21 st Century Lessons Introduction to Tape Diagrams

21 st Century Lessons Introduction to Tape Diagrams 6. RP. 3; RP. 3 a Day 3 1

Warm Up OBJECTIVE: SWBAT solve ratio problems by using a tape diagram. Language Objective: SWBAT discuss ratio problem solving with a partner and in groups. Write each ratio as a fraction in lowest terms. What is the ratio of… 1. Girls to boys? 1: 1 2. People wearing pants to people who are not? 4: 1 3. People wearing white to people who are in jeans? 4. Write a sentence about what your answer to #2 means. 3: 2 Agenda 7

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. Agenda 9

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? Agenda 10

Launch Here’s the definition: A ratio is a relationship between two or more quantities. But, why would I want to use or think about a ratio? Here’s a short video that will show ratios are used in a few real life situations. Agenda 11

Launch – Think, Pair, Share Think for one minute about an answer to these questions: Ø What is a job that uses a ratio? Ø How was a ratio useful in that job? Lefty share your answers with Righty. Now Righty share your answers with Lefty. Does anyone want to share what their partner told them? Agenda 12

Launch – Think, Pair, Share Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow. 3: 5 Class – What is the ratio of red to yellow in Zack’s orange paint? Partner Share 3 to 5 or 3: 5 or 3 5 Agenda 13

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. Agenda 14

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? Agenda 15

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? Agenda 16

Explore – Mini-Lesson New Tool: Tape Diagram 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? Now let’s look at the question. Agenda 17

Explore – Mini-Lesson New Tool: Tape Diagram 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 If this tape shows 4 boys then… 1. If there are 4 boys in the class, how many girls are there? Agenda 18

Explore – Mini-Lesson New Tool: Tape Diagram 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 2 4 2 This tape How manyis students 4 boys. arewe So in one put 4 box? above the tape. 2 1. If there are 4 boys in the class, how many girls are there? Agenda 19

Explore – Mini-Lesson New Tool: Tape Diagram 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 2 2 4 2 2 ? 2 We. Important don’t yet. Rule: know Thethe number in each number of box girlsmust be the same for every tape. so we put a ? for the length of that tape. 1. If there are 4 boys in the class, how many girls are there? Agenda 20

Explore – Mini-Lesson New Tool: Tape Diagram 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 2 2 4 2 2 ? 2 Now we can answer the question. 1. If there are 4 boys in the class, how many girls are there? 6 Agenda 21

Explore – Mini-Lesson New Tool: Tape Diagram 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 First, the tapes. know. draw 8 girls. boys We can put a question girls mark for what we 8 don’t know. 2. If there are 8 girls in the class, how many boys are there? Now let’s look at the question. Agenda 22

Explore – Mini-Lesson New Tool: Tape Diagram Let’s try another one. Example 2) The ratio of boys to girls in a class is 3 to 2. ? boys girls 4 4 8 How many students does each box This makes 8 girls. represent? 4 2. If there are 8 girls in the class, how many boys are there? Agenda 23

Explore – Mini-Lesson New Tool: Tape Diagram Let’s try another one. Example 2) The ratio of boys to girls in a class is 3 to 2. ? boys 4 4 girls 4 4 8 4 Remember: Every box must have the same quantity. 2. If there are 8 girls in the class, how many boys are there? Can you answer the question using 12 the diagram? 24 Advanced: Think of one way you could prove that the numbers in each box should be 4. Tell your partner. 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. Agenda 25

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. Agenda 26

Discuss Check with a partner to see if you have the same answers. See if you used your tape diagram tools in the same way. You have 10 minutes. Agenda 27

If you and your partner cannot agree on a Discuss diagram, put a star next to the problem. Let’s look at questions 3 and 4. Check to see if you and your partner completed the tape diagrams in the same way. Agenda 28

Discuss Answers 6 6 sour oranges 4 4 8 6 6 6 4 8 red marbles Agenda 29

Discuss Did you and your partner complete the tape diagrams the same way? Did you get the same answers? Agenda 30

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 playing 8 resting 8 8 8 10 8 apples 5 5 oranges 5 5 15 5 Agenda 31

Discuss (optional) Each pair will share with another pair to see if you have the same answers. See if you used tape diagrams the same way. Each group of four will be assigned one problem (3, 4, 5, or 6) from the class work. One person will need to put their group’s work on the board. You will have 10 minutes. No time? Click for Answers Slides 32 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? Agenda 33

Exit Ticket New Tool: Tape Diagram 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. Use tape diagrams as a tool to find out how much yellow paint Zack will need to buy to make his orange paint. Agenda 34

Exit Ticket New Tool: Tape Diagram Let’s solve this problem using a tape diagram. Theknow: question is: orange How many cups of yellow paint does Zack We Zack’s paint is made by mixing And, we know: he bought 24 cups of red paint. hisevery shade orange paint? 3 need cupsto ofmake red for 5 of cups of yellow. Since Nowevery we can boxfigure must have out how the This is a 3: 5 ratio of red to yellow. same many quantity… cups each box represents. If 3 the boxes are 24 Let’s label diagram. then… red yellow 8 8 24 8 8 ? Let’s draw the tapes. 8 8 That means the answer is: 40 cups of yellow paint Agenda 35

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 20 strawberries 20 20 Answer: So the number of grapes is 20. Agenda 36

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