Using Tape Diagrams with Part-Whole Ratio Problems

Using Tape Diagrams with Part-Whole Ratio Problems

Lesson Target

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. 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? 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. 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. 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. Agenda

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

Explore – Mini-Lesson New Tool: Tape Diagram 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 We don’t know the amounts of each juice so… 80 oz. What is the ratio in the problem? 10 10 10 10 10 Grape First, let’s draw the tapes. T O T A L Orange to grape is 5:3. So… 10 10 10 ? 30 Because 80 ÷ 8 = 10 Or algebraically: 8b = 80 So… b = 10 50 oz Now we can see that the orange juice is… So, if 8 boxes equals 80 ounces, then each box 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 Let’s practice this next one together. Continue to put your work on your whiteboard Agenda

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 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? 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 Agenda

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 ? 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 4 roses ? 8 Answer:8 roses 4 roses Vocabulary Agenda

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

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 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. ____________ Agenda

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? 36 If all four boxes equals 48 slices, then that means that each box is equal to … So the amount of pepperoni pizza is… 12 12 12 pepperoni ____________ 48 slices T O T A L ________ 12 cheese ____________ 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 Agenda

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 orange 9 9 9 9 45 T O T A L brown 9 9 Answer: 9 brown candies Agenda

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 pencils 7 7 ? T O T A L eraser 7 Answer: 21 pencils & erasers 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? 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? 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.

Using Tape Diagrams with Part-Whole Ratio Problems