1. 21 st Century Lessons Ratio Tables and Graphing Primary Lesson Designer(s): Stephanie Conklin 1

2. Warm Up Agenda 2 Complete these problems: 1) Label the x-axis, y-axis and origin. 2) Plot the point (2,4) 3) Plot the point (-2, -4) 4) How are the two points related? x-axis y-axis The origin is the point (0,0) The points are the same distance from the origin. Objective: Students will use tables to graph real-world rate examples. Language Objective: Students will review vocabulary relating to graphs like origin, x-axis, y-axis and positive slope.

3. Agenda: 1) Warm Up (Individual) 2) Launch - Chocolate Chip Cookies (Whole Class and Partner Work) 3) Explore – Tour de France Example (Partner Work) 4) Summary (Whole Class) 5) Practice (Partner Work and Whole Class) 6) Assessment (Individual) 3 Objective: Students will use tables to graph real-world rate examples. Language Objective: Students will review vocabulary relating to graphs like origin, x-axis, y-axis and positive slope.

4. Launch Agenda 4 Chocolate Chips Cookies Recipe 1 cup butter, softened 1 cup white sugar 1 cup packed brown sugar 2 eggs 2 teaspoons vanilla extract 3 cups all-purpose flour 1 teaspoon baking soda 2 teaspoons hot water 1/2 teaspoon salt 2 cups chocolate chips Sarah and Tyreak are planning a bake sale to raise money for their local food shelter. They want to make A LOT of chocolate chip cookies! Here is the recipe for chocolate chip cookies:

5. Launch – Partner Work Agenda 5 Sara and Tyreak decide that they will need more than 1 batch of cookies of their sale. Answer the questions below to help Sara and Tyreak! 1) In 1 batch of cookies, how many cups of white sugar will be needed? 2) In 4 batches of cookies, how many cups of white sugar will be needed? 3) How did you get your answer in #2? Be ready to explain! 4) How many eggs do Sara and Tyreak need to make 3 batches of cookies? 5) What do you think is the most important ingredient to making chocolate chip cookies?

6. Launch – Partner Work Agenda 6 Sara and Tyreak decide that they will need more than 1 batch of cookies of their sale. Answer the questions below to help Sara and Tyreak! 1) In 1 batch of cookies, how many cups of white sugar will be needed? 2) In 4 batches of cookies, how many cups of white sugar will be needed? 3) How did you get your answer in #2? Be ready to explain! 4) How many eggs do Sara and Tyreak need to make 3 batches of cookies? 5) What do you think is the most important ingredient to making chocolate chip cookies? 1 cup of white sugar 4 cups of white sugar 6 eggs for 3 batches of cookies

7. Launch – Whole Class Agenda 7 Sara and Tyreak decide they will make as many batches of cookies as they can! However, they only have 12 cups of chocolate chips! How many batches can they make? Let’s use one of our tools to help us!A TABLE!!! Hey, wait! Have you used a table before? If so when? Mmmm cookies! Hey, wait! Have you used a table before? If so when? Mmmm cookies!

8. Launch – Whole Class Agenda 8 We can use a table to help use organize information, especially when we need a lot of information! Create a table that compares # of batches to cups of chocolate chips. What always goes in the first row of a table? What always goes in the first row of a table? # of batches Cups of chocolate chips What do we already know about 1 batch of cookies and cups of chocolate chips? What do we already know about 1 batch of cookies and cups of chocolate chips? 1 2 Let’s fill in the rest of the chart, and follow the pattern! 2 4 3 6 4 8 5 10 6 12 0

9. Launch – Whole Class Agenda 9 Let’s answer our question! How many batches of chocolate chip cookies can Sara and Tyreak make with 12 cups of chocolate chips? 0 0 # of batches Cups of chocolate chips 1 2 2 4 3 6 4 8 5 10 6 12 Sara and Tyreak can make 6 batches of cookies!

