1. 21 st Century Lessons Comparing Ratios using Tables and Graphs 6.RP.3 1

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

3. 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. 4 Lesson ObjectiveObjective: Students will compare ratios using unit rates, tables and graphs. Language Objective: Students will review and apply vocabulary like ratio, ratio table, rates, and unit rates. Lesson DescriptionThis lesson asks students to compare ratios using tables and also graphs. This lesson assumes that students have reviewed how to graph points from a table but will provide a brief review prior to tackling comparing ratios with tables. We will focus on using unit rates to help students compare different real-world examples. The next lesson in this unit will focus on more complicated examples of using tables to compare real-world examples. Lesson Overview (1 of 3)

5. 5 Lesson Vocabulary Ratio Table – a table that include two quantities being compared Ratio – a comparison of two different values Unit Rate – a comparison of two different values where the second value is 1 unit Materials -Class set of notes -Rulers for Graphing Scaffolding We will use frequent partner talk and pair-shares to review ratio tables. We will then use practice from the Warm-Up to help students practice using tables to find a unit rate. The class notes can be provided to students with or without answers as an accommodation. Enrichment For graphing examples, students with strong skills may want to graph both ratios on one coordinate plane, almost like a system of equations. - Teachers can provide alternative examples for students to practice this higher skill, examples can be found on websites. Online Resources for Absent Students http://www.indiana.edu/~atmat/units/ratio/ratio_t3.htm http://www.aaamath.com/rat.htm http://www.internet4classrooms.com/skill_builders/ratio_proportion_ math_sixth_6th_grade.htm Lesson Overview (2 of 3)

6. 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. 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 AfterBefore this lesson, students have used tables to find ratios of real- world examples. This lesson will extend student learning by asking students to compare different ratios using a ratio table and graphing. Students will also learn which tools (graphs or tables) are best for them to compare real-world ratios. Topic BackgroundToday’s lesson relates to the real-world in many ways; we will use money and speed as two major real-world examples. Further, we will focus on how to use tables to extrapolate data when given tables.

7. Warm Up Agenda 7 The fastest train in the world is in China. The train can travel 1,400 miles in 4 hours. If you were on this train, how many miles would you travel in 3 hours? Hint: We may need to use a table to help us!! Objective: Students will compare ratios using unit rates, tables and graphs. Language Objective: Students will review vocabulary relating to graphs like origin, x-axis, y-axis and positive slope. Answer: You will travel 1,050 miles on the train! Wow!

8. Agenda: 1) Warm Up (Individual) 2) Launch – Reebok versus Nike Sneakers (Partner Work and Whole Class) 3) Explore – Speed and Price (Partner Work) 4) Summary (Whole Class) 5) Practice (Partner Work and Whole Class) 6) Assessment (Individual) 8 Objective: Students will compare ratios using unit rates, tables and graphs. Language Objective: Students will review vocabulary relating to graphs like origin, x-axis, y-axis and positive slope.

9. Launch – Partner Work Agenda 9 Create a table and graph to represent this situation. Kevin is captain of his basketball team this year, and is researching prices for sneakers for his team of 12 players. Some players on Kevin’s team want to buy sneakers and some do not. Kevin calls Reebok and finds that the price for 12 pairs for sneakers is $816. Help Kevin determine how much money he will need for each player ! Answers

10. Answers for Reebok Shoes Agenda 10 Kevin is captain of his basketball team this year, and is researching prices for sneakers for his team of 12 players. Some players on Kevin’s team want to buy sneakers and some do not. Kevin calls Reebok and finds that the price for 12 pairs for sneakers is $816. Help Kevin determine how much money he will need for each player !

