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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21st Century Lessons – Teacher Preparation
Please do the following as you prepare to deliver this lesson:
•
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.
•
Feel free to customize this file to match the language and
routines in your classroom.
*1st Time Users of 21st Century Lesson:
Click HERE for a detailed description of our project.
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Lesson Overview (1 of 3)
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.
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Lesson Overview (2 of 3)
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Lesson
Vocabulary
Ratio – a relationship between two or more amounts
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
Tape diagram – a drawing that looks like a segment of tape, used to illustrate
number relationships. It is also known as a strip diagram, bar model, fraction
strip, or length model. These models work particularly well to show
comparisons between part-to-part or part-to-whole ratios.
Thinking Blocks website for a video demo of how to use tape diagrams to solve
ratio problems and practice problems with feedback.
http://www.thinkingblocks.com/tb_ratios/ratios.html
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.
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Warm Up
OBJECTIVE: SWBAT solve ratio problems by using a tape diagram.
Language Objective: SWBAT discuss ratio problem solving with a
partner and in groups.
Write each ratio as a fraction
in lowest terms.
What is the ratio of…
1. Girls to boys? 1:1
2. People wearing pants to
people who are not? 4:1
3. People wearing white to
people who are in jeans?
4. Write a sentence about what your answer to #2 means. 3:2
Agenda
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Agenda:
OBJECTIVE: SWBAT solve ratio problems by using a tape diagram.
Language Objective: SWBAT discuss ratio problem solving with a
partner and in groups.
1) Warm Up - independent
2) Launch – partners
3) Explore:
Predict - independent
Mini-Lesson – whole class
Practice & Discuss – independent & partners
4) Summary - independent
5) Exit Ticket - independent
6) Assessment - independent
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Launch
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.
Agenda
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Launch
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?
Agenda
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Launch
Here’s the definition:
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. 
Agenda
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Launch – Think, Pair, Share
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?
Lefty share your answers with Righty.
Now Righty share your answers with Lefty.
Does anyone want to share what their
partner told them?
Agenda
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Launch – Think, Pair, Share
Zack’s orange paint is made by mixing
3 cups of red for every 5 cups of yellow.
3:
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
Class – What is the ratio of red to
yellow in Zack’s orange paint?
3 to 5 or 3:5 or 3
5
Agenda
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Explore – Strategize
Zack bought 24 cups of red paint.
How much yellow paint will Zack need to
buy to make his shade of orange paint?
3:
Write down in your notes any
ideas you have about how to
answer this question.
Agenda
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Explore – Mini-Lesson
Before we solve Zack’s problem, let’s look at some
simpler problems to get ready. Read this problem.
Example 1) The ratio of boys to girls in a class is 2 to 3.
1. If there are 4 boys in the class, how many girls are
there?
Agenda
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Explore – Mini-Lesson
Let’s learn about a helpful tool for ratio problems that
could help you with all sorts of ratio problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
1. If there are 4 boys in the class, how many girls are
there?
Agenda
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Explore – Mini-Lesson
New Tool: Tape Diagram
We can use a tape diagram to solve ratio math problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
boys
girls
Each box represents a
number in the original
ratio.
1. If there are 4 boys in the class, how many girls are
there?
Now let’s look at the question.
Agenda
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Explore – Mini-Lesson
New Tool: Tape Diagram
We can use a tape diagram to solve ratio math problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
boys
If this tape shows 4
boys then…
girls
1. If there are 4 boys in the class, how many girls are
there?
Agenda
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Explore – Mini-Lesson
New Tool: Tape Diagram
We can use a tape diagram to solve ratio math problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
4
boys
girls
2
2
This tape
How
manyisstudents
4 boys.
arewe
So
in one
put 4box?
above
the tape.
2
1. If there are 4 boys in the class, how many girls are
there?
Agenda
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Explore – Mini-Lesson
New Tool: Tape Diagram
We can use a tape diagram to solve ratio math problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
4
boys
girls
2
2
2
2
?
2
Rule:
We Important
don’t yet
know
Thethe
number
in each
number
of box
girlsmust
be the same for every tape.
so we put a ? for the
length of that tape.
1. If there are 4 boys in the class, how many girls are
there?
Agenda
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Explore – Mini-Lesson
New Tool: Tape Diagram
We can use a tape diagram to solve ratio math problems.
Example 1) The ratio of boys to girls in a class is 2 to 3.
4
boys
girls
2
2
2
2
?
2
Now we can answer
the question.
1. If there are 4 boys in the class, how many girls are
there?
6
Agenda
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Explore – Mini-Lesson
New Tool: Tape Diagram
Let’s try another one.
Example 2) The ratio of boys to girls in a class is 3 to 2.
?
We can label what we
First,
the tapes.
know.draw
8 girls.
boys
We can put a question
girls
mark for what we
8
don’t know.
2. If there are 8 girls in the class, how many boys are
there?
Now let’s look at the question.
Agenda
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Explore – Mini-Lesson
New Tool: Tape Diagram
Let’s try another one.
Example 2) The ratio of boys to girls in a class is 3 to 2.
?
boys
girls
4
4
8
How many students
does
each box
This makes
8 girls.
represent? 4
2. If there are 8 girls in the class, how many boys are
there?
Agenda
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Explore – Mini-Lesson
New Tool: Tape Diagram
Let’s try another one.
Example 2) The ratio of boys to girls in a class is 3 to 2.
?
boys
4
4
girls
4
4
8
4
Remember:
Every box must have
the same quantity.
2. If there are 8 girls in the class, how many boys are
there?
Can you answer the question using
12 the diagram?
Advanced: Think of one way you could prove that the
numbers in each box should be 4. Tell your partner.
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Agenda
Explore
Tape Diagrams can be a helpful tool for solving problems.
Check this out for more about how tape diagrams work:
Click “Watch video” for a demonstration.
Agenda
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Practice
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.
Agenda
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Discuss
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.
Agenda
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Discuss
If you and your partner cannot agree on a
diagram, put a star next to the problem.
Let’s look at questions 3 and 4. Check to
see if you and your partner completed the
tape diagrams in the same way.
Agenda
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Discuss Answers
6
6 sour oranges
4
4
4
4
8
6
6
6
6
6
4
8 red marbles
Agenda
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Discuss
Did you and your partner complete the tape diagrams
the same way? Did you get the same answers?
Agenda
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Discuss
Did you and your partner complete the tape diagrams
the same way? Did you get the same answers?
24 children playing
10 apples
24
playing
8
resting
8
8
8
10
8
apples
5
5
oranges
5
5
15
5
Agenda
Agenda
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Discuss (optional)
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 Slides
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Agenda
Summary – Write in your notebook
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?
Agenda
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Exit Ticket
New Tool: Tape Diagram
Now that you learned a new tool use it to solve Zack’s
paint problem.
Remember:
Zack’s orange paint is made by mixing
3 cups of red for every 5 cups of yellow.
He bought 24 cups of red paint.
Use tape diagrams as a tool to find out how much yellow
paint Zack will need to buy to make his orange paint.
Agenda
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Exit Ticket
New Tool: Tape Diagram
Let’s solve this problem using a tape diagram.
Theknow:
question
is: How
many
cups
of yellow
paint does Zack
We
Zack’s
orange
paint
is
made
by
mixing
And, we know: he bought 24 cups of red paint.
hisevery
shade
of orange
paint?
3need
cupsto
ofmake
red for
5 cups
of yellow.
Since
Nowevery
we can
boxfigure
must have
out how
This is a 3:5 ratio of red to yellow.
themany
samecups
quantity…
each box
represents.
If 3the
boxes
are 24
Let’s label
diagram.
then…
red
yellow
8
8
24
8
8
8
8
?
Let’s draw the tapes.
8
8
That means the answer is: 40 cups of yellow paint
Agenda
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Assessment
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?
grapes
20
strawberries
20
20
20
20
Answer: So the number of grapes is 20.
Agenda
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21st Century Lessons
The goal…
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.
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21st Century Lessons
The people…
Directors:
Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee
Ted Chambers - Co-director of 21st Century Lessons
Tracy Young - Staffing Director of 21st Century Lessons
Leslie Ryan Miller - Director of the Boston Public Schools Office of
Teacher Development and Advancement
Emily Berman- Curriculum Director (Social Studies) of 21st Century Lessons
Carla Zils – Curriculum Director (Math) of 21st Century Lessons
Brian Connor – Technology Coordinator
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