Introduction to Tape Diagrams

Warm Up Write each ratio as a fraction in lowest terms. 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… Girls to boys? People wearing pants to people who are not? People wearing white to people who are in jeans? 1:1 4:1 4. Write a sentence about what your answer to #2 means. 3:2 Agenda

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

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

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 how ratios are used in a few real life situations.  Agenda

Launch – Think, Pair, Share Think for one minute about an answer to these questions: What is a job that uses a ratio? 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

Launch – Think, Pair, Share Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow. Lefty – Tell Righty the ratio of red to yellow in Zack’s orange paint. 3:5 Righty – Tell Lefty the ratio of yellow to red in Zack’s orange paint. 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

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. 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? 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? 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? 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? 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 This tape is 4 boys. So we put 4 above the tape. How many students are in one box? 2 2 boys girls 2 1. If there are 4 boys in the class, how many girls are there? 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? 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? 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? 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? 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? 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

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

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. 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 ? 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 Answer: So the number of grapes is 20. Agenda