1. Using Tape Diagrams and Ratio Tables to Solve Ratio Problems
21st Century Lessons
Using Tape Diagrams and Ratio Tables to Solve Ratio Problems
Primary Lesson Designer:
Lisa Schad

2. This project is funded by the American Federation of Teachers.

3. 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.

4. Lesson Overview (1 of 3) Lesson Objective
Content Objective: SWBAT solve ratio problems by using tape diagrams and ratio tables. Language Objective: SWBAT describe how to solve a ratio problem to other students in a small group.
Lesson Description
Students will work to solve several ratio problems independently using tape diagrams or ratio tables. Then they will work in small groups to become experts in how to solve just one of the assigned problems. Groups will then be mixed up for a jigsaw share. Each student will present to the others in their small group how to solve their expert problem using one of the tools. They will listen to others’ presentations so that they can be sure they have the correct answers and have used the tools properly. Then they will solve a last exit ticket problem on their own using the tool of their choice.

5. Lesson Overview (2 of 3) Lesson Vocabulary Materials
Ratio – a relationship between two or more amounts
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.
Ratio table – a model for organizing equivalent ratios.
Materials
Worksheets, half sheets of lined paper for exit ticket, notebook and pen or pencil. The teacher may wish to use some device for indicating each student’s expert group (a table tent, sticky, etc.)
Scaffolding
Small group instruction, reciprocal teaching and frequent student conversations allow both ELL and students with learning differences access to the content with low-risk opportunities to practice and seek clarification.
Enrichment
Students need an additional challenge can make connections with algebra using the Problem D extension page.
Online Resources for Absent Students
Thinking Blocks website for practice with Tape Diagrams:

6. 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.
Before and After
Students have learned about tape diagrams and ratio tables and now they will practice using these tools in several problem scenarios. They will learn next about unit rate and comparing rates, then percents and a new tool, the double number line. All tools from the unit will be practiced in later lessons.
Topic Background
Many of the problems used in today’s lessons are meant to represent the variety of ways that ratio problems come up in real-world scenarios. Students should be thinking about connections between the tools that they are using.

7. A Word About PowerPoint
These Presentation Files were designed to be used on a PC version of MS PowerPoint. Many of the features will work on PowerPoint for Mac 2011 but some are not compatible with older versions .
Please test your file before using in class!

8. Warm Up
OBJECTIVE: SWBAT solve ratio problems by using tape diagrams and ratio tables. Language Objective: SWBAT describe how to solve a ratio problem to other students in a small group.
Describe something on the American flag that has each given ratio.
1. 6 to 7
White stripes to
red stripes
(Time on this slide – 3 min) Time passed 3 min
In-Class Notes
You may want to have one student identify how many red and white stripes there are. And another how many stars if it is clear that many students cannot determine this.
Preparation Notes
Make sure students recognize that a simplified ratio can be equivalent to a variety of ratios.
3:25 = 6:50 = 9:75 etc
2. 7 to 13
3. 6 to 13
4. 3 to 25
Red stripes to
all stripes
White stripes to
all stripes
White stripes
to stars
Agenda

9. Agenda:
OBJECTIVE: SWBAT solve ratio problems by using tape diagrams and ratio tables. Language Objective: SWBAT describe how to solve a ratio problem to other students in a small group.
1) Warm Up - independent
2) Launch – Think, Pair, Share – partners
3) Explore:
Problem Set Practice - independent
Expert Groups – small group
Jigsaw Share – small groups
(Time on this slide – 1 min) Time passed 4 min
In-Class Notes
Brief introduction
Preparation Notes
4) Summary - independent
5) Exit Ticket - independent

10. Launch – Think, Pair, Share
You have learned about two great tools for solving ratio problems. Can you name the tools?
T A P E D I A G R A M S
R A T I O T A B L E S
Lefty – Tell Righty what a tape diagram is.
Righty – Tell Lefty what a ratio table is.
(Time on this slide – 2 min) Time passed 6 min
In-Class Notes
Share out descriptions of the tools and how they are helpful.
Preparation Notes
If you created anchor charts for these tools keep them close at hand for review.
Today you are going to practice using both tools.
Agenda

11. Explore – Independent Practice
You will now practice solving some ratio problems. Your teacher will assign you 1 problem set to focus on. If you finish quickly do any of the other problem sets.
You will need to do all the problem sets before the end of class.
(Time on this slide – 15 min) Time passed 21 min
In-Class Notes
Tell students to finish as much as they can in this time. They will turn in all finished problems but they will get help to understand how to do all of them before the sheet is turned in.
Preparation Notes
Students work independently, in as much as they are able. Struggling students may benefit from partnering with a more experienced and confident student for this exercise.
You have 15 minutes.
Agenda

