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

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

3 *1 st Time Users of 21 st Century Lesson: Click HERE for a detailed description of our project.HERE 21 st 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.

4 Lesson ObjectiveSWBAT find similarities and differences among several ratio problem-solving tools. LO: They will write about the similarities and differences using ratio vocabulary. Lesson DescriptionStudents 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)

5 Lesson VocabularyRatio, equivalent, rate, unit rate, quantity, value MaterialsPosters, markers, graph paper, half sheet paper for Exit Slip ScaffoldingThe 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. EnrichmentThe in-class practice worksheet has extension problems for advanced students. Online Resources for Absent Students How to use unit rates to solve problems: How to use a ratio table to solve proportions: How to use tape diagrams to solve problems: Lesson Overview (2 of 3)

6 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 AfterIn 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 BackgroundHere’s a great resource justifying teaching students to use tools such as these for problem solving: Click “MODEL-DRAWING vs CONVENTIONAL METHODS”

Warm Up SWBAT find similarities and differences among several ratio problem-solving methods. Language Objective: They will write about the similarities and differences using ratio vocabulary. Agenda 7 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 8 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 9 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 table Unit rate Double Number Line Pick one tool and use it to solve this problem on the worksheet.

Launch – Problem Solving 10 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 table Unit rate Double Number Line The answer is 30 minutes. Did you get that? Teacher reference

Launch – Problem Solutions 11 Agenda A racecar travels 60 miles in 40 minutes. At that rate, how much time would it take to travel 45 miles? 60 miles 40 min = 1.5 miles 1 min = 45 miles 30 min miles mins Return to lesson These solution methods have been provided for teacher reference.

Explore - Directions 12 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 13 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 14 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 15 Agenda Stay and Stray How it works

Explore – Poster Presentations: Stay and Stray Agenda 16  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 17  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 18 This is what it looks like after making the posters. The student with the “P” is the first presenter. Poster 1 Poster 2 Poster 5 Poster 3 Poster 4 Poster 6 PP P P P P Group A Group B Group C Group D Group E Group F Then this happens… For teacher reference: What comes next? For teacher reference: What comes next? Click above for info

Teachers: Here are some visuals to better understand this strategy Agenda 19 Poster 1 Poster 2 Poster 5 Poster 3 Poster 4 Poster 6 PP P P P P This is what it looks like when you have the 1 st presentation. Please continue: What comes next? Please continue: What comes next? Go back to the lesson.

Agenda 20 Poster 1 Poster 2 Poster 5 Poster 3 Poster 4 Poster 6 For the second round, someone else will speak. Everyone else will move to the next poster. PP P P P P Please continue: What comes next? Please continue: What comes next? Go back to the lesson. Teachers: Here are some visuals to better understand this strategy

Agenda 21 Poster 1 Poster 2 Poster 5 Poster 3 Poster 4 Poster 6 Continue for 3 rounds. Not everyone will present but they should all be listening as if they will be next. PP P P P P Go back to the lesson. Teachers: Here are some visuals to better understand this strategy

Explore – Poster Presentations: Stay and Stray Agenda 22  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 23  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 2 nd presentation:

Explore – Poster Presentations Agenda 24 Poster Presentations

Explore – Poster Presentation #1 Agenda 25 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 26 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 27 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 28 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 29 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) 30 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 31 Let’s discuss two of these tools. What is something that is the same and something that is different about them. 60 miles 40 mins = 1.5 miles 1 min = 45 miles 30 min miles mins Can you name each of these tools? Unit rate Ratio table Double Number Line Agenda

Summary 32 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 33 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 34 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 Minutes ÷ 2 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 pm

Back to Lesson 35 1 st Time Users of 21 st Century Lessons Welcome to 21 st Century Lessons! We are a non-profit organization that is funded through an AFT (American Federation of Teachers) Innovation Grant. Our mission is to increase student achievement by providing teachers with free world-class lessons that can be taught via an LCD projector and a computer. 21 st Century Lessons are extremely comprehensive; we include everything from warm–ups and assessments, to scaffolding for English language learners and special education students. The lessons are designed into coherent units that are completely aligned with the Common Core State Standards, and utilize research-based best practices to help you improve your students’ math abilities. Additionally, all of our lessons are completely modifiable so you can adapt them if you like. Description of 21 st Century Lessons: Next Slide