10. Launch – Whole Class Agenda 10 Let’s go one step further and GRAPH our table! # of batches Cups of choc. chips 00 12 24 36 48 510 612 What 3 things do we need to label on our graph? # of batches Cups of choc. chips Batches of Choc. Chip Cookies

11. Launch – Whole Class Agenda 11 Let’s go one step further and GRAPH our table! # of batches Cups of choc. chips 00 12 24 36 48 510 612 # of batches Cups of choc. chips Batches of Choc. Chip Cookies

12. Explore – Partner Work Agenda 12 In the Tour de France, athletes from all over the world compete to be the fastest cyclist by riding everyday for up to 8 hours! In last year’s race, American cyclists averaged a rate of 75 miles in 3 hours. Using this information, fill in the chart below and create a graph! Then answer the questions on your hand-out!. HoursTotal Miles Biked 0 1 2 3 4 5 6 7 8

13. Explore Agenda 13 In the Tour de France, athletes from all over the world compete to be the fastest cyclist by riding everyday for up to 8 hours! In last year’s race, American cyclists averaged a rate of 75 miles in 3 hours. HoursTotal Miles Biked 00 125 250 375 4100 5125 6150 7175 8200 Hours Miles per hour Tour de France Race

14. Explore – Partner Work Agenda 14 Use the Tour de France graph and table to answer the following questions! 1) In 2 hours, how far will the cyclists have gone? 2) If a cyclist traveled 125 miles, how many hours has he been biking? 3) In questions #1 and #2, did you use the graph or the table? Why? 4) Estimate, to the nearest hour, how long it would take a cyclist to go 170 miles? 5) Estimate how many miles a cyclist would bike after 2 hours and 30 minutes? Explain how you got your answer. 6) What does the first point (0,0) on the graph represent?

15. Explore – Check your answers! Agenda 15

16. Summary – Partner and Whole Class 16 Agenda Answer the following question with a partner, and be prepared to share your opinion with the class. What is a better way to represent a rate, a table or graph? Explain your choice!

17. Practice – Partner Work 17 Agenda

18. Practice Answers – Whole Class 18 Agenda

19. Assessment (Individual) 19 Agenda MinutesTotal Miles 00 10 2014 30 40 50 60 In 20 minutes, Jacob drove 14 miles. Fill in the table to answer this question: How many miles did Jacob drive in 1 hour? MinutesTotal Miles 00 107 2014 3021 4028 5035 6042 Jacob drove 42 miles in 1 hour.

20. Back to Lesson 20 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

21. 21 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

22. 22 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

23. 23 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

24. 24 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

25. 25 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

26. 26 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

27. 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… 27

28. 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… 28

29. 29 *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.

30. 30 Lesson ObjectiveObjective: Students will use tables to graph real-world rate examples. Language Objective: Students will review vocabulary relating to graphs like origin, x-axis, y-axis and positive slope. Lesson DescriptionThis lesson will first review students knowledge of applying ratio tools to solve real world problems. We will first look at a recipe and ask students to answer questions about making multiple batches of cookies. Then from this question, we will launch in a review of creating ratio tables, and then finally will graph this information to show a linear relationship. We will complete 1 example on cookies and graphing as a whole class, and then students will work in pairs to try a different problems on speed. Lastly, students will work on a challenge problem (negative slope) to graph their problems and answer follow-up questions. A summary and assessment, along with class work will be provided as a means to assess student learning. Lesson Overview (1 of 3)

31. 31 Lesson VocabularyRatio Table – a table that include two quantities being compared Coordinate Plane – the x-y axis where we can graph points (x,y) X-axis: horizontal line on a coordinate plane Y-axis: vertical line on a coordinate plane Materials-Class set of notes -Rulers ScaffoldingWe 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 graphing coordinate points. The class notes can be provided to students with or without answers as an accommodation. EnrichmentStudents will identify positive and negative slopes when graphing ratio tables. - 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.webmath.com/gpoints.html http://www.khanacademy.org/math/algebra/algebra- functions/e/graphing_points Lesson Overview (2 of 3)

32. 32 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 help identify equivalent ratios and also practiced finding ratios using a variety of tools. This is one of the more difficult skills in this unit, and after this students will continue their study of lines and proportionality in 7 th grade standards. Topic BackgroundToday’s lesson relates to the real-world in many ways; we will use recipes and speed as two major real-world examples. Further, we will focus on how to find total distance traveled using graphs.