Warm UpOBJECTIVE: SWBAT solve ratio problems by using a tape diagram.Language Objective: SWBAT discuss ratio problem solving with a partner and in groups.Agenda*Write each ratio as a fraction in lowest terms.What is the ratio ofGirls to boys?People wearing pants to people who are not?People wearing white to people who are in jeans?4. Write a sentence about what your answer to #2 means. 1:14:13:2

LaunchAgenda*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.

LaunchAgenda*Zacks 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?

LaunchAgenda*A ratio is a relationship between two or more quantities.But, why would I want to use or think about a ratio?Heres a short video that will show how ratios are used in a few real life situations. Heres the definition:

Launch Think, Pair, ShareAgenda*Zacks 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 Zacks orange paint.Righty Tell Lefty the ratio of yellow to red in Zacks orange paint.Partner ShareClass What is the ratio of red to yellow in Zacks orange paint?3 to 5or 3:5

Explore StrategizeAgenda*Zack bought 24 cups of red paint. How much yellow paint will Zack need to buy to make his shade of orange paint?

Explore Mini-LessonAgenda*Before we solve Zacks problem, lets look at some simpler problems to get ready. Read this problem.1. If there are 4 boys in the class, how many girls are there?Example 1) The ratio of boys to girls in a class is 2 to 3.

Explore Mini-LessonAgenda*Lets learn about a helpful tool for ratio problems that could help you with all sorts of ratio problems.1. If there are 4 boys in the class, how many girls are there?Example 1) The ratio of boys to girls in a class is 2 to 3.

Explore Mini-LessonAgenda*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. 1. If there are 4 boys in the class, how many girls are there?Each box represents a number in the original ratio.

Explore Mini-LessonAgenda*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. 1. If there are 4 boys in the class, how many girls are there?

Explore Mini-LessonAgenda*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. boys1. If there are 4 boys in the class, how many girls are there?girls2How many students are in one box? 22This tape is 4 boys.So we put 4 above the tape.4

Explore Mini-LessonAgenda*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. boys1. If there are 4 boys in the class, how many girls are there?girlsImportant Rule:The number in each box must be the same for every tape.222224?We dont yet know the number of girls so we put a ? for the length of that tape.

Explore Mini-LessonAgenda*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. boys1. If there are 4 boys in the class, how many girls are there?girlsNow we can answer the question.4?22222

Explore Mini-LessonAgenda*Lets try another one.Example 2) The ratio of boys to girls in a class is 3 to 2. 2. If there are 8 girls in the class, how many boys are there?First, draw the tapes.We can label what we know. 8 girls.We can put a question mark for what we dont know.8?

Explore Mini-LessonAgenda*Lets try another one.Example 2) The ratio of boys to girls in a class is 3 to 2. boys2. If there are 8 girls in the class, how many boys are there?44girlsHow many students does each box represent? 4This makes 8 girls.?8

Explore Mini-LessonAgenda*Lets try another one.Example 2) The ratio of boys to girls in a class is 3 to 2. boys42. If there are 8 girls in the class, how many boys are there?444girlsRemember:Every box must have the same quantity.4Can 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.

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ExploreAgenda*Check this out for more about how tape diagrams work:Click Watch video for a demonstration.Tape Diagrams can be a helpful tool for solving problems.

PracticeAgenda*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. Dont worry you will discuss it when you are finished.

DiscussAgenda*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.

DiscussAgenda*Lets look at questions 3 and 4. Check to see if you and your partner completed the tape diagrams in the same way.If you and your partner cannot agree on a diagram, put a star next to the problem.

Agenda*666666 sour oranges444448 red marblesDiscuss Answers68

DiscussAgenda*Did you and your partner complete the tape diagrams the same way? Did you get the same answers?

DiscussAgenda*applesorangesplayingresting888882424 children playing 1510 apples55555Did you and your partner complete the tape diagrams the same way? Did you get the same answers?Agenda10

Summary Write in your notebookAgenda*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?

