go math grade 5 lesson 7.9 homework answer key

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HOUGHTON MIFFLIN HARCOURT GO MATH! Grade 5

Textbook: HOUGHTON MIFFLIN HARCOURT GO MATH! Grade 5 ISBN: 9780547587813

Use the table below to find videos, mobile apps, worksheets and lessons that supplement HOUGHTON MIFFLIN HARCOURT GO MATH! Grade 5 book.

Fluency with Whole Numbers and Decimals

Place value, multiplication, and expressions.

Domains Number and Operations in Base Ten

Common Core Standards CC.5.OA.1, CC.5.OA.2, CC.5.NBT.1, CC.5.NBT.2, CC.5.NBT.5, CC.5.NBT.6

Place Value and Patterns

Place value of whole numbers, powers of 10 and exponents, multiplication patterns, multiply by 1-digit numbers, multiply by 2-digit numbers, relate multiplication to division, multiplication and division, numerical expressions, evaluate numerical expressions, divide whole numbers.

Domains Number and Operations in Base Ten Numbers and Operations-Fractions

Common Core Standards CC.5.NBT.6, CC.5.NF.3

Place the First Digit

Divide by 1-digit divisors, division with 2-digit divisors, partial quotients, estimate with 2-digit divisors, divide by 2-digit divisors, interpret the remainder, adjust quotients, add and subtract decimals.

Common Core Standards CC.5.NBT.1, CC.5.NBT.3a, CC.5.NBT.3b, CC.5.NBT.4, CC.5.NBT.7

Thousandths

Place value of decimals, compare and order decimals, round decimals, decimals addition, decimals subtraction, estimate decimals sums and differences, add decimals, subtract decimals, patterns with decimals, add and subtract money, multiply decimals.

Domains Numbers and Operations in Base Ten

Common Core Standards CC.5.NBT.2, CC.5.NBT.7

Multiplication Patterns with Decimals

Multiply decimals and whole numbers, multiplication with decimals and whole numbers, multiply using expanded form, multiply money, decimals multiplication, zeros in the product, divide decimals, division patterns with decimals, division decimals by whole numbers, estimate quotients, division of decimals by whole numbers, decimal division, write zeros in the dividend, decimals operations, operations with fractions, add and subtract fractions with unlike denominators.

Domains Number and Operations-Fractions

Common Core Standards CC.5.NF.1, CC.5.NF.2

Addition with Unlike Denominators

Subtraction with unlike denominators, estimate fractions sums and differences, common denominators and equivalent fractions, add and subtract fractions, add and subtract mixed numbers, subtraction with renaming, patterns with fractions, practice addition and subtraction, use properties of addition, multiply fractions.

Domains Numbers and Operations-Fractions

Common Core Standards CC.5.NF.4a, CC.5.NF.4b, CC.5.NF.5a, CC.5.NF.5b, CC.5.NF.6

Multiply Fractions and Whole Numbers

Fraction and whole number multiplication, multiply fraction, compare fraction factors and products, fraction multiplication, area and mixed numbers, compare mixed numbers factors and products, multiple mixed numbers, find unknown length, division fractions.

Domains Numbers and Operations – Fractions

Common Core Standards CC.5.NF.3, CC.5.NF.7a, CC.5.NF.7b, CC.5.NF.7c

Divide Fractions and Whole Numbers

Use multiplication, connect fractions to division, fraction and whole-number division, interpret division with fractions, geometry and measurement, algebra: patterns and graphing.

Domains Operations and Algebraic Thinking Measurement and Data Geometry

Common Core Standards CC.5.OA.3, CC.5.MD.2 CC.5.G.1, CC.5.G.2

Ordered Pairs

Line graphs, numerical patterns, graph and analyze relationships, convert units of measure.

Domains Measurement and Data

Common Core Standards CC.5.MD.1

Customary Length

Customary capacity, multistep measurement problems, metric measures, customary and metric conversions, elapsed time, geometry and volume.

Domains Measurement and Data Geometry

Common Core Standards CC.5.MD.3, CC.5.MD.3a, CC.5.MD.3b, CC.5.MD.4, CC.5.MD.5a, CC.5.MD.5b, CC.5.MD.5c, CC.5.G.3, CC.5.G.4

Quadrilaterals

Properties of two-dimensional figures, three-dimensional figures, unit cubes and solid figures, understand volume, estimate volume, volume of rectangular prisms, apply volume formulas, compare volumes, find volume of composed figures.

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Go Math Interactive Mimio Lesson 7.9 Multiply Mixed Numbers

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Go Math! Grade 5 Teacher Edition

Description: Go Math! Grade 5 Teacher Edition

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__ 21,840 24,336 gg CorrectionKey=NL-A gg CorrectionKey=NL-A 5_mnlese694762_c07l02.indd 256 6/16/2022 12:11:52 PM

47,430 49,011 527 × 93 3 1 2 1.6 ×_ 0.7 1 12 14.2 _ × 7.6 107 92 3.59 _ × 4.8 17 232 5.7 ×_ 0.8 35.1 ×_ 8.4 2.19 ×_ 6.3 . . . 34 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c07r02.indd 34 13/05/22 10:41 AM MTSS RtI1 Name LESSON 7.2 Enrich A Chain of Products Find the product. 1 5.4 × 3.2 17.28 2 Multiply the product in Exercise 1 by 1.5. 25.92 3 Multiply the product in Exercise 2 by 0.5. 12.96 4 Multiply the product in Exercise 3 by 2.5. 32.4 5 Multiply the product in Exercise 4 by 9.4. 304.56 6 Multiply the product in Exercise 5 by 3.2. 974.592 7 Which exercise has a product that is less than the product in the exercise just before it? Explain. The product in Exercise 3 is less than the product in Exercise 2, because I multiplied by a number less than 1. 34 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c07e02.indd 34 13/05/22 10:38 AM

TM and Version 2.0 Differentiated Centers Kit Grab Problem Solving Applications Have students read Problem 22 and describe the steps they will use to solve the problem. Problem 23 Students are required to use the solution of one multiplication problem to solve another. Math on the Spot Use this video to help students model and solve this type of problem. Construct arguments and critique reasoning of others. Problem 24 Students need to determine which answer is correct and explain their reasoning. Problem 25 This problem assesses the students’ ability to determine a product using place-value strategies. Students who answered True to all of the problems may have only been examining the digits in the problems. For example, the factors in 25b were multiplied with no decimal points. The product shown contains the correct digits, but the decimal point is not in the correct location. World Real MP 5 Evaluate Formative Assessment I Can Have students demonstrate and explