Contents Domain 1 Operations and Algebraic Thinking.... 1 Lesson 1 Write and Interpret Expressions... Lesson Order of Operations... 14 Lesson 3 Evaluate Expressions with Grouping Symbols... 6 Lesson 4 Patterns.... 38 Lesson 5 Graph Patterns.... 50 Domain Number and Operations in Base Ten... 63 Lesson 6 Multiply Whole Numbers... 64 Lesson 7 Divide Whole Numbers... 76 Lesson 8 Quotients as Equations... 88 Lesson 9 Read and Write Decimals... 100 Lesson 10 Compare Decimals... 11 Lesson 11 Round Decimals... 14 Lesson 1 Multiply and Divide by Powers of Ten.. 136 Lesson 13 Add Decimals... 148 Lesson 14 Subtract Decimals... 160 Lesson 15 Multiply Decimals... 17 Lesson 16 Divide Decimals... 184 Domain 3 Number and Operations Fractions... 197 Lesson 17 Equivalent Fractions... 198 Lesson 18 Improper Fractions and Mixed Numbers... 10 Lesson 19 Add Fractions.... Lesson 0 Subtract Fractions... 34 Lesson 1 Understand Multiplication of Fractions.. 46 Lesson Multiply Fractions... 58 Lesson 3 Fractions as Division... 70 Lesson 4 Divide Fractions... 8 ii Contents M_676NASE_5_PDF.indd 14/1/16 8:5 am
Domain 4 Measurement and Data... 95 Lesson 5 Convert Customary Units... 96 Lesson 6 Convert Metric Units... 308 Lesson 7 Understand Volume.... 30 Lesson 8 Volumes of Rectangular Prisms... 33 Lesson 9 Line Plots... 344 Domain 5 Geometry... 357 Lesson 30 Coordinate System.... 358 Lesson 31 Ordered Pairs... 370 Lesson 3 Plane Figures... 38 Lesson 33 Triangles... 394 Lesson 34 Quadrilaterals.... 406 Key Terms and Definitions... 418 Diagnostic Assessments....A1 Contents iii M_676NASE_5_PDF.indd 3 14/1/16 8:5 am
LESSON 19 Add Fractions Coached Instruction ERROR ANALYSIS Alberto corrected Holly s mistake in the problem below. Analyze their work. Which is the best estimate for the sum of 5 7 1 4 5? A. 1 B. between _ and 1 C. 1 D. greater than 1 HOLLY S METHOD I added the numerators and then added the denominators. 5_ 7 1 4_ 5 5 5 1 4 7 1 5 5 9 1 The fraction 9 1 in simplest form is 3 _ 4. Since 4 5 _ 1 and 4_ 4 5 1, the sum 3 _ 4 is between 1 _ and 1. I think Choice B is correct. Alberto realizes that Holly made a mistake. ALBERTO S CORRECTION I compared each addend to _ 1 and 1. 5_ 7 is greater than 1 _, and less than 1. 4_ 5 is also greater than 1 _ and less than 1. The sum of two fractions greater than _ 1 will be greater than 1. I drew a number line to check. 5_ 7 0 1 I can see that the sum will be greater than 1, so Choice D is correct. 4_ 5 Domain 3: Number and Operations Fractions
DISCUSS What was Holly s mistake? How can she prevent that mistake in the future? APPLY Susie and Winston are finding the sum of 5 and _. Susie thinks the sum is 8 less than 1. Winston thinks the sum is greater than 1. Who is correct? Justify your answer. Lesson 19: Add Fractions 3
