your answer to #2 means.

1:1

4:1

3:2

Agenda:

1) Warm Up - independent

2) Launch – partners3) Explore:

4) Summary - independent

5) Exit Ticket - independent

6) Assessment - independent

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OBJECTIVE: SWBAT solve ratio problems by using a tape diagram.Language Objective: SWBAT discuss ratio problem solving with a partner and in groups.

Predict - independentMini-Lesson – whole classPractice & Discuss – independent & partners

Launch

Agenda

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Abby and Zack are mixing red and yellow paint to make an orange color to paint their kitchen table. They each think they have the perfect shade of orange.

Launch

Agenda

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Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow.

This sounds like a ratio. What are ratios again?

This sounds like a ratio. What are ratios again?

Launch

Agenda

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A ratio is a relationship between two or more quantities.

But, why would I want to use or think about a ratio?

Here’s a short video that will show how ratios are used in a few real life situations.

Here’s the definition:



Launch – Think, Pair, Share

Agenda

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Think for one minute about an answer to these questions:What is a job that uses a ratio?How was a ratio useful in that job?

Does anyone want to share what their partner told them?

Lefty share your answers with Righty.

Now Righty share your answers with Lefty.

Launch – Think, Pair, Share

Agenda

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Lefty – Tell Righty the ratio of red to yellow in Zack’s orange paint.Righty – Tell Lefty the ratio of yellow to red in Zack’s orange paint.

Partner Share

Partner Share

Class – What is the ratio of red to yellow in Zack’s orange paint?

3 to 5 or 3:5 or 3 5

Explore – Strategize

Agenda

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Zack bought 24 cups of red paint.

How much yellow paint will Zack need to buy to make his shade of orange paint? How much yellow paint will Zack need to buy to make his shade of orange paint?

Write down in your notes any ideas you have about how to answer this question.

Explore – Mini-Lesson

Agenda

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Before we solve Zack’s problem, let’s look at some simpler problems to get ready. Read this problem.

1. If there are 4 boys in the class, how many girls are there?

Example 1) The ratio of boys to girls in a class is 2 to 3.


Agenda

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Let’s learn about a helpful tool for ratio problems that could help you with all sorts of ratio problems.Let’s learn about a helpful tool for ratio problems that could help you with all sorts of ratio problems.




Agenda

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We can use a tape diagram to solve ratio math problems.



Each box represents a number in the original ratio.

Now let’s look at the question.

New Tool: Tape Diagram New Tool: Tape Diagram

boys

girls


Agenda

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boys

girls



If this tape shows 4 boys then…


Agenda

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boys


girls 2


How many students are in one box? 2 2 This tape is 4 boys.So we put 4 above the tape.

4


Agenda

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boys


girls


Important Rule:The number in each box must be the same for every tape.

Important Rule:The number in each box must be the same for every tape.

2 22 2 2

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?

We don’t yet know the number of girls so we put a ? for the length of that tape.


Agenda

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boys


girls

Now we can answer the question.


4

?

2 22 2 2


Agenda

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Let’s try another one.


2. If there are 8 girls in the class, how many boys are there?

First, draw the tapes.

Now let’s look at the question.


boys

girls

We can label what we know. 8 girls.We can put a question mark for what we don’t know.8

?


Agenda

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boys


4 4girls

How many students does each box represent? 4


This makes 8 girls.

?

8


Agenda

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boys 4


4

4 4girls

Remember:Every box must have the same quantity.

Remember:Every box must have the same quantity.

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Can you answer the question using the diagram?


Advanced: Think of one way you could prove that the numbers in each box should be 4. Tell your partner.

Advanced: Think of one way you could prove that the numbers in each box should be 4. Tell your partner.

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Explore

Agenda

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Check this out for more about how tape diagrams work:

Click “Watch video” for a demonstration.

Tape Diagrams can be a helpful tool for solving problems.

http://www.thinkingblocks.com/tb_ratios/ratios.html

Practice

Agenda

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You will have 15 minutes to work on solving some ratio problems using the tape diagrams tool. You might feel a little confused and want to talk about it. Don’t worry – you will discuss it when you are finished.

http://www.online-stopwatch.com/

Discuss

Agenda

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Check with a partner to see if you have the same answers. See if you used your tape diagram tools in the same way. You have 10 minutes.


