Post on 17-Jan-2016
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
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.
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”
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!
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.
Explore – Poster Presentations: Stay and Stray
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.
Explore – Poster Presentations: Stay and Stray
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
Explore – Poster Presentations: Stay and Stray
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:
Explore – Poster Presentations: Stay and Stray
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.
Explore – Poster Presentation #2
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.
Explore – Poster Presentation #2
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.
You may begin the presentation. You have 4 minutes.
Explore – Poster Presentation #3
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.
Explore – Poster Presentation #3
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.
You may begin the presentation. You have 3 minutes.
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
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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?
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?
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
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
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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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