Compare Jack s and Sumi s methods of solving the problem below. What is the sum of 3 4 1 5 in simplest form? 6 A. 4 5 B. 3 C. 1 4 5 D. 1 7 1 JACK S METHOD First, I drew a model for each fraction. Then I drew lines so that both models have 6 rows and 4 columns. The model for _ 3 has 18 of 4 parts shaded. 4 The model for _ 5 has 0 of 4 parts shaded. 6 Together, there are 38 of 4 parts shaded, or 38 38 4 14 4 5 4 4 1 14, or 1 4 5 14 4 4 4 5 7 1 14 4 The sum is 1 7. Choice D is correct. 1 SUMI S METHOD 4. I looked for a common multiple of 4 and 6. Multiples of 4: 4, 8, 1, 16 Multiples of 6: 6, 1, 18 I wrote equivalent fractions using 1 as the denominator. 4 5 3 3 3 4 3 3 5 9 1 5_ 6 5 5 3 5 10 6 3 1 Then I added the numerators of the fractions. 9 1 1 10 1 5 9 1 10 5 19 1 1 19 1 5 1 1 1 7, or 1 1 7 1 Choice D is correct. 4 Domain 3: Number and Operations Fractions
DISCUSS Which step in Jack s method shows how he finds a common denominator? Why is it different than the denominator Sumi used? APPLY What is the sum of 6 1 5 in simplest form? 9 A. 7 B. 7 15 18 C. 8 9 D. 1 _ 9 Choose a method to solve. Show how you know with a picture or explanation. Lesson 19: Add Fractions 5
Compare Stephanie s and Justin s methods of solving the problem below. The fifth-grade classes at Orchard Elementary School collected newspaper for recycling. The table shows the number of pounds each class collected. The fifth graders set a goal to collect at least 0 pounds of newspaper. Did they reach their goal? Newspaper Collected Fifth-Grade Class Number of Pounds Mrs. Brown 4 _ 4 Mr. Hayes 4 _ Mr. Hathaway 5 _ 4 Miss Steven 6 _ STEPHANIE S METHOD I added all of the numbers in the table. Before adding, I changed halves to fourths so that the fractions have a common denominator. 4 4 1 4 1 5 3 _ 4 1 6 5 4 4 1 4 4 1 5 3 _ 4 1 6 4 5 19 19 1 8_ 5 19 1 5 1 4 The fifth graders collected a total of 1 pounds of newspaper, so they collected more than their goal. JUSTIN S METHOD 8_ 4 I added the whole numbers and fractions separately and used estimation. First, I mentally added the whole numbers: 4 1 4 1 5 1 6 5 19. Then I looked at the fractions. I know that the sum of _ 1 4 1 will be less than 1. I know that the sum of _ 3 4 1 will be greater than 1. So, I know that the sum of all four fractions will be greater than 1. Since 19 1 1 5 0, I can tell that the fifth graders reached their goal. 6 Domain 3: Number and Operations Fractions
DISCUSS Whose method would you use to solve a problem like this? If you were asked for the exact amount collected, which method would be best? APPLY Did Mrs. Brown s and Mr. Hathaway s classes combined collect more or fewer pounds of newspaper than Mr. Hayes and Miss Steven s classes combined? Show your work and justify your answer. Lesson 19: Add Fractions 7
Lesson Practice Part 1 Choose the correct answer. 1. What is 4 _ 9 1 9? A. 3 B. 9 C. 5_ 9 D. 3 4. What is 3 5 _ 6 1 3? A. 5 3 B. 5 C. 6 D. 6. What is 1 3 _ 4 1 3 8? A. 4 3 B. 4 C. 4 7_ 8 D. 5 3. Paulo shaded _ 1 of a grid. Then he 3 shaded another _ of the grid. What 5 fraction of the grid did he shade? A. 5 B. 3 10 C. 5 D. 11 15 5. Sophie takes tap and ballet. Today she practiced tap for _ 3 hour and ballet 4 for hour. How many hours did Sophie spend practicing dance? A. 3 hour B. 1 4 hours C. 1 8 hours D. 1 hours 6. Frances has 5 _ 1 yards of red yarn and 6 5_ yards of blue yarn. How many 6 yards of yarn does she have in all? A. 3 3 yards B. 7 3 yards C. 7 5_ 6 yards D. 8 yards 8 Domain 3: Number and Operations Fractions
