Warm Up Write each ratio as a fraction in lowest terms. OBJECTIVE: solve ratio problems by using a tape diagram. Language Objective: discuss ratio problem solving with a partner and in groups. Write each ratio as a fraction in lowest terms. What is the ratio of… Girls to boys? People wearing pants to people who are not? People wearing white to people who are in jeans? 1:1 4:1 (Time on this slide – 5 min) Time passed 5 min In-Class Notes Only the simplified answers will come up when you click through. #2 is originally 8:2 then simplifies to 4:1 (4 white tops, 1 white dress, 1 pair of white sneakers) #3 is originally 6:4 then simplifies to 3:2 #4 possible answer: For every four people wearing pants, one person is not. Preparation Notes We are looking to see that students remember how to identify a ratio, simplify it, and can use the language of ratio to explain its meaning. 4. Write a sentence about what your answer to #2 means. 3:2 Agenda

TAPE DIAGRAMS Best used when the two quantities have the same units. Highlights the multiplicative relationship between quantities.

TAPE DIAGRAMS The ratio for three parts yellow paint to two parts blue paint can be shown with the following tape diagram: 5 What is the total number of parts represented? 1 5 How much of the total does each rectangle represent? If the tape diagram represents 5 cups of paint then each of these rectangles would represent how much? 1 cup If the diagram represents a total of one gallon, then each rectangle represents how much? 1 of a gallon 5 What part of the gallon is yellow paint? 3 of a gallon 5

USING TAPE DIAGRAMS TO SOLVE PROBLEMS Slimy Gloopy mixture is made by mixing glue and liquid laundry starch in a ratio of 3 to 2. How much glue and how much starch is needed to make 85 cups of Slimy Gloopy mixture? GLUE: STARCH: Start by making your base tape diagram: The total amount represents how much? 5 parts = 85 cups Each part represents how much? 1 part = 85 ÷ 5 = 17 cups Amount of glue in 85 cups: 3 parts= 3 x 17 = 51 cups Amount of starch in 85 cups 2 parts= 2 x 17 = 34 cups You need 51 cups of glue and 34 cups of starch for 85 cups of Slimy Gloopy mixture. Adapted from commoncoretools.wordpress.com

Launch 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. (Time on this slide – 1 min) Time passed 7 min In-Class Notes Brief introduction Preparation Notes This begins the narrative of Abby and Zack that continues throughout the next lesson. Agenda

Launch Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow. This sounds like a ratio. What are ratios again? (Time on this slide – 1 min) Time passed 8 min In-Class Notes Let students think for a moment about what a ratio is. You could even do a Think, Pair, Share if time permits. Preparation Notes This sets up a review of vocabulary. Agenda

3:5 Explore – Strategize Zack bought 24 cups of red paint. How much yellow paint will Zack need to buy to make his shade of orange paint? 3:5 Write down in your notes any ideas you have about how to answer this question. (Time on this slide – 1 min) Time passed 15 min In-Class Notes Students are NOT meant to solve this problem before the lesson. This slide is a preview of the overarching question that gives students a clear need for the Tape Diagrams tool. The teacher may want to point out or highlight from any student questions that Zack’s original ratio is 3 red to 5 yellow. Some students may get the answer right away. Some may only write down the question. That’s ok. The point is to establish a need for the tape diagram tool. They will all have to prove the answer using the tool for the exit ticket. Let speedy students know this. “Nice work. We are going to learn about a way to visually show how you get this answer. It’s a pretty nice tool for ratio problems – I really think you will like it.” For students who don’t know how to begin, “I see that you are struggling with your strategy for this problem. Lucky for you we are going to learn a really helpful tool for solving this problem. I really think you will like it.”  Agenda

Explore – Mini-Lesson Before we solve Zack’s problem, let’s look at some simpler problems to get ready. Read this problem. Example 1) The ratio of boys to girls in a class is 2 to 3. 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – ½ min) Time passed 16 min In-Class Notes Students are NOT solving this problem. It is an example used to illustrate the tape diagrams tool. Click through to get to the heart of the lesson: the introduction to the tape diagram Preparation Notes You will want to spend a good deal of preparation time reviewing the next slides so that you thoroughly understand how a tape diagram is created and used. Drawing an accurate model is very important. Agenda

