Using Tape Diagrams with Part-Whole Ratio Problems

Lesson Target Content Objective: SWBAT solve part-whole ratio problems by using a tape diagram. Learning Target: SWBAT identify the ratio in a word problem and translate the words into a tape diagram.

Warm Up Crystal and her brother Marcus have some cookies. 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. Crystal and her brother Marcus have some cookies. I have 9 cookies. 1. If there are 5 chocolate chips in each cookie, how many chips are in all the cookies? But I have 6. 9 x 5 + 6 x 5 = 75 chips 2. What part of a dozen cookies does Crystal have? (Time on this slide – 3 min) Time passed 3 min In-Class Notes Practice intended to point students toward thinking multiplicatively. Can be completed in their notebooks. Preparation Notes Hint: A dozen is 12! ¾ dozen 3. If Crystal ate one cookie each day, how many weeks would her cookies last? 1 2/7 weeks Crystal Marcus 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. (Time on this slide – 1 min) Time passed 5 min In-Class Notes This is an on-going narrative through the “tools” lessons 03-05. Preparation Notes Agenda

Launch – Think, Pair, Share Righty – Tell Lefty the ratio of red to total in Abby’s orange paint. Partner Share Lefty – Tell Righty the ratio of yellow to total in Zack’s orange paint. Abby’s orange paint is made by mixing 1 cup of red for every 3 cups of yellow. Zack’s orange paint is made by mixing 3 cups of red for every 5 cups of yellow. (Time on this slide – 3 min) Time passed 8 min In-Class Notes This Think, Pair, Share makes use of the language Lefty and Righty to designate each of the two students in a pre-arranged pairing. This will be used in future lessons. If you haven’t already designate which of each two students is Lefty and who is Righty. Preparation Notes Agenda

Explore – Predict They will need a gallon of orange paint for the project. Hint: A gallon is 16 cups. 1. How can Abby make enough of her orange paint for the project? 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. (Time on this slide - 2 min) Time passed 10 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: Abby’s original ratio results in a total of 4 cups of paint but she will need 16 cups Zack’s original ratio makes 8 cups of orange paint, but he will need 16 cups Abby will want the same orange color whether it is 4 cups or 16 cups. Zack wants his same color of orange. So ratios will help the relationship to be the same for different amounts. Preparation Notes Agenda

Explore – Mini-Lesson Tape Diagram Tool Follow along by filling out the whiteboard as we go. (Time on this slide – 1 min) Time passed 12 min In-Class Notes Students are using this worksheet throughout the guided practice in today’s lesson. Make sure each student has one and knows the expectations for its use. Preparation Notes Print out these worksheets to keep students’ attention focused. Agenda

? ? 80 oz. 10 10 10 10 10 10 10 10 Explore – Mini-Lesson 50 30 50 oz New Tool: Tape Diagram Explore – Mini-Lesson Example 1) A recipe for fruit punch says to use 5 ounces of orange juice for every 3 ounces of grape juice. Janice’s punch bowl can hold 80 ounces of punch. How much orange juice is that? How much grape juice? 50 ? All of these boxes from both tapes make 80 ounces of punch. Orange Grape We don’t know the amounts of each juice so… 80 oz. What is the ratio in the problem? 10 10 10 10 10 First, let’s draw the tapes. Orange to grape is 5:3. So… T O T A L 10 10 10 ? 30 (Time on this slide – 8 min) Time passed 20 min In-Class Notes Cue students to write “orange” and “grape” on worksheet when diagram appears. Why is each box 10? This is the crux of the problem. You may want to play the animation several times to ensure all students understand why each box contains 10. Preparation Notes Because 80 ÷ 8 = 10 Or algebraically: 8b = 80 So… b = 10 50 oz So, if 8 boxes equals 80 ounces, then each box is… Now we can see that the orange juice is… Now let’s look at what’s given. Why 10? And the grape juice is … 30 oz Agenda

Explore – Guided Practice Tape Diagram Tool Explore – Guided Practice Let’s practice this next one together. Continue to put your work on your whiteboard (Time on this slide – 1 min) Time passed 21 min In-Class Notes Brief slide Preparation Notes Agenda

Explore – Guided Practice Tape Diagram Tool Explore – Guided Practice A florist makes Mother’s 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? Guided Practice #1 Hint: A dozen is 12. Now You: Label the tape diagram with the information from the problem. Let’s see how you did! Here are the tapes: _____________ What is the ratio in the problem? (Time on this slide – 3 min) Time passed 24 min In-Class Notes It is important that students identify the initial ratio given in the problem as the first step. This will also be the first step in the next tool that they learn: ratio tables. Preparation Notes Pink to yellow is 1:2. _____________ What is a bouquet?  Vocabulary: Agenda