36 1 st Time Users of 21 st Century Lessons The lesson that you are currently looking at is part of a unit that teaches the following Common Core Standards: 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. Standards for This Unit Next SlideBack to Lesson

37 1 st Time Users of 21 st Century Lessons In order to properly use 21 st Century Lessons you will need to possess or arrange the following things: Required: PowerPoint for P.C. (any version should work) Note: Certain capabilities in the PowerPoint Lessons are not compatible with PowerPoint for Mac, leading to some loss of functionality for Mac PowerPoint users. An LCD projector Pre-arranged student groups of 2 – (Many lessons utilize student pairings. Pairs should be seated close by and be ready to work together at a moment’s notice. Scissors – at least 1 for every pair Requirements to teach 21 st Century Lessons: Next SlideBack to Lesson

38 1 st Time Users of 21 st Century Lessons Computer speakers that can amplify sound throughout the entire class “Calling Sticks” – a class set of popsicle sticks with a student’s name on each one A remote control or wireless presenter tool– to be able to advance the PowerPoint slides from anywhere in your classroom Personalize PowerPoints by substituting any names and pictures of children we included in the PowerPoint with names and pictures of your own students. Since many lessons utilize short, partner-processing activities, you will want a pre- established technique for efficiently getting your students’ attention. (“hands- up”, Count from “5” to “0” etc.) Project onto a whiteboard so you or your students can solve problems by hand. (Lessons often have a digital option for showing how to solve a problem, but you may feel it is more effective to show the work by hand on a whiteboard.) Internet connectivity – without the internet you may not have full functionality for some lessons. Strongly Suggested to teach 21 st Century Lessons: Next SlideBack to Lesson

39 1 st Time Users of 21 st Century Lessons We suggest spending minutes reviewing a lesson before teaching it. In order to review the lesson run the PowerPoint in “Slideshow “- Presenters View and advance to the “Lesson Overview” slide. By clicking on the various tabs this slide will provide you with a lot of valuable information. It is not necessary to read through each tab in order to teach the lesson, but we encourage you to figure out which tabs are most useful for you. Note: All of our lessons are designed to be taught during a minute class. If your class is shorter than this you will have to decide which sections to condense/remove. If your class is longer we suggest incorporating some of the “challenge” questions if available. Lesson Preparation (Slide 1 of 2) Next Slide Back to Lesson

40 1 st Time Users of 21 st Century Lessons After reviewing the overview slide, click your way through the PowerPoint. As you go, make sure to read the presenter note section beneath each slide. The note section is divided into two sections: “In-Class Notes” and “Preparation Notes.” The In-Class Notes are designed to be concise, bulleted information that you can use “on the fly” as you teach the lesson. Included in In-Class Notes are: a) a suggested time frame for the lesson, so you can determine whether you want to speed up, slow down, or skip an activity, b) key questions and points that you may want to bring up with your students to get at the heart of the content, and c) answers to any questions being presented on the slide. The Preparation Notes use a narrative form to explain how we envision the activity shown on the slide to be delivered as well as the rationale for the activity and any insight that we may have. Lesson Preparation (Slide 2 of 2) Next SlideBack to Lesson

41 1 st Time Users of 21 st Century Lessons There are several features which have been incorporated into our PowerPoint lessons to help make lessons run more smoothly as well as to give you access to additional resources during the lesson should you want them. These features include: Agenda Shortcuts – On the agenda slide, click on any section title and you will advance to that section. Click the agenda button on any slide to return to the agenda. Action Buttons – On certain slides words will appear on the chalk or erasers at the bottom of the chalkboard. These action buttons give you access to optional resources while you teach. The most common action buttons are: Scaffolding – gives on-screen hints or help for that slide Answers – reveals answers to questions on that slide Challenge – brings up a challenge questions for students Agenda – will return you to the agenda at the beginning of the lesson Features built into each PowerPoint lesson Back to Lesson

The goal of 21 st 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 st Century Lessons The goal… 42

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 21 st Century Lessons Brian Connor – Technology Coordinator 21 st Century Lessons The people… 43