Lesson 6.1. Addition with Unlike Denominators Essential Question How can you use models to add fractions that have different denominators?

Transcription

1 Name Addition with Unlike Denominators Essential Question How can you use models to add fractions that have different denominators? Investigate Hands On Lesson 6.1 Number and Operations Fractions 5.NF.A.1, 5.NF.A. MATHEMATICAL PRACTICES MP5, MP6, MP7 Hilary is making a tote bag for her friend. She uses 1_ yard of blue fabric and 1_ yard of red fabric. How much fabric does Hilary use? Materials fraction strips MathBoard A. Find 1_ + 1_. Place a 1_ strip and a 1_ strip under the 1-whole strip on your MathBoard. B. Find fraction strips, all with the same denominator, that are equivalent to 1_ and 1_ and fit exactly under the sum 1_ + 1_. Record the addends, using like denominators. sum 1 Image Credits: (r) Houghton Mifflin Harcourt C. Record the sum in simplest form. 1_ + 1_ 5 _ So, Hilary uses _ yard of fabric. Draw Conclusions 1. Describe how you would determine what fraction strips, all with the same denominator, would fit exactly under 1_ + 1_. What are they?. MATHEMATICAL PRACTICE 5 Use Concrete Models Explain the difference between finding fraction strips with the same denominator for 1_ + 1_ and 1_ + 1_. Math Talk MATHEMATICAL PRACTICES Use Models How can you tell if the sum of the fractions is less than 1? Chapter 6 51

2 Make Connections Hands On Sometimes, the sum of two fractions is greater than 1. When adding fractions with unlike denominators, you can use the 1-whole strip to help determine if a sum is greater than 1 or less than 1. Use fraction strips to solve. _ 5 + 1_ STEP 1 Work with another student. Place three 1_ fraction strips under the 5 1-whole strip on your MathBoard. Then place a 1_ fraction strip beside the three 1_ 5 strips. STEP Find fraction strips, all with the same denominator, that are equivalent to _ and 1_. Place the fraction strips under 5 the sum. At the right, draw a picture of the model and write the equivalent fractions. 5 = _ 1 = _ STEP Add the fractions with like denominators. Use the 1-whole strip to rename the sum in simplest form. Think: How many fraction strips with the same denominator are equal to 1 whole? Share and Show MATH BOARD = _ + _ = _, or _ Math Talk MATHEMATICAL PRACTICES 6 In what step did you find out that the answer is greater than 1? Explain. Use fraction strips or i Tools to find the sum. Write your answer in simplest form _ + _ 8 = _ + _ = _ 1_ + _ 5 = _ + _ = _ 5

3 Name Use fraction strips or i Tools to find the sum. Write your answer in simplest form... _ 8 + 1_ = _ + _ = + 1_ = _ + _ = _ Use fraction strips to find the sum. Write your answer in simplest form. 5. _ = _ 6. 1_ = 7. _ 1_ + 10 = _ 8. _ + 1_ 6 = 9. _ 5_ 8 + 1_ = _ _ 5 = _ 11. WRITE Math Explain how using fraction strips with like denominators makes it possible to add fractions with unlike denominators. 1. DEEPER Luis is making two batches of muffins for a school picnic. One batch of muffins uses 1_ cup of oats and 1_ cup of flour. What is the total number of cups of oats and flour needed for two batches? Explain how you use fraction strips to solve the problem. Chapter 6 Lesson 1 5

4 MATHEMATICAL PRACTICES M 1. SMARTER Maya makes trail mix by combining 1_ cup of mixed nuts, 1_ cup of dried fruit, and 1_ 6 cup of chocolate morsels. What is the total amount of ingredients in her trail mix? 1. Pose a Problem Write a new problem using different amounts for ingredients Maya used. Each amount should be a fraction with a denominator of,, or. 15. MATHEMATICAL PRACTICE Use Diagrams Solve the problem you wrote. Draw a picture of the fractions strips you use to solve your problem. 16. Explain why you chose the amounts you did for your problem. 17. SMARTER Alexandria used 1_ Personal Math Trainer cup of grapes and _ cup of strawberries combined to make a fruit snack. How many cups of grapes and strawberries did she use? Use the tiles to complete the fraction strip model to show how you found your answer. The fractions may be used more than once or not at all _ cups of grapes and raisins 5

5 Name Addition with Unlike Denominators Use fraction strips to find the sum. Write your answer in simplest form _ + _ = 5, or _ + 1 _ Practice and Homework Lesson 6.1 COMMON CORE STANDARD 5.NF.A.1, 5.NF.A. Use equivalent fractions as a strategy to add and subtract fractions.. _ _ 1 1. _ _ 5. 1 _ + 5 _ 8 6. _ + _ 7. 1 _ + _ 5 8. _ + 1 _ 9. 7 _ _ Problem Solving 10. Brandus bought 1_ pound of ground turkey and _ pound of ground beef to make sausages. How many pounds of meat did he buy? 11. To make a ribbon and bow for a hat, Stacey needs 5_ 6 yard of black ribbon and _ yard of red ribbon. How much total ribbon does she need? _ 1. WRITE Math Write a story problem that involves adding fractions with unlike denominators. Include the solution. _ Chapter 6 55

6 Lesson Check (5.NF.A.) 1. Hirva ate 5_ 8 of a medium pizza. Elizabeth ate 1_ of the pizza. How much pizza did they eat altogether?. Bill ate 1_ pound of trail mix on his first break during a hiking trip. On his second break, he ate 1_ 6 pound. How many pounds of trail mix did he eat during both breaks? Spiral Review (5.NBT.A.1, 5.NBT.A., 5.NBT.B.5, 5.NBT.B.6, 5.NBT.B.7). In 78,1,69, what digit is in the ten thousands place?. Matt ran 8 laps in 1,56 seconds. If he ran each lap in the same amount of time, how many seconds did it take him to run 1 lap? 5. Gilbert bought shirts for $15.90 each, including tax. How much did he spend? Julia has 1 pounds of nuts. There are 16 ounces in one pound. How many ounces of nuts does she have? FOR MORE PRACTICE GO TO THE Personal Math Trainer