21 st Century Lessons Using Tape Diagrams with

21 st Century Lessons Using Tape Diagrams with Part. Whole Ratio Problems Primary Lesson Designer: Lisa Schad 1

Warm Up 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. But I have 6. 1. If there are 5 chocolate chips in each cookie, how many chips are in all the cookies? 9 x 5 + 6 x 5 = 75 chips 2. What part of a dozen cookies does Crystal have? Hint: A dozen is 12! ¾ dozen Crystal Marcus 3. If Crystal ate one cookie each day, how many weeks 1 2/7 weeks would her cookies last? Agenda 2

Agenda: 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. 1) Warm Up - independent 2) Launch – Think, Pair, Share - partners 3) Explore: Predict - independent Mini-Lesson – whole class Guided Practice – independent & whole group 4) Exit Ticket – Tape Diagrams for Abby & Zack - independent 5) Summary – Painting Project - independent 3

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 4

Launch – Think, Pair, Share r e n t r a P are Sh Righty – Tell Lefty the ratio of red to total in Abby’s orange paint. 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. Agenda 5

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. Agenda 6

Explore – Mini-Lesson Do you remember the tool you learned about last time? TAPE DIAGRAMS! Let’s see if we can use tape diagrams for a problem involving a total amount. Agenda 7

Explore – Mini-Lesson Tape Diagram Tool Follow along by filling out the worksheet as we go. Agenda 8

Explore – Mini-Lesson New Tool: Tape Diagram TOTAL 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 these ? Weofdon’t boxes from What is 10 the ratio in the problem? know the Orange 80 tapes 10 draw 10 the tapes. 10 10 both First, let’s Orange to grape is 5: 3. So… amounts of Grape 10 10 10 make 80 oz. juice each of 30 ? Because 80 ÷ 8 = 10 ounces so… oz Now can equals see that 80 the orange juice is… 50 punch. So, if 8 we boxes ounces, then each algebraically: 8 b = 80 Now let’s look at what’s. Orgiven. Why 10? box Andis… the grape juice is … 30 oz So… b = 10 Agenda 9

Explore – Guided Practice Tape Diagram Tool Let’s practice this next one together. Continue to put your work on the worksheet. Agenda 10

Explore – Guided Practice Tape Diagram Tool 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? Hint: A dozen is 12. Guided Practice #1 Here are the tapes: _______ What is the ratio in the problem? _______ Pink to yellow is 1: 2. What is a bouquet? 11 Vocabulary: Now Let’s. You: see how Labeldid! the tape you diagram with the information from the problem. Agenda

Vocabulary Back to Lesson Bouquet - a pretty collection of flowers sometimes with a bow usually given as a gift to someone. Roses Agenda 12

Explore – Guided Practice Tape Diagram Tool 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 4 yellow 4 12 4 ? 8 Vocabulary 13 TOTAL pink And thethat 3 I know answer: That makes boxes is equal Yellow rosesso the pink to 12 roses needed equal to is. . . each box has… 4 Answer: 8 4 roses Agenda

Explore – Guided Practice Tape Diagram Tool Try the next one on your own. Remember to put your work on the worksheet. Agenda 14

Explore – Guided Practice Tape Diagram Tool 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 Let’s howthe you did! ratio. see Draw Istapes. there anyone ______ who The ratio of pepperoni ____ Then fill see out Ok, let’s it to cheese is 3: 1. can draw the what diagram ______ thefind diagram should look and the like. answer? and find the answer. Agenda 15

Explore – Guided Practice Tape Diagram Tool 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? Answer: slices 1236 slices 36 12 12 48 slices ____ TOTAL If all four boxes So the amount equals 48 slices, of pepperoni ______ then that means pepperoni pizza is… that each box is ______ cheese equal to … Agenda 16

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 Agenda 17

Explore – Independent Practice Answers Independent Practice #3 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 9 brown 9 9 45 TOTAL orange 9 Answer: 9 brown candies Agenda 18

Explore – Independent Practice Answers Independent Practice #4 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 14 7 eraser 7 7 ? TOTAL pencils Answer: 21 pencils & erasers Agenda 19

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? Answer: 48 tablespoons total Agenda 20

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? 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 21

Exit Ticket – in your notebook 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. Challenge Problem 22 Agenda

Exit Ticket – in your notebook Abby’s Orange Hint: A gallon is 16 cups. How much red and yellow paint will each child need to make a gallon of orange paint? ? red The 4 ratio is red Total: 16 4 4 to yellow 1: 3 yellow 4 ? If 4 boxes equals 16 cups, then each box is 4 cups. So… Abby will need 4 cups of red paint and 12 cups of yellow paint. Zack’s Orange ? 2 ratio 2 is 2 red The 2 3: 5 2 2 yellow to 2 yellow ? 23 If 8 boxes equals 16 cups, then Total: each box is 2 cups. So… 2 16 Zack will need 6 cups of red and 10 cups of yellow paint. Challenge Problem Agenda

Challenge Problem Thinking about Tools Try this one: Vera and Jane help peeling potatoes for a soup kitchen. Jane can peel 13 potatoes in the time it takes Vera to peel 9. If Jane peeled 65 potatoes one Sunday then how many potatoes did the girls peel altogether? Answer: 110 potatoes altogether Think About It: A tape diagram is probably not the best tool for solving this problem? Why? Can you see a connection between how you solved it & a tape diagram? 24 Back to Exit Ticket Agenda

Summary Tape Diagram Tool Lefty – Tell Righty something about Abby’s tape diagram. Righty – Tell Lefty something about Zack’s tape diagram. Abby’s Orange red yellow Zack’s Orange ? Total: 4 4 4 ? 4 16 red yellow 2 2 ? 2 2 Total: 2 2 16 ? Agenda 25