7. What is 7 _ 9 1 6? A. 17 18 B. 8_ 9 15 C. 18 D. 5_ 6 8. What is 1 _ 5 8 1 3 A. 4 B. 3 13 16 C. 3 7 D. 3 16 16? 9. Blake bought _ 3 pound of cashew nuts, 8 8 pound of almonds, and _ 5 pound of walnuts. 6 A. What is the total weight of the nuts that Blake bought? Write the answer in simplest form. Show your work. B. Explain how you found your answer for Part A. Lesson 19: Add Fractions 9
Lesson Practice Part Choose the correct answer. 1. Which sum is less than 1? A. 8 1 5 B. 5 1 C. 3 1 4 D. 5_ 8 1 3. Sebastian added _ a sum of 5 _ 8 3 1 and computed 5. Which sentence is true? A. Sebastian is correct because 1 3 5 5 and 3 1 5 5 8. B. Sebastian is incorrect because 5 _ 8 is less than 3 _ 5. C. Sebastian is incorrect because 5 _ 8 is less than _ 3. D. Sebastian is correct because when the addends are simplified the sum is 5 _ 8. 3. Skylar read a book for _ 1 hours and 4 then spoke on the phone for 1 _ 1 hours. How much time did Skylar spend reading and talking on the phone? A. 3 3 hours C. 4 4 hours B. 3 4 hours D. 4 4 hours 4. Ava made a rectangular drawing. The width of the drawing is 3 _ 1 inches. The length is 1 7 _ 8 inches longer than the width. What is the length of the drawing? A. 4 4_ 5 inches B. 5 8 inches C. 5 4 inches D. 5 8 inches 5. Find the sum. 5 1 1 5 5 A. 1 1 30 B. 1 1 60 C. 59 60 D. 8 17 6. Brooke walked 1 _ 1 miles from her 4 home to the park. She walked _ 5 8 mile longer on the way home. How far did Brooke walk in all? A. 1 miles C. miles B. 1 7_ 8 miles D. 3 8 miles 30 Domain 3: Number and Operations Fractions
7. Which sum is greater than 1? 1 A. 1 7 B. 4 1 5 C. 8 1 4 10 D. 3 1 1 8. Camden jogged 3 7 miles in the park 10 and then _ 3 mile back home. How far 4 did Camden jog in all? 9 A. 4 0 miles B. 4 5 miles 7 C. 4 0 miles D. 3 11 14 miles 9. Find the sum. A. 5 7_ 9 B. 6 3 4 3 1 1 5_ 6 5 C. 6 D. 6 3 10. Emilia lives 1 _ 3 miles east of school. 5 Valentina lives 1 _ 1 miles west of school. How far do Emilia and Valentina live from each other? A. 4_ 7 miles 9 B. 10 miles C. 3 miles D. 3 1 10 miles 11. Of the DVDs sold at the Meloy garage sale, _ 1 are comedies, _ 1 are dramas, 3 4 and _ 1 are music. 6 A. What fraction of the DVDs are comedies or dramas? Show your work. B. What fraction of the DVDs are dramas or music? Show your work. C. Did the Meloys sell any other type of DVDs? Explain your answer. Lesson 19: Add Fractions 31
1. Is the sum of _ 3 7 1 5 less than 1 or greater than 1? Show your work and explain 1 your answer. 13. What is the sum of _ 3 8 1 4_ in simplest form? Show your work. 6 3 Domain 3: Number and Operations Fractions
14. Malcolm ran four days last week. The table shows the distance he ran each day. Day Distance (in miles) Monday 3 5 Wednesday 4 Thursday 6 Saturday 3 4 How far did Malcolm run on Monday and Wednesday? Show your work. Did Malcolm run farther on Thursday and Saturday than he did on Monday and Wednesday? Explain your answer and show your work. Lesson 19: Add Fractions 33