21 st Century Lessons Using Tape Diagrams with Part- Whole Ratio Problems 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 ObjectiveContent Objective: SWBAT solve part-whole ratio problems by using a tape diagram. Language Objective: SWBAT identify the ratio in a word problem and translate the words into a tape diagram. Lesson DescriptionThis lesson is predominantly guided practice intended to help students to acquire the ability to use a tape diagram for ratio problems involving a total. Students will receive a worksheet with incomplete tape diagrams that they will complete while watching the animations and listening to the teacher explanations. This is the second lesson on tape diagrams and the first tool of the unit. (Other tools include ratio tables and double number lines.) Students will have a lot of guidance in this lesson with a slow release to practice on their own. A practice lesson follows. Lesson Overview (1 of 3) 5 Lesson VocabularyTape diagram a model used to illustrate the multiplicative relationships in a proportion. MaterialsClass work, tape diagram interactive lesson worksheet, homework ScaffoldingThis lesson provides a scaffolding for special education and ELL students that can assist students throughout future lessons by concretizing the relationships in a proportion. Some students may find it helpful to hold onto this model longer than others. EnrichmentAdditional problems are available for advanced students who can solve similar problems without the use of the tool. Help these students to identify the connections between their method and that used in the tape diagrams. Online Resources for Absent Students The best resource online is Thinking Blocks who also have a video tutorial on how to use their excellent virtual manipulative tape diagrams: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 AfterStudents begin this unit with an introduction to the language of ratios and begin building the concept of two quantities in relationship with each other. Problem solving holds two equivalent ratios together. Tape diagrams are an important tool for students at this level who may need concrete models for seeing these relationships and how multiplication and division help us to discover and manipulate them. Topic BackgroundTape diagrams are used routinely and with great effect in the mathematics taught in high-achieving countries of Asia and Europe, most notably in Singapore. Warm Up OBJECTIVE: SWBAT solve part-whole ratio problems by using a tape diagram. Language Objective: SWBAT identify the ratio in a word problem and translate the words into a tape diagram. Agenda 7 But I have 6. I have 9 cookies. Crystal and her brother Marcus have some cookies. 1. If there are 5 chocolate chips in each cookie, how many chips are in all the cookies? 2. What part of a dozen cookies does Crystal have? 3. If Crystal ate one cookie each day, how many weeks would her cookies last? Crystal Marcus Hint: A dozen is 12! 9 x x 5 = 75 chips dozen 1 2/7 weeks Agenda: 1) Warm Up - independent 2) Launch Think, Pair, Share - partners 3) Explore: 5) Summary Painting Project - independent 4) Exit Ticket Tape Diagrams for Abby & Zack - independent 8 OBJECTIVE: SWBAT solve part-whole ratio problems by using a tape diagram. Language Objective: SWBAT identify the ratio in a word problem and translate the words into a tape diagram. Predict - independent Mini-Lesson whole class Guided Practice independent & whole group Launch Agenda 9 Abby and Zack are mixing red and yellow paint to make an orange color to paint their kitchen table. They each think they have the perfect shade of orange. Launch Think, Pair, Share Agenda 10 Abbys orange paint is made by mixing 1 cup of red for every 3 cups of yellow. Zacks orange paint is made by mixing 3 cups of red for every 5 cups of yellow. Lefty Tell Righty the ratio of yellow to total in Zacks orange paint. Righty Tell Lefty the ratio of red to total in Abbys orange paint. Partner Share Explore Predict Agenda 11 They will need a gallon of orange paint for the project. 1. How can Abby make enough of her orange paint for the project? Hint: A gallon is 16 cups. 2. How can Zack make enough of his orange paint for the project? Write down in your notes any ideas you have about how to answer these questions. Explore Mini-Lesson Agenda 12 Do you remember the tool you learned about last time? T A P E D I A G R A M S ! Lets see if we can use tape diagrams for a problem involving a total amount. Explore Mini-Lesson Agenda 13 Tape Diagram Tool Follow along by filling out the worksheet as we go. Explore Mini-Lesson Agenda 14 Example 1) A recipe for fruit punch says to use 5 ounces of orange juice for every 3 ounces of grape juice. Janices punch bowl can hold 80 ounces of punch. How much orange juice is that? How much grape juice? Now lets look at whats given. New Tool: Tape Diagram First, lets draw the tapes. Orange Grape ? ? We dont know the amounts of each juice so All of these boxes from both tapes make 80 ounces of punch. 80 oz. So, if 8 boxes equals 80 ounces, then each box is Now we can see that the orange juice is And the grape juice is 50 oz 30 oz T O T A L Why 10? Because 80 8 = 10 Or algebraically: 8b = 80 So b = 10 What is the ratio in the problem? Orange to grape is 5:3. So Explore Guided Practice Agenda 15 Lets practice this next one together. Continue to put your work on the worksheet. Tape Diagram Tool Explore Guided Practice Agenda 16 A florist makes Mothers Day bouquets of a dozen roses with a ratio of 1 pink rose to every 2 yellow roses. How many yellow roses are needed for 1 bouquet? Vocabulary: Here are the tapes: Now You: Label the tape diagram with the information from the problem. _____________ Lets see how you did! Hint: A dozen is 12. Guided Practice #1 What is the ratio in the problem? Pink to yellow is 1:2. What is a bouquet? What is a bouquet? Tape Diagram Tool Vocabulary Agenda 17 Bouquet - a pretty collection of flowers sometimes with a bow usually given as a gift to someone. Roses Back to Lesson Explore Guided Practice Agenda 18 A florist makes Mothers Day bouquets of a dozen roses with a ratio of 1 pink rose to every 2 yellow roses. How many yellow roses are needed for 1 bouquet? Vocabulary pink yellow ? ? 