Explore – Mini-Lesson Let’s learn about a helpful tool for ratio problems that could help you with all sorts of ratio problems. Example 1) The ratio of boys to girls in a class is 2 to 3. 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – ½ min) Time passed 16 min In-Class Notes We want students to be very clear that there are several very useful tools for working with ratios. The tape diagram is the first of these tools that they will learn about. Preparation Notes This lesson is an introductory lesson for students on a visual model for ratio problem solving called here, the tape diagram. It is also referred to as a “unit bar model” in Singapore Mathematics. Many high-achieving countries use this visual model for ratio problem solving. Students can just watch the diagram creation without writing anything unless your students have trouble with this kind of instruction. Then have students draw the diagram with you. This will obviously take more time and require the lesson to be broken into 2 days. Agenda

New Tool: Tape Diagram Explore – Mini-Lesson We can use a tape diagram to solve ratio math problems. Example 1) The ratio of boys to girls in a class is 2 to 3. boys girls Each box represents a number in the original ratio. 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – 3 min) Time passed 19 min In-Class Notes Go slowly and make sure that students realize that the “4 boys” in the problem belongs written above or below the appropriate tape. Now let’s look at the question. Agenda

New Tool: Tape Diagram Explore – Mini-Lesson We can use a tape diagram to solve ratio math problems. Example 1) The ratio of boys to girls in a class is 2 to 3. If this tape shows 4 boys then… boys girls 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – 1 min) Time passed 20 min In-Class Notes Make sure they see that the first step is to set up the tape diagram with information that is given to us. This can take time but it is time well-spent. Agenda

New Tool: Tape Diagram Explore – Mini-Lesson We can use a tape diagram to solve ratio math problems. Example 1) The ratio of boys to girls in a class is 2 to 3. 4 How many students are in one box? This tape is 4 boys. So we put 4 above the tape. 2 2 boys girls 2 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – 2 min) Time passed 22 min In-Class Notes This slide can be replayed over and over to show students how we get to “2” in each box. You distribute the 4 into the two boxes in the tape. Agenda

The number in each box must be the same for every tape. New Tool: Tape Diagram Explore – Mini-Lesson We can use a tape diagram to solve ratio math problems. Example 1) The ratio of boys to girls in a class is 2 to 3. 4 We don’t yet know the number of girls so we put a ? for the length of that tape. 2 2 Important Rule: The number in each box must be the same for every tape. boys 2 2 2 girls ? 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – 1 min) Time passed 23 min In-Class Notes Very important rule. This is the key to students being able to recreate and use a tape diagram. Preparation Notes Make sure you spend time to make sure you fully understand the model and how to explain it. Agenda

New Tool: Tape Diagram Explore – Mini-Lesson We can use a tape diagram to solve ratio math problems. Example 1) The ratio of boys to girls in a class is 2 to 3. 4 2 2 Now we can answer the question. boys 2 2 2 girls ? 1. If there are 4 boys in the class, how many girls are there? (Time on this slide – 1 min) Time passed 24 min In-Class Notes If you use the tool correctly it is extremely simple to find the answer to the question asked. 6 Agenda

? 8 Explore – Mini-Lesson Let’s try another one. New Tool: Tape Diagram Explore – Mini-Lesson Let’s try another one. Example 2) The ratio of boys to girls in a class is 3 to 2. ? We can label what we know. 8 girls. boys girls First, draw the tapes. We can put a question mark for what we don’t know. 8 2. If there are 8 girls in the class, how many boys are there? (Time on this slide – 2 min) Time passed 26 min In-Class Notes Make sure students realize that this is a different problem. Now let’s look at the question. Agenda

4 ? 8 Explore – Mini-Lesson Let’s try another one. New Tool: Tape Diagram Explore – Mini-Lesson Let’s try another one. Example 2) The ratio of boys to girls in a class is 3 to 2. ? How many students does each box represent? boys This makes 8 girls. 4 4 girls 4 8 2. If there are 8 girls in the class, how many boys are there? (Time on this slide – 2 min) Time passed 28 min In-Class Notes Again, here is a very important step. If there are 8 girls and the ratio indicates we must make 2 boxes for a ratio of 3:2 then we can distribute the 8 into the 2 boxes. Students may, of course, realize this “distribution” as division. This would be desired but does not need to be pushed early. Agenda

Every box must have the same quantity. New Tool: Tape Diagram Explore – Mini-Lesson Let’s try another one. Example 2) The ratio of boys to girls in a class is 3 to 2. ? Remember: Every box must have the same quantity. boys 4 4 4 4 4 girls 8 2. If there are 8 girls in the class, how many boys are there? (Time on this slide – 2 min) Time passed 30 min Preparation Notes Advanced box comes as a click at the end of this slide. Use if you want to. 12 Can you answer the question using the diagram? Advanced: Think of one way you could prove that the numbers in each box should be 4. Tell your partner. Agenda

