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

This project is funded by the American Federation of Teachers.

Warm Up y-axis x-axis The points are the same distance from 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. y-axis  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 (5 min) Time passed In-Class Notes This Do Now will allow for students to review how to graph coordinate points. This also is an important time for teachers to pause and see which students do not yet have this skill. In this lesson we will be graphing points for positive integers only but the internet links will act as a review for students who may need more reinforcement. For question #4, we have included one possible observation but teachers should call on students to hear other answers – an answer like a reflection or rotation would be very exciting! Preparation Notes The points are the same distance from the origin. The origin is the point (0,0) Agenda

Agenda: 1) Warm Up (Individual) 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. 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) (1 min) Time passed In-Class Notes Teachers can review objective with students and agenda for the day. Preparation Notes

Launch 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: 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 (1 min) Time passed In-Class Notes For this launch, teachers should read through this problem – and may want to ask for student volunteers to read. Preparation Notes Class notes for each students Agenda

Launch – Partner Work 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? (5 min) Time passed In-Class Notes Teachers should hand out scaffolded class notes at this time. For this launch, teachers should pre-read questions with students and then give them 3-4 mins to answer questions in partners. Preparation Notes Class notes for each students Agenda

Launch – Partner Work 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 (3-5 min) Time passed In-Class Notes Students can write answers on board or teachers can call on students for answers using call sticks. There are no answers for #3 and #5 as these are questions that we would like students to answer themselves. We will use question #5 to launch into using tables to organize our work. Preparation Notes Class notes for each students 6 eggs for 3 batches of cookies Agenda

Launch – Whole Class 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! (1-2 min) Time passed In-Class Notes Teachers can ask a student to read the question and then discuss as a whole group when they have used tables and why tables are important. We will fill in the table in the next slide. Preparation Notes Class notes for each students Agenda

Launch – Whole Class 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. # of batches Cups of chocolate chips 0 0 1 2 2 4 3 6 4 8 What do we already know about 1 batch of cookies and cups of chocolate chips? 5 10 Let’s fill in the rest of the chart, and follow the pattern! (3 min) Time passed In-Class Notes Students should fill in their table as the teacher leads them through filling in the table. The first question that cookie monster asks, “What do we always put in first row of a table” – we want to remind students to always fill in the first row with labels, i.e. # of batches and cups of choc. Cups. If possible teachers can ask students to fill in each part of the table. Teachers should point out that we keep increasing our cups by 2 each time we make a new batch of cookies. Preparation Notes Class notes for each students 6 12 What always goes in the first row of a table? Agenda

Launch – Whole Class Let’s answer our question! How many batches of chocolate chip cookies can Sara and Tyreak make with 12 cups of chocolate chips? # of batches Cups of chocolate chips 1 2 2 4 3 6 4 8 5 10 6 12 (3-5 min) Time passed In-Class Notes Students try to answer this question on their own using the table. Teachers can ask students to write in their answer on their class notes. Preparation Notes Class notes for each students Sara and Tyreak can make 6 batches of cookies! Agenda

Launch – Whole Class Let’s go one step further and GRAPH our table! Batches of Choc. Chip Cookies # of batches Cups of choc. chips 1 2 4 3 6 8 5 10 12 Cups of choc. chips (3 min) Time passed In-Class Notes Students should label their graphs in class notes and then try to plot the points along with teachers The next slide has the graph with correct points plotted but teachers may want to ask students to come to the board to plot points or to work on plotting as a whole group. The next slide will show the graph already completed. Preparation Notes Class notes for each students # of batches What 3 things do we need to label on our graph? Agenda

Launch – Whole Class Let’s go one step further and GRAPH our table! Batches of Choc. Chip Cookies # of batches Cups of choc. chips 1 2 4 3 6 8 5 10 12 Cups of choc. chips (3 min) Time passed In-Class Notes Students should label their graphs in class notes and then try to plot the points along with teachers The next slide has the graph with correct points plotted but teachers may want to ask students to come to the board to plot points or to work on plotting as a whole group. Preparation Notes Class notes for each students # of batches Agenda

Explore – Partner Work 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!. Hours Total Miles Biked 1 2 3 4 5 6 7 8 (3 min) Time passed In-Class Notes Teachers should leave this up for students to view as they work with their partners. The next slide shows the graph with line already so teachers may want to help scaffold students work by asking for students to first fill in table, then to plot points and label graph and lastly to connect points. Teachers may need to help students with table, and remind them to first find the unit rate before they can determine the pattern. Preparation Notes Class notes for each students Agenda

Explore Tour de France Race Hours 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. Tour de France Race Hours Total Miles Biked 1 25 2 50 3 75 4 100 5 125 6 150 7 175 8 200 Miles per hour (3 min) Time passed In-Class Notes Students can check their answer first for the table and then for the graph. Teachers can also review with students how to connect lines and plot points using the previous slides. Then students can try to answer the questions on the next slide. Teachers should reinforce that this line will continue on with a positive slope. Preparation Notes Class notes for each students Hours Agenda

Explore – Partner Work 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? (5 min) Time passed In-Class Notes Teachers can pre-read the questions with students or have students begin work on their own. The next slide will show answers for some of the questions so teachers may want to stay on this slide before jumping to all the answers. Teachers may want to use calling sticks to hear student responses. For question #3, students can use either table or graph – we will return to this question for our summary. For question #6, we hope that students realize this point is the origin and also the point where no one has started time or started biking. Preparation Notes Class notes for each students Agenda

Explore – Check your answers! (3 min) Time passed In-Class Notes Students can check their answers. If teachers have time, they may want to have students write answers on previous slide or call out each questions’ answer one at a time. Then, teachers can address each solution and offer an opportunity for discussion for each question. Please note that question #3 is an opinion questions, and teachers may want to use calling sticks to hear student responses. Also, there is no explanation for #5, this again is a great chance for teachers to call on students. Preparation Notes Class notes for each students Agenda

Summary – Partner and Whole Class 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! (5 min) Time passed In-Class Notes Teachers should give students 2-3 minutes to discuss and then take a vote on who likes tables or graphs better. Teachers should ask if any student thinks that both ways are equal or if there is another tool that we used earlier (i.e. tape diagrams) that they liked better. The goal of this question is really to help students see that both tools, tables and graphs, can useful in their own ways (i.e. table for seeing actual values and graph for seeing big picture or trend of data). Preparation Notes None Agenda

Practice – Partner Work (10 min) Time passed In-Class Notes Teachers can give students time to work on the class work in small groups or individually. Teachers may want to post the answers to the table in Nichole’s running question within the first couple of minutes to ensure that students are on the right track. Preparation Notes Class work Agenda

Practice Answers – Whole Class (2-3 min) Time passed In-Class Notes Teachers can post answers as students work or review once time for partner work is done. If teachers have time, they may want to have students write answers on previous slide or call out each questions’ answer one at a time. Then, teachers can address each solution and offer an opportunity for discussion for each question. Students should be sure to check their tables first and then ensure that their graphs are correct based on that. Preparation Notes Class work Agenda

Assessment (Individual) In 20 minutes, Jacob drove 14 miles. Fill in the table to answer this question: How many miles did Jacob drive in 1 hour? Minutes Total Miles 10 20 14 30 40 50 60 Minutes Total Miles 10 7 20 14 30 21 40 28 50 35 60 42 Jacob drove 42 miles in 1 hour. (3-4 min) Time passed In-Class Notes Teachers can ask students to make their own table and then fill in the chart. Teachers may want to remind students that 60 minutes = 1 hours of time. Students can complete this question on an index card, sticky note, etc. to be collected or the teacher can call on students to volunteer to fill in the chart. Preparation Notes None Agenda