12 Hint: A dozen is 12. I know that 3 boxes is equal to 12 roses so each box has 4 roses That makes the pink equal to 4 roses And the answer: Yellow roses needed is... Answer: 8 roses 4 8 Guided Practice #1 T O T A L Tape Diagram Tool Explore Guided Practice Agenda 19 Try the next one on your own. Remember to put your work on the worksheet. Tape Diagram Tool Explore Guided Practice Agenda 20 Mrs. Stanford is having a class pizza party. She has found that students prefer pepperoni pizza to cheese pizza in a ratio of 3 to 1. If she needs 48 slices of pizza in total, how many slices of pepperoni will she need? ____________ ________ Lets see how you did! Identify the ratio. Draw the tapes. Then fill out the diagram and find the answer. Is there anyone who can draw the diagram and find the answer? Ok, lets see what it should look like. The ratio of pepperoni to cheese is 3:1. Tape Diagram Tool Explore Guided Practice Agenda 21 Mrs. Stanford is having a class pizza party. She has found that students prefer pepperoni pizza to cheese pizza in a ratio of 3 to 1. If she needs 48 slices of pizza in total, how many slices of pepperoni will she need? ____________ ________ pepperoni cheese 48 slices If all four boxes equals 48 slices, then that means that each box is equal to slices So the amount of pepperoni pizza is Answer: 36 slices 36 T O T A L Tape Diagram Tool Explore Independent Practice Agenda 22 There are two more tape diagram ratio problems for you to solve on your own on your worksheet. Show your work. Circle your answer. Answer #3 Answer #4 Challenge Answers Tape Diagram orange brown 45 T O T A L 9 Answer: 9 brown candies Explore Independent Practice Answers Agenda 23 The ratio of orange to brown candies in a bag of M & Ms is 4:1. If there are 45 orange and brown candies in the bag of M & Ms altogether then how many brown candies are there? Independent Practice # Ratio of orange to brown is 4:1 Explore Independent Practice Answers Agenda 24 For every eraser in a pencil box there are 2 pencils. If there are 14 pencils in the box, then how many pencils and erasers are there altogether? Independent Practice #4 pencils eraser ? T O T A L 14 Answer: 21 pencils & erasers Ratio of pencils to erasers is 2:1 77 7 Explore Independent Practice Challenge Answers Agenda 25 To make the Perfectly Pink paint color you use 8 parts of white paint for every one part of red paint. If 27 cups of Perfectly Pink paint is mixed up in a bucket, then how many cups of red paint were used? Challenge Practice #5 Answer: 3 cups red paint The ratio of flour to sugar in a cake recipe is 7 to 5. If the recipe calls for 20 tablespoons of sugar, then how many tablespoons of flour and sugar will be required in total? Challenge Practice #6 Answer: 48 tablespoons total Explore Independent Practice Challenge Answers Agenda 26 A water molecule has a ratio of 2 Hydrogen atoms for every 1 Oxygen atom. If there are 27 atoms that make up some water, then how many Hydrogen atoms are there? Challenge Practice #7 Answer: 18 atoms of H The ratio of flour to sugar in a cake recipe is 7 to 5. If the recipe calls for 20 tablespoons of sugar, then how many tablespoons of flour and sugar will be required in total? Extension: For the problem above: If 4 tablespoons equals cup, then how many cups of flour and how many cups of sugar are required for the cake? Challenge Practice #8 Answer: 20 tbsp sugar 4 = 5 quarter cups or 1 cups sugar 28 tbsp flour 4 = 7 quarter cups or 1 cups flour Answer: 20 tbsp sugar 4 = 5 quarter cups or 1 cups sugar 28 tbsp flour 4 = 7 quarter cups or 1 cups flour Exit Ticket in your notebook Agenda 27 The painting project will require a gallon of orange paint. 1. How many cups of red paint and yellow paint will Abby need to make enough of her orange paint for the project? Hint: A gallon is 16 cups. 2. How many cups of red paint and yellow paint will Zack need to make enough of her orange paint for the project? Use tape diagrams to determine how much red and how much yellow paint each child needs. Challenge Problem Challenge Problem red yellow Total: 16 ? ? red yellow Total: 16 ? ? Exit Ticket in your notebook Agenda 28 How much red and yellow paint will each child need to make a gallon of orange paint? Hint: A gallon is 16 cups. Challenge Problem If 4 boxes equals 16 cups, then each box is 4 cups. So Abby will need 4 cups of red paint and 12 cups of yellow paint. If 8 boxes equals 16 cups, then each box is 2 cups. So Zack will need 6 cups of red and 10 cups of yellow paint. Abbys Orange Zacks Orange The ratio is red to yellow 1:3 The ratio is red to yellow 3: Challenge Problem Agenda 29 Try this one: Thinking about Tools Vera and Jane help peeling potatoes for a soup kitchen. Jane can peel 13 potatoes in the time it takes Vera to peel 9. If Jane peeled 65 potatoes one Sunday then how many potatoes did the girls peel altogether? Answer: 110 potatoes altogether Think About It: A tape diagram is probably not the best tool for solving this problem? Why? Can you see a connection between how you solved it & a tape diagram? Back to Exit Ticket Back to Exit Ticket Summary Agenda 30 Lefty Tell Righty something about Abbys tape diagram. Righty Tell Lefty something about Zacks tape diagram. red yellow Total: 16 ? ? red yellow Total: 16 ? ? Abbys Orange Zacks Orange Tape Diagram Tool Back to Overview 31 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 32 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 33 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 34 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 35 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 36 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 37 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 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 38 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 39