Practice You will have 15 minutes to work on solving some ratio problems using the tape diagrams tool. You might feel a little confused and want to talk about it. Don’t worry – you will discuss it when you are finished. (Time on this slide - 15 min) Time passed 50 min In-Class Notes This screenshot is a cue for students so that they know what page to have in front of them. Answers will be provided later in the slideshow. Agenda

If you and your partner cannot agree on a diagram, put a star next to the problem. Discuss Let’s look at questions 3 and 4. Check to see if you and your partner completed the tape diagrams in the same way. (Time on this slide – 4 min) Time passed 64 min In-Class Notes Students will star problems that they are having trouble agreeing about. Take a poll to find out how many students had trouble with #3? How many had trouble with #4? Etc. You can then decide if you want to go over each problem or only those that many students had trouble with. Answers including tape diagrams are found by clicking a button on this or any of the next 2 slides. Preparation Notes If you only have a 60 min block the slides from here on out may be used for another day. Students review their work together. Answer button can be used to walk students through the tape diagram drawing process. Then small group discussion, reflection, independent exit ticket and assessment for understanding. Agenda

Discuss Answers 6 8 6 6 6 6 6 6 sour oranges 4 4 4 4 4 8 red marbles (Time on this slide – 1 min) Time passed 65 min 4 4 8 red marbles 8 Agenda

Explore Tape Diagrams can be a helpful tool for solving problems. Check this out for more about how tape diagrams work: Click “Watch video” for a demonstration. (Time on this slide – 5 min) Time passed 35 min In-Class Notes Click the internet symbol to link to the Thinking Blocks website that has an interactive applet for using tape diagrams to solve ratio problems. Preparation Notes You can further explore this website with students to practice using tape diagrams or what they call “Thinking Blocks”. If you have access to a computer lab this would be a great activity to have students work on. http://www.thinkingblocks.com/ThinkingBlocks_Ratios/TB_Ratio_Main.html Agenda

Discuss Did you and your partner complete the tape diagrams the same way? Did you get the same answers? (Time on this slide – 4 min) Time passed 69 min In-Class Notes Click “answers” button for detailed answer diagrams. Agenda

Discuss Did you and your partner complete the tape diagrams the same way? Did you get the same answers? 24 children playing 10 apples 24 10 (Time on this slide – 1 min) Time passed 70 min playing 8 8 8 apples 5 5 resting 8 oranges 5 5 5 Agenda 8 15 Agenda

Summary – Write in your notebook What is one thing you like about the tape diagrams as a tool? What is one thing that is difficult? Is there anything that is confusing about using tape diagrams as a tool? (Time on this slide – 5 min) Time passed 80 min In-Class Notes Have students take 3-5 minutes to write sentences that answer these three questions. Select 3 students at random to answer one of the questions by reading their writing. Agenda

New Tool: Tape Diagram Exit Ticket Now that you learned a new tool use it to solve Zack’s paint problem. Remember: Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow. He bought 24 cups of red paint. (Time on this slide – 4 min) Time passed 84 min In-Class Notes For the exit ticket it is important that students make a tape diagram to prove that they have mastered the objective for the lesson. Use tape diagrams as a tool to find out how much yellow paint Zack will need to buy to make his orange paint. Agenda

24 8 8 8 8 8 8 8 8 ? 40 cups of yellow paint Exit Ticket New Tool: Tape Diagram Exit Ticket Let’s solve this problem using a tape diagram. The question is: How many cups of yellow paint does Zack need to make his shade of orange paint? We know: Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow. And, we know: he bought 24 cups of red paint. Since every box must have the same quantity… Now we can figure out how many cups each box represents. If 3 boxes are 24 then… This is a 3:5 ratio of red to yellow. 24 Let’s label the diagram. red yellow 8 8 8 Let’s draw the tapes. 8 8 8 8 8 (Time on this slide – 1 min) Time passed 85 min In-Class Notes For the exit ticket it is important that students make a tape diagram to prove that they have mastered the objective for the lesson. ? 40 cups of yellow paint That means the answer is: Agenda

Assessment Carefully review the tape diagram tool and solution. What is wrong here? The ratio of grapes to strawberries in a fruit salad is 4 to 1. If there are 20 grapes in the salad then how many strawberries are there? grapes strawberries 20 20 20 20 20 (Time on this slide – 5 min) Time passed 90 min In-Class Notes This is a very quick assessment and is not meant to take a long time. Students can write answers to this question in their notebook or on a small paper to be turned in with only their suggestions on what to do to correct the problem. Answer: So the number of grapes is 20. Agenda