Vocabulary Back to Lesson Bouquet - a pretty collection of flowers sometimes with a bow usually given as a gift to someone. Roses (Time on this slide - min) Time passed In-Class Notes Students are NOT solving this problem. It is an example used to illustrate the tape diagrams tool. Preparation Notes Agenda

Explore – Guided Practice Tape Diagram Tool Explore – Guided Practice A florist makes Mother’s 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? Guided Practice #1 Hint: A dozen is 12. ? 4 And the answer: Yellow roses needed is... I know that 3 boxes is equal to 12 roses so each box has… That makes the pink equal to 4 pink 12 T O T A L 4 4 yellow (Time on this slide – 3 min) Time passed 27 min In-Class Notes These two slides contain the animation for one problem and should be considered together. Make sure students know where the total amount goes in the tape diagram. Preparation Notes 4 roses ? 8 Answer:8 roses 4 roses Vocabulary Agenda

Explore – Guided Practice Tape Diagram Tool Explore – Guided Practice Try the next one on your own. Remember to put your work on the worksheet. (Time on this slide – 1 min) Time passed 28 min In-Class Notes Brief Slide. Preparation Notes Agenda

Explore – Guided Practice Tape Diagram Tool Explore – Guided Practice 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? Identify the ratio. Draw the tapes. Then fill out the diagram and find the answer. Let’s see how you did! Is there anyone who can draw the diagram and find the answer? ________ The ratio of pepperoni to cheese is 3:1. ____________ Ok, let’s see what it should look like. ____________ (Time on this slide – 7 min) Time passed 35 min In-Class Notes Students are solving this problem more independently than before. Ask for a student volunteer to try this problem (with as much help from the class as you like) The animation will follow to show the intended use of the tape diagram for solving the problem. Preparation Notes Agenda

Explore – Guided Practice Tape Diagram Tool Explore – Guided Practice 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? 36 If all four boxes equals 48 slices, then that means that each box is equal to … So the amount of pepperoni pizza is… pepperoni 12 12 12 ____________ 48 slices T O T A L 12 ________ ____________ cheese (Time on this slide – 5 min) Time passed 40 min In-Class Notes Students do not need to identify the amount of cheese since that is not the question in the problem. Preparation Notes Answer: 36 slices 12 slices Agenda

Explore – Independent Practice Tape Diagram 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 (Time on this slide – 10 min) Time passed 50 min In-Class Notes There are four challenge problems you can give to more advanced students that use some more sophisticated numbers. You may give them these additional problems and tell them to do them in place of the ones on the worksheet. Or these could be used with the whole class if time permits. If your class is ready and there is time, you can have one of your advanced students demonstrate their problem and solution to the class. Click the “answers” button to see the answers to the two standard problems from the worksheet. Preparation Notes Agenda

Explore – Independent Practice Answers 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? Ratio of orange to brown is 4:1 orange brown 45 T O T A L 9 Answer: 9 brown candies 9 9 9 9 9 (Time on this slide – included in lesson slide) In-Class Notes Click the Green Button to go back to the lesson. Preparation Notes Agenda

Explore – Independent Practice Answers 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? Ratio of pencils to erasers is 2:1 pencils eraser ? T O T A L 14 Answer: 21 pencils & erasers 7 7 7 (Time on this slide – included in lesson slide) In-Class Notes Click the Green Button to go back to the lesson. Preparation Notes Agenda

Explore – Independent Practice Challenge Answers Challenge Practice #5 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? Answer: 3 cups red paint Challenge Practice #6 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? (Time on this slide – included in lesson slide) In-Class Notes Click the Green Button to go back to the lesson. Or click the other green button for additional solutions. Preparation Notes Answer: 48 tablespoons total Agenda

Explore – Independent Practice Challenge Answers Challenge Practice #7 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? Answer: 18 atoms of H Challenge Practice #8 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 ¼ cup, then how many cups of flour and how many cups of sugar are required for the cake? (Time on this slide – included in lesson slide) In-Class Notes Click the Green Button to go back to the lesson. Preparation Notes Answer: 20 tbsp sugar ÷ 4 = 5 quarter cups or 1 ¼ cups sugar 28 tbsp flour ÷ 4 = 7 quarter cups or 1 ¾ cups flour Agenda

Exit Ticket – use the half sheet of paper provided The painting project will require a gallon of orange paint . Hint: A gallon is 16 cups. 1. How many cups of red paint and yellow paint will Abby need to make enough of her orange paint for the project? 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. (Time on this slide – 5 min) Time passed 55 min In-Class Notes Click “Challenge Problem” for an alternate Exit Ticket for advanced students or if your class is ready to reach beyond tape diagrams. Answer to this Exit Ticket is found by clicking to the next slide. Preparation Notes This Exit Ticket connects back to the problem presented at the beginning of the lesson that students should now be able to answer using tape diagrams.