12. Explore – Expert Groups
You will be split into 6 small groups. Everyone in your group just did the same problem set you did.
You will become an expert on that problem!
Each member of the expert group will create an expert description of how to solve the problem.
Use either a tape diagram, a ratio table, or a shortcut for those tools to solve the problem. Show your work!
(Time on this slide – 2 min) Time passed 23 min
In-Class Notes
Pre-select students for expert groups based on ability. The problems get harder from A – D.
Problem D has extension challenge questions for advanced students.
Preparation Notes
Students will work in expert groups for 10 minutes and then in mixed groups for 15 min.
Here is a key for the Class work so you can check that each expert group has the right answers:
Problem Set A – The Moon and Stars
Answer: 27 star-shaped beads
Problem Set B – Lemonade
Answer: 45 cups lemon juice
Problem Set C – Salad Dressing
Answers:
a.) Completed table
9 3 12
b.) 32 tbsp of salad dressing
Problem Set D – Skate Park
Answer: 3,000 people in favor of the Skate Park
Make sure you can describe how to solve the problem to another person. You may want to practice!
Agenda

13. Explore – Expert Groups
Work together with your expert group to solve the problem using a tool. Show your work. Write a description of what to do. You will have only 10 minutes.
(Time on this slide – 10 min) Time passed 33 min
In-Class Notes
Pass out “expert” worksheets.
Make sure students fill in the information on the “expert” worksheet. This ensures that the conversations are productive.
Preparation Notes
Have copies of Problem D extension challenge problems for advanced students.
Thoughtfully group students so that they can feel very confident about at least one problem.
The problems get harder from A – D.
Agenda

14. Explore – Problem Review: Jigsaw
We are going to do a “Jigsaw” sharing of the problems.
I will mix up the groups. Each new group will include at least one expert on each of the problem sets.
Sometimes there will be more than one expert for a problem in the same group.
(Time on this slide – 3 min) Time passed 36 min
In-Class Notes
Re-sort the students into heterogeneous groups at the end of this slide.
Preparation Notes
Reorganize students into groups of at least A,B,C, and D but you will almost definitely need to have more than one of each Problem type in a group. (Ex A, A, B, C, C, D could be one group. The repetition will be a good experience.)
Agenda

15. Explore – Problem Review: Jigsaw
In your new groups, read each problem together and brainstorm how to solve it. Take a minute or so to think for each problem.
Experts, now it’s your turn to tell the group how you solved the problem. Everyone needs to write a solution on their own papers.
Umm, excuse me, I’m an expert on the problem. Shouldn’t I just tell the group what to do?
Oh, ok. Give them a chance to think about it first. Sure!
You are responsible for having a complete and correct worksheet at the end, so listen carefully!
(Time on this slide – 3 min) Time passed 36 min
In-Class Notes
Re-sort the students into heterogeneous groups at the end of this slide.
Preparation Notes
Reorganize students into groups of at least A,B,C, and D but you will almost definitely need to have more than one of each Problem type in a group. (Ex A, A, B, C, C, D could be one group. The repetition will be a good experience.)
Experts, please wait until your group has brainstormed first before you tell them what you know!
Agenda

16. Explore – Jigsaw Share Jigsaw Share
You may begin sharing. Each person will have 3 minutes.
(Time on this slide – 18 min) Time passed 54 min
In-Class Notes
Keep students on a strict timeline. Cue them each time 3 min has passed.
Stopwatch links to online stopwatch.
Collect class work papers at the end of the sharing.
Preparation Notes
Video link is not exactly the same problem as Problem A but it is very similar. It shows connections between the strategies. You may want to slow down and pause to ask students to reflect on some of the questions in it. Link is:
Optional: Video Review of Problem A
Agenda

17. Explore – Review and Complete
Practice Problems
Wrap it up! Make sure you have solutions for every problem. All work should be complete.
Turn in your work!
(Time on this slide – 2 min) Time passed 56 min
In-Class Notes
Keep students on a strict timeline. Cue them each time 3 min has passed.
Stopwatch links to online stopwatch.
Collect class work papers at the end of the sharing.
Preparation Notes
Video link is not exactly the same problem as Problem A but it is very similar. It shows connections between the strategies. You may want to slow down and pause to ask students to reflect on some of the questions in it. Link is:
Agenda

18. Summary Write your responses in your notebook.
What is one thing you liked about the lesson today?
What is one thing that was difficult today?
(Time on this slide – 3 min) Time passed 59 min
In-Class Notes
This is a quick process of the activity.
Preparation Notes
Is there anything that is still confusing about solving ratio problems (so far)?
Agenda

19. Exit Ticket
Use any tool you wish to solve this problem. Show all your work. Write your responses in your notebook.
The ratio of Grade 6 students to Grade 7 students on a field trip is 7:5. In all, 84 students went on the trip. How many 6th grade students went on the field trip?
(Time on this slide – 3 min) Time passed 62 min
In-Class Notes
Best to pass out half-sheets of notebook paper so that students can turn in this assessment.
Preparation Notes
This is a pretty critical assessment of whether or not students benefitted from the activity.
Agenda

20. 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.

21. 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