21 st Century Lessons Comparing Ratio Problem- Solving Tools Primary Lesson Designer: Lisa Schad 1

21st Century Lessons

Comparing Ratio Problem-Solving Tools

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 SWBAT find similarities and differences among several ratio problem-solving tools. LO: They will write about the similarities and differences using ratio vocabulary.

Lesson Description Students have learned about a variety of tools for solving ratio problems and have had some practice using them. To deepen their understanding of the relationships of equivalent ratios, scaling and unit rate students will use at least two different methods to solve a single problem. Then they will listen and speak about a variety of methods. Finally they will practice using an unfamiliar method and compare it to a more familiar one. Students will understand that each tool relies on the same fundamental understandings of a ratio – that the two quantities change in relation to each other, that a ratio is scalable, that multiplication and division allow you to find equivalent ratios, and that you can interpolate any number of ratios in between two known ratios.

Lesson Overview (1 of 3)

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Lesson Vocabulary Ratio, equivalent, rate, unit rate, quantity, value

Materials Posters, markers, graph paper, half sheet paper for Exit Slip

Scaffolding The Stay and Stray strategy for sharing methods of problem solving is intended to encourage speaking and very active listening in the lesson and is a wonderful strategy for ELL students. Working in groups allows reluctant students or those with special considerations to get extra help.

Enrichment The in-class practice worksheet has extension problems for advanced students.

Online Resources for Absent Students

How to use unit rates to solve problems: http://www.eduplace.com/math/mathsteps/6/e/How to use a ratio table to solve proportions:http://video.google.com/videoplay?docid=3077649462844128257How to use tape diagrams to solve problems:http://www.thinkingblocks.com/tb_ratios/ratios.html


http://www.eduplace.com/math/mathsteps/6/e/

http://video.google.com/videoplay?docid=3077649462844128257

http://video.google.com/videoplay?docid=3077649462844128257

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

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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.

Before and After In this unit students have learned how to use a variety of tools for solving ratio and rate problems: tape diagrams, ratio tables, unit rate, and double number lines. This lesson pulls most of these tools together for comparison. (Tape diagrams are only used when the quantities have the same units.) In later lessons students will not be cued as to which tool to use.

Topic Background Here’s a great resource justifying teaching students to use tools such as these for problem solving: http://thesingaporemaths.comClick “MODEL-DRAWING vs CONVENTIONAL METHODS”

http://thesingaporemaths.com/

Warm UpSWBAT find similarities and differences among several ratio problem-solving methods. Language Objective: They will write about the similarities and differences using ratio vocabulary.

Agenda7

25 World Records were broken at the 2012 Summer Olympics.Use these rounded times to find the unit rate of each record.

1. The US Women’s team ran the 400 meter relay in just over 40 seconds.What was their unit rate?

2. Dana Vollmer (US) swam the 100 meter

breaststroke in a bit more than 50 seconds.

What was her unit rate?

3. Is the rate of the Women’s relay actually faster or slower than the unit rate you found? How about Vollmer’s?

Agenda:

1) Warm Up 2) Launch – Racecar Problem – independent & partner

3) Explore – Stay and Stray Share – small groups

4) Summary – Compare tools – independent (or partners), whole class

5) Exit Slip - independent

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SWBAT find similarities and differences among several ratio problem-solving methods. Language Objective: They will write about the similarities and differences using ratio vocabulary.

Launch – Think, Pair, Share

Agenda

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A racecar travels 60 miles in 40 minutes. At that rate, how much time would it take to travel 45 miles?

What tool could you use to solve this problem?

Ratio tableRatio table Unit rateUnit rate Double Number LineDouble Number Line

Pick one tool and use it to solve this problem on the worksheet.

Launch – Problem Solving

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Agenda

A racecar travels 60 miles in 40 minutes. At that rate, how much time would it take to travel 45 miles?

Now pick another tool and solve the problem again!

Ratio tableRatio table Unit rateUnit rate Double Number LineDouble Number Line

The answer is 30 minutes. Did you get that?

Teacher referenceTeacher reference

Explore - Directions

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Agenda

You will be put into one of 6 groups.

Briefly share your work with each other. Count how many different tools were used at your table.

Your teacher will assign each group one tool to present.

Your group will make a poster presentation on how to use that tool for the racecar problem.

Explore – Poster-Making

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Agenda

Quickly make a poster that shows how to use the tool you are presenting.

• Put the tool name as the title of the poster.• Show every step to solve the problem.• Circle the answer. Make sure to put the units.• Put the name of everyone in the group on the poster.• You have 10 minutes. Tool: Ratio Table• Go!

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

Explore – Poster Presentation Practice

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Agenda

Each student in the group must be able to present the poster to another group of students.

• Take turns explaining the poster.• Make sure each student can explain how to use that tool to solve the problem.

• You have 5 minutes.