Discuss

Agenda

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Let’s look at questions 3 and 4. Check to see if you and your partner completed the tape diagrams in the same way.

If you and your partner cannot agree on a diagram, put a star next to the problem.If you and your partner cannot agree on a diagram, put a star next to the problem.

Agenda

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6 6 6 6

66 sour oranges

4 4 4

4 48 red marbles

Discuss Answers

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Discuss

Agenda

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Did you and your partner complete the tape diagrams the same way? Did you get the same answers?

Discuss

Agenda

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apples

oranges

playing

resting

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8

8 8 8

24

24 children playing 24 children playing

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10 apples10 apples

5 5

55 5

Did you and your partner complete the tape diagrams the same way? Did you get the same answers?

Agenda

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Discuss (optional)

Agenda

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Each pair will share with another pair to see if you have the same answers. See if you used tape diagrams the same way.

Each group of four will be assigned one problem (3, 4, 5, or 6) from the class work. One person will need to put their group’s work on the board.

You will have 10 minutes.

No time? Click for

Answers SlidesNo time? Click for

Answers Slides


Summary – Write in your notebook

Agenda

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What is one thing you like about the tape diagrams as a tool?

What is one thing that is difficult?

Is there anything that is confusing about using tape diagrams as a tool?

Exit Ticket

Agenda

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Now that you learned a new tool use it to solve Zack’s paint problem.


Use tape diagrams as a tool to find out how much yellow paint Zack will need to buy to make his orange paint.Use tape diagrams as a tool to find out how much yellow paint Zack will need to buy to make his orange paint.


Remember:

He bought 24 cups of red paint.

Exit Ticket

Agenda

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Let’s solve this problem using a tape diagram. We know: Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow.


And, we know: he bought 24 cups of red paint.

This is a 3:5 ratio of red to yellow.

Let’s draw the tapes.red

yellow

Let’s label the diagram.24

Now we can figure out how many cups each box represents. If 3 boxes are 24 then…

?

8 8 8

The question is: How many cups of yellow paint does Zack need to make his shade of orange paint?

Since every box must have the same quantity…

8 8 8 8 8

That means the answer is:

Assessment

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Agenda

Carefully review the tape diagram tool and solution. What is wrong here?

The ratio of grapes to strawberries in a fruit salad is 4 to 1. If there are 20 grapes in the salad then how many strawberries are there?

The ratio of grapes to strawberries in a fruit salad is 4 to 1. If there are 20 grapes in the salad then how many strawberries are there?

grapes

strawberries

20 20 20 20

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Answer: So the number of grapes is 20.

The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in urban and turnaround schools, by bringing together teams of exemplary educators to develop units of high-quality, model lessons. These lessons are intended to:

•Support an increase in student achievement; •Engage teachers and students; •Align to the National Common Core Standards and the Massachusetts curriculum frameworks;•Embed best teaching practices, such as differentiated instruction; •Incorporate high-quality multi-media and design (e.g., PowerPoint); •Be delivered by exemplary teachers for videotaping to be used for professional

development and other teacher training activities; •Be available, along with videos and supporting materials, to teachers free of charge via the

Internet. •Serve as the basis of high-quality, teacher-led professional development, including mentoring between experienced and novice teachers.

21st Century LessonsThe goal…

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Directors:Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues CommitteeTed Chambers - Co-director of 21st Century LessonsTracy Young - Staffing Director of 21st Century LessonsLeslie Ryan Miller - Director of the Boston Public Schools Office of

Teacher Development and AdvancementEmily Berman- Curriculum Director (Social Studies) of 21st Century LessonsCarla Zils – Curriculum Director (Math) of 21st Century LessonsBrian Connor – Technology Coordinator

21st Century Lessons

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21 st Century Lessons Introduction to Tape Diagrams Primary Lesson Designer: Lisa Schad 1.

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Transcript of 21 st Century Lessons Introduction to Tape Diagrams Primary Lesson Designer: Lisa Schad 1.