21 st Century Lessons Introduction to Ratio Tables 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 Objective Content Objective: SWBAT solve ratio problems by using a ratio table. Language Objective: They will write about their understanding of ratio equivalence. Lesson Description The lesson begins with a review of the ratios for Abby and Zacks orange paint. These characters will continue to present overarching context for the problem solving lessons. They will also watch a short video that showcases ratios in use in everyday life. The main idea that students should understand is that equivalent ratios preserve the flavor in a recipe situation. Therefore equivalent ratios are not only equivalent because of math, but because in real life they are the same taste just more or less total quantity. There is an overarching question that is introduced before the mini- lesson that can be solved using the tool they learn today, ratio tables. Students will be shown how ratio tables are created based on information in a problem. They will have a guided practice with a lot of partner work. They will also practice independently. At the end of the lesson, for the exit ticket, students revisit the problem introduced before the mini-lesson and solve it using the ratio table tool. Lesson Overview (1 of 3) 5 Lesson Vocabulary Ratio a relationship between two or more amounts Ratio table a model for organizing equivalent ratios. Materials No additional materials outside of a notebook and pen/pencil for students. Scaffolding Students who require additional support will be aided by the multiple opportunities to check their work with a partner (or small group). Visual tools like the ratio table are an excellent aid to students with learning differences. ELL students will benefit from the opportunities to speak and write about the content. Enrichment Advanced students can focus on solving problems with both tools learned so far, tape diagrams and ratio tables, and look for similarities and differences. Push students to see the multiplicative nature of the solution strategies as well as shortcuts multiplication provides. Online Resources for Absent Students Ratio Tables Practice Online:Short Video explanation of using a ratio table for problem solving.Stop Animation Video: Taste of Ratios https://vimeo.com/ Lesson Overview (2 of 3) 6 Lesson Overview (3 of 3) Common Core State Standard 6RP3 Use ratio reasoning to solve real-world problems 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 AfterThis lesson introduces another tool for ratio problem solving: the ratio table. Previously they have learned about tape diagrams and have been introduced to the language of ratios. After this lessons students will apply these tools to problem solving situations. They will also learn another tool: double number lines and connect this work to the algebraic tools of graphing and equations. Topic Background Ratios come in handy when mixing a color of paint and in maintaining the same flavor in a recipe that is enlarged or scaled down, as the problems in this lesson show. The ratio table has a strong link to work done in the algebra strand. It is not a far stretch to use the table to graph the direct variation in a ratio relationship. The rate is, of course, the slope. Warm Up OBJECTIVE: SWBAT solve ratio problems by using a ratio table. Language Objective: They will write about their understanding of ratio equivalence. Agenda 7 Write the ratios as fractions in lowest terms. 1. The number of red bears to all gummi bears. 2. There are 4 vans and 12 cars in a parking lot. Write the ratio of cars to vans. 3. There are 20 pens and 8 pencils in Lis pencil box. Write the ratio of pencils to pens. Answer Agenda: OBJECTIVE: 1) Warm Up - Independent 2) Launch Independent & Whole Class 3) Explore: 4) Summary - Independent 5) Exit Ticket - Independent 6) Assessment - Independent 8 OBJECTIVE: SWBAT solve ratio problems by using a ratio table. Language Objective: They will write about their understanding of ratio equivalence. Predict Independent Mini-Lesson - Whole Class & Partners Guided Practice Independent & Partners Launch Agenda 9 Remember Abby and Zack? They are mixing red & yellow paint to make an orange color to paint their kitchen table. They each think they have the perfect shade of orange. Launch Agenda 10 Abbys orange is made with one cup of red paint for every 3 cups of yellow paint. Zacks orange paint is made by mixing 3 cups of red for every 5 cups of yellow. 1. Write that as a ratio of red to yellow in your notebook. 2. Write that as a ratio of red to yellow in your notebook. 1:3 or 1/3 or 1 to 3 3:5 or 3/5 or 3 to 5 Launch - Strategize Agenda 11 Abby and Zack are working on making larger amounts of paint in each shade of orange. At the end of the day they found this recipe but they couldnt figure out whose paint it makes. Can you? 15 cups of red paint & 25 cups of yellow paint Write down in your notes any ideas you have about how to solve this problem. recipe definition batch definition Explore Mini-Lesson Agenda 12 Lets learn about another helpful tool for ratio problems. Lets say you love to make and eat cake. Your recipe calls for two eggs and one cup of flour for each batch. If you have 6 eggs, how much flour would you need to make the maximum amount of cake? Explore Mini-Lesson Agenda 13 Lets learn about another helpful tool for ratio problems. Lets say you love to make and eat cake. Your recipe calls for two eggs and one cup of flour for each batch. If you have 6 eggs, how much flour would you need to make the maximum amount of cake? You could draw a picture. Then you could make copies until you get to six eggs. Explore Mini-Lesson Agenda 14 Seems like this takes a long time, dont you think? You could record the numbers for each batch in a table. This table gives you the same information as the pictures. But faster! Eggs246 Cups of flour123 New Tool: Ratio Table This is a ratio table. Explore Mini-Lesson Agenda 15 Question: Will 2 eggs and 1 cup of flour make a cake that tastes the same as one with 4 eggs and 2 cups of flour? Eggs246 Cups of flour123 New Tool: Ratio Table Will thisand this make cake that has the same taste? Partners: Take turns asking each other this question and listening. Prove your answer. Explore Mini-Lesson Agenda 16 Share Out: What do you think? Do these columns in the ratio table make the same tasting cake? Eggs246 Cups of flour123 New Tool: Ratio Table Explore Mini-Lesson Agenda 17 Its true! Each column in the table is a ratio. Each ratio is equivalent. That makes cake that tastes the same. Eggs246 Cups of flour123 New Tool: Ratio Table How do you know the ratios are equivalent? Discuss this with your partner. Prove that the ratios are equivalent. Explore Mini-Lesson Agenda 18 Eggs246 Cups of flour123 Because New Tool: Ratio Table Its true! Each column in the table is a ratio. Each ratio is equivalent. That makes cake that tastes the same. 2 1 = 4 2 = 6 3 Explore Mini-Lesson Agenda 19 Its true! Each column in the table is a ratio. Each ratio is equivalent. That makes cake that tastes the same. Eggs246 Cups of flour123 A cake made with 2 eggs and 1 cup of flour will taste the same as New Tool: Ratio Table Explore Mini-Lesson Agenda 20 Eggs246 Cups of flour123 A cake made with 2 eggs and 1 cup of flour will taste the same as A cake made with 4 eggs and 2 cups of flour will taste the same as New Tool: Ratio Table Its true! Each column in the table is a ratio. Each ratio is equivalent. That makes cake that tastes the same. Explore Mini-Lesson Agenda 21 Eggs246 Cups of flour123 A cake made with 2 eggs and 1 cup of flour will taste the same as A cake made with 4 eggs and 2 cups of flour will taste the same as One made with 6 eggs and 3 cups of flour. New Tool: Ratio Table Its true! Each column in the table is a ratio. Each ratio is equivalent. That makes cake that tastes the same. Explore - video 22 Agenda This video may help. Here is a video about the taste of equivalent ratios. https://vimeo.com/user /tasteofratios/ Guided Practice 23 Agenda Try this! PB&J Trail Mix is made by combining 7 ounces of peanuts with 5 ounces of raisins. A ratio table has been started to show this relationship for different batches of trail mix. Peanuts (in ounces) Raisins (in ounces) 515 Copy the table. Work with your partner to fill in every box with the amounts to maintain the same flavor. New Tool: Ratio Table Guided Practice 24 Agenda Try this! PB&J Trail Mix is made by combining 7 ounces of peanuts with 5 ounces of raisins. A ratio table has been started to show this relationship for different batches of trail mix. Peanuts (in ounces) Raisins (in ounces) 515 Lets see how you did! Here are the missing values New Tool: Ratio Table Guided Practice 25 Agenda Peanuts (in ounces) Raisins (in ounces) New Tool: Ratio Table What method did you and your partner use to fill in the table? What do you notice about the numbers in the peanuts row? What do you notice about the numbers in the raisins row? Guided Practice 26 Agenda There are mathematical statements we can say with certainty about the trail mix based on this ratio table. We can say Peanuts (in ounces) Raisins (in ounces) 515 Lefty: Tell Righty one more sentence based on the table For every 7 oz of peanuts you have 5 oz of raisins. or for every 10 oz of peanuts you have 14 oz of raisins. Righty: Tell Lefty a different sentence using the table. New Tool: Ratio Table Independent Practice 27 Agenda You will practice using your new tool, ratio tables, to solve ratio word problems. You will have 15 minutes to complete the class work. You will have a chance to check your work at the end of the work session. Independent Practice - Review 28 Agenda Here are the answers to the worksheet. Please check your work to make sure you have the correct answers. Put a question mark next to any problems you had wrong or you have a question about. Problem #1 Problem #2 Problem #3 Problem #4 Summary 29 Agenda Explain, in writing, why Trail Mix with 14 ounces of peanuts and 10 ounces of raisins tastes the same as one with 7 ounces of peanuts and 5 ounces of raisins. Peanuts (in ounces) Raisins (in ounces) PB&J Trail Mix Explain why thisand this will have the same taste. Summary 30 Agenda Read your writing to your partner. Will Trail Mix with 14 ounces of peanuts and 10 ounces of raisins tastes the same as one with 7 ounces of peanuts and 5 ounces of raisin? Peanuts (in ounces) Raisins (in ounces) PB&J Trail Mix Explain why thisand this will have the same taste. Exit Ticket Agenda cups of red & 25 cups of yellow paint Use the ratio table tool to figure out whose orange paint, Abbys or Zacks, is made with this recipe. There is space on your worksheet. Assessment Write your answers in your notes. 32 Agenda 1) Which ratio table can be used to solve the problem below? Jenny discovers that she has 8 shirts for every 5 pants. If she has 40 shirts, how many pants does she have? shirts pants shirts pants shirts pants A. B. C. 2) What is the correct answer to the problem? 