Tool: Ratio Table


Explore – Stay and Stray

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Agenda

Stay and StrayHow it works

Explore – Poster Presentations: Stay and Stray

Agenda

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You will travel around the classroom looking at posters and hearing presentations.

Before we start, make sure that everyone in the group is capable of explaining how to find the answer to the problem on the poster using the tool you were assigned.

What we are doing is called “Stay and Stray”

Your job is to listen very carefully to each presentation because you might have to give the presentation for that poster to the next group, even if you didn’t make it.


Agenda

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There are six stations in the classroom. Each tool will have two posters.

The posters are numbered 1 – 6.

There are six small groups that will start off standing at the station where their poster is hung.

The small groups are lettered A – F.


Agenda

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This is what it looks like after making the posters. The student with the “P” is the first presenter.

Poster 1Poster 1 Poster 2Poster 2Poster 5 Poster 5

Poster 3Poster 3Poster 4 Poster 4

Post

er 6

Post

er 6

P P

P

PP

P

Group A Group B

Group C

Group CGroup D Group DGroup EG

roup

FG

roup

F

Then this happens…

For teacher reference: What comes next?

For teacher reference: What comes next?

Click above for info


Agenda

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One person from each group will be chosen to present your poster for the first time. Everyone else in the group will travel to the next poster in the sequence for the first presentation. Remember: When you listen to a presentation you must pay very close attention. You may be chosen to present the poster to the next group of students.

Before the first presentation:


Agenda

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One person from each group standing in front of a poster will be chosen to present the poster for the second round of presentations. Everyone else in the group will travel to the next poster in the sequence for the second presentation.

If you have already presented one time you will not present a second time even if it sounds like you.

The teacher will describe the person who will present.

Before the 2nd presentation:

Explore – Poster Presentations

Agenda

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Poster Presentations

Explore – Poster Presentation #1

Agenda

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Are you ready? The person in each group who will be the first presenter is …

The oldest student in each group.

If you are not the presenter then move to the next poster in the sequence.

That is, if you made Poster #1, then you should be at Poster #2 (unless you are presenting Poster #1). People who made #2 should be at Poster #3. Etc.

You may begin the presentation. You have 5 minutes.



Agenda

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Ok, time is up. It is time to determine who is the next presenter for the poster in front of you. That person is …

The student whose birthday is earliest in the year.

Everyone else will move on to the next poster in the sequence.

Move to your next poster.


Agenda

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Now presenters you will have 4 minutes to explain how to get the answer using the tool on your poster.

Everyone else, listen carefully. You may be the next presenter. Ask good questions if you don’t understand how to get the answer or how to use the tool on the poster.




Agenda

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Ok, time is up. It is time to determine who is the next presenter for the poster in front of you. That person is …

The student who has the longest hair.

Now everyone besides the presenter will move on to the next poster in the sequence.

Move to your next poster.

If the person being described has already presented then don’t consider that person. Choose among the remaining group members.


Agenda

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Now presenters you will have 3 minutes to explain how to get the answer to the question on your poster.

Everyone else, listen carefully. You will use this tool to solve problems later.


Summary – Individual (or partners)

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8 You will now compare and contrast two of the tools.8 Pick any two tools. Write their names on the lines.8 Find some ways they are the same and some ways they are different. You may work with a partner if it helps.8 Fill in the chart with some bullet points.

Agenda

Summary – Whole Class Discussion

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Let’s discuss two of these tools. What is something that is the same and something that is different about them.

60 miles40 mins = 1.5 miles

1 min = 45 miles30 min

0

0

60

40

30

20

15

10

45

30

milesmins

Can you name each of these tools?

Can you name each of these tools? Unit rateUnit rate

Ratio tableRatio table Double Number LineDouble Number Line

Agenda

Summary

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Agenda

Now use your bullet points to write sentences. Make sure you use ratio vocabulary words. Click forward for word bank.

Ratio Word Bank: ratio rate equivalent value unit rate quantity

Ratio Word Bank: ratio rate equivalent value unit rate quantity

Exit Slip

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Agenda

Jaden noticed that he read 16 pages in 32 minutes last night. If his book has 72 pages left, how long will it take him to finish the book if he continues to read at that rate?

Use any tool you like to solve this problem. Show all your work.

Challenge: If he starts at 7:45 pm and reads straight through to the end, at what time will he finish, at this rate?


Exit Slip

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Agenda

Jaden noticed that he read 16 pages in 32 minutes last night. If his book has 72 pages left, how long will it take him to finish the book if he continues to read at that rate?

Pages 16 8 4 36

Minutes 32 16 8 72

÷ 2

÷ 2

÷ 2

÷ 2

X 9

X 9

Answer: 36 minutes Challenge: If he starts at 8:00 pm and reads straight through to the end, at what time will he finish, at this rate?


7:45 pm + 36 minutes = 9:21 pm7:45 pm + 36 minutes = 9:21 pm

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

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Documents

21 st Century Lessons Comparing Ratio Problem- Solving Tools Primary Lesson Designer: Lisa Schad 1