Exit TicketAgenda*Now that you learned a new tool use it to solve Zacks paint problem. Zacks orange paint is made by mixing 3 cups of red for every 5 cups of yellow.Use tape diagrams as a tool to find out how much yellow paint Zack will need to buy to make his orange paint.Remember:He bought 24 cups of red paint.

Exit TicketAgenda*Lets solve this problem using a tape diagram. We know: Zacks 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.This is a 3:5 ratio of red to yellow.Lets draw the tapes.Lets label the diagram.24Now we can figure out how many cups each box represents. If 3 boxes are 24 then?888The question is: How many cups of yellow paint does Zack need to make his shade of orange paint?Since every box must have the same quantity88888That means the answer is:

Assessment*AgendaCarefully 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? 2020202020Answer: So the number of grapes is 20.

(Time on this slide 5 min) Time passed 5 minIn-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 NotesWe 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.

*(Time on this slide 1 min) Time passed 7 minIn-Class Notes Brief introduction

Preparation NotesThis begins the narrative of Abby and Zack that continues throughout the next lesson.

*(Time on this slide 1 min) Time passed 8 minIn-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 NotesThis sets up a review of vocabulary.*(Time on this slide 2 min) Time passed 10 minIn-Class Notes Make sure students have the definition for a ratio in their notes somewhere. Acceptable if they can turn to it from prior lesson. Click www symbol for link to video. Reflection questions on video follow.

Preparation Notes Clicking the internet symbol will bring you to a very short video clip (1:19) you can play that will show students how ratios are used in a variety of jobs.*(Time on this slide 2 min) Time passed 14 minIn-Class Notes Students should see that 3:5 is a different ratio than 5:3 and to make sure to read carefully.

Preparation NotesAnytime students take time to talk to each other about the content you are increasing the language usage and helping your ELL students.

*(Time on this slide 1 min) Time passed 15 minIn-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 Zacks original ratio is 3 red to 5 yellow. Some students may get the answer right away. Some may only write down the question. Thats 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. Its a pretty nice tool for ratio problems I really think you will like it. For students who dont 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.

*(Time on this slide min) Time passed 16 minIn-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.*(Time on this slide min) Time passed 16 minIn-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 NotesThis 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.

*(Time on this slide 3 min) Time passed 19 minIn-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.

*(Time on this slide 1 min) Time passed 20 minIn-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.

*(Time on this slide 2 min) Time passed 22 minIn-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.

*(Time on this slide 1 min) Time passed 23 minIn-Class Notes Very important rule. This is the key to students being able to recreate and use a tape diagram.

Preparation NotesMake sure you spend time to make sure you fully understand the model and how to explain it.

*(Time on this slide 1 min) Time passed 24 minIn-Class Notes If you use the tool correctly it is extremely simple to find the answer to the question asked.

*(Time on this slide 2 min) Time passed 26 minIn-Class Notes Make sure students realize that this is a different problem.

*(Time on this slide 2 min) Time passed 28 minIn-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.

*(Time on this slide 2 min) Time passed 30 minPreparation Notes Advanced box comes as a click at the end of this slide. Use if you want to.*(Time on this slide 5 min) Time passed 35 minIn-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 NotesYou 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*(Time on this slide - 15 min) Time passed 50 minIn-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.

*(Time on this slide 10 min) Time passed 60 minIn-Class Notes Have students put a star next to any problems that have different solutions.

*(Time on this slide 4 min) Time passed 64 minIn-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.*(Time on this slide 1 min) Time passed 65 min*(Time on this slide 4 min) Time passed 69 minIn-Class Notes Click answers button for detailed answer diagrams.

*(Time on this slide 1 min) Time passed 70 min

*(Time on this slide 5 min) Time passed 80 minIn-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.

*(Time on this slide 4 min) Time passed 84 minIn-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.

*(Time on this slide 1 min) Time passed 85 minIn-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.

*(Time on this slide 5 min) Time passed 90 minIn-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.

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