33 Class Work Problem # Back to Lesson Next Solution 34 Class Work Problem # people people Back to Lesson Next Solution 35 Class Work Problem #3 Back to Lesson Next Solution It will be 160 oz just double the amount for 50 oz of peanuts. 36 Class Work Problem #4 Back to Lesson Summary Exit Ticket Hint Agenda 37 Go to the solution Hint: Make two ratio tables : one for Abbys paint and one for Zacks paint Hint: Make two ratio tables : one for Abbys paint and one for Zacks paint red1 yellow3 red3 yellow5 15 cups of red & 25 cups of yellow paint Whose orange paint, Abbys or Zacks, is made with this recipe? Back to Lesson 38 Whose recipe is it? cups of red paint & 25 cups of yellow paint Its Zacks orange paint. See it in the table? Back to Lesson Assessmen t Click for solution. A recipe is the directions for how to make something, usually food. Here is an example: 39 Vocabulary - recipe You Will Need: 1 Stick Butter, Margarine 1 Egg Cookie mix 1.Heat Oven to 375 Degrees. 2.Stir Softened Butter and Egg and stir In Cookie Mix Until Soft Dough Forms. 3.Drop dough by rounded teaspoonfuls 2 inches apart onto ungreased cookie sheet. 4.Bake minutes. You Will Need: 1 Stick Butter, Margarine 1 Egg Cookie mix 1.Heat Oven to 375 Degrees. 2.Stir Softened Butter and Egg and stir In Cookie Mix Until Soft Dough Forms. 3.Drop dough by rounded teaspoonfuls 2 inches apart onto ungreased cookie sheet. 4.Bake minutes. Back to Lesson batch definition A batch means making the recipe one time. Sometimes we cook a lot of food and make many batches at once. 40 Vocabulary - batch Back to Lesson recipe definition Back to Overview 41 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 warmups 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 42 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: 6RP3 Use ratio reasoning to solve real-world problems 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. Standards for This Unit Back to OverviewNext Slide 43 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 moments notice. Scissors at least 1 for every pair Requirements to teach 21 st Century Lessons: Back to OverviewNext Slide 44 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 students 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: Back to OverviewNext Slide 45 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) Back to OverviewNext Slide 46 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) Back to OverviewNext Slide 47 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 OverviewNext Slide 48 1 st Time Users of 21 st Century Lessons Overview Slide Tab Descriptions (Slide 1 of 3) #CategoryDescription 1Lesson ObjectiveA description of what your students should know or be able to do by the end of the lesson. We also include a Student-Friendly Objective, written in a manner students can more easily comprehend and digest. 2Lesson Math VocabularyA list of the math vocabulary used in this lesson, with student-friendly definitions. 3Common Core State Standard Over 40 states have adopted the Common Core State Standards. This tab lists the Common Core Standard being taught in the lesson. (Massachusetts state standards are usually identical to the Common Core, if the MA standard is different it is also listed here.)Back to OverviewNext Slide 49 1 st Time Users of 21 st Century Lessons Overview Slide Tab Descriptions (Slide 2 of 3) #CategoryDescription 4Lesson DescriptionThis is probably the most important tab on the overview slide. Here, in a narrative form, the lesson designer takes you from beginning to end of the lesson. We often describe the pedagogical approach that we are using as well as the rationale for using this approach. We also discuss the big ideas of this lesson as well as any essential understandings. 5Background InformationThis tab covers: a) interesting historical facts related to the days objective, b) how the lessons mathematics is used in the real world, and c) a brief description of the research supporting the practices used in the lesson (sometimes with a link to the source). 6ScaffoldingDescription of what supports the lesson utilizes for ELL students, Special Education students, and those who may be struggling to learn the concept/skill. Back to OverviewNext Slide 50 1 st Time Users of 21 st Century Lessons Overview Slide Tab Descriptions (Slide 3 of 3) #CategoryDescription 7EnrichmentOn this tab we state an advanced objective for students who have already mastered (or master quickly) the standard objective. We also give a short description on how teachers can support these students. 8MaterialsThis is a list of materials required for this lesson. Some of these items may be hyperlinked to the actual document or website. In addition, there is a lesson outline which can be printed out. 9Online Resources for Absent Students Links to videos and practice problems that students who are absent (or need a review) can use independently to learn the days objective. 10Before and AfterAn explanation on how the concept and skills in the days lesson fit into the larger mathematics picture (i.e. what related concepts have students learned previously and what future concepts are we helping build a foundation for). Back to Overview 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 51 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 52