11. Launch – Partner Work Agenda 11 Follow-up Questions: 1)Did you label your x-axis, y-axis and graph? 2)What is the cost of each pair of sneakers? 3)How much will Kevin’s basketball team pay for 9 pairs of sneakers? 4)If two more people join the team, how much will 14 pairs of sneakers costs in total? Answers

12. Launch – Partner Work Agenda 12 Follow-up Questions: 1)Did you label your x-axis, y-axis and graph? Yes, because we are brilliant mathematicians! 2)What is the cost of each pair of sneakers? $68 per pair 3)How much will Kevin’s basketball team pay for 9 pairs of sneakers? $612 4)If two more people join the team, how much will 14 pairs of sneakers costs in total? $952

13. Launch Continued Agenda 13 Kevin also calls Nike to ask how much Air Jordan’s will cost. Nike only sells Air Jordan sneakers in sets of 4 for $288. Help Kevin determine how much 12 pairs of sneakers will cost using a table and graph. Answers

14. Answers for Nike Question: Agenda 14 Kevin also calls Nike to ask how much Air Jordan’s will cost. Nike only sells Air Jordan sneakers in sets of 4 for $288. Help Kevin determine how much up to 12 pairs of sneakers will cost using a table and graph.

15. Launch – Partner Work Agenda 15 Follow-up Questions: 1)How is this Nike question different than the previous Reebok question? 2)What is the cost of each pair of Nike sneakers? 3)How much will Kevin’s basketball team pay for Nike sneakers if all 12 people from his team want the shoes? 4)If two more people join the team, how much will 14 pairs of Nike sneakers cost in total? Answers

16. Launch – Partner Work Agenda 16 Follow-up Questions: 1)How is this Nike question different than the previous Reebok question? We need to label our own table and graph 2)What is the cost of each pair of Nike sneakers? $72 3)How much will Kevin’s basketball team pay for Nike sneakers if all 12 people from his team want the shoes? $864 4)If two more people join the team, how much will 14 pairs of Nike sneakers cost in total? $1,008

17. Challenge Question Agenda 17 What brand of shoes will cost Kevin’s team the least amount of money? Right on! Let’s look at the unit rate! Reebok ShoesNike Shoes We need to figure out how to compare the Reebok and Nike shoes. Any ideas? Man, Nike shoes are expensive! Do you think they will still be more expensive even for 15 pairs? Why or why not? Reebok will always be cheaper!

18. Explore – Partner Work Agenda 18 Jessica and Jacque both are on track team. Use the tables below to determine who had the fastest time? Let’s find the unit rate to compare Jessica and Jacque’s times! Answers Jacque’s Time Jessica’s Time

19. Jessica and Jacque both are on track team. Use the tables below to determine who had the fastest time? Jacque’s Time Jessica’s Time Let’s find the unit rate to compare Jessica and Jacque’s times! 33 22 Jessica’s pace is faster than Jacque’s pace! Explore – Partner Work Agenda 19

20. Explore – Partner Work Agenda 20 Mei and Chris are both selling candy bars for a school fundraiser. Are they selling them at different rates? Answers

21. Explore – Partner Work Agenda 21 Mei and Chris are both selling candy bars for a school fundraiser. Are they selling them at different rates? Mei is selling her candy bars at a lower rate than Chris. Chris is charging $0.25 more for each candy bar. 1.75 1.50

22. Summary – Partner and Whole Class 22 Agenda Answer the following question with a partner, and be prepared to share your opinion with the class. What is a real-world situation where using a table would help you compare numbers?

23. Practice – Partner Work 23 Agenda

24. Practice Answers – Whole Class 24 Agenda

25. Kati and Ling are both riding their bikes. The table below shows how far they have traveled (in miles) over a certain time (in minutes). Who is slower? Kati’s Ride Ling’s Ride Kati is slower than Ling by 1 minute! Total MilesMinutes 1 224 448 MinutesTotal Miles 1 333 555 Total MilesMinutes 112 224 448 MinutesTotal Miles 111 333 555 Assessment (Individual) 25 Agenda

26. Back to Lesson 26 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

27. 27 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: Standards for This Unit Next SlideBack to Lesson

28. 28 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

29. 29 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

30. 30 1 st Time Users of 21 st Century Lessons We suggest spending 30-45 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 45-55 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

31. 31 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

32. 32 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

33. 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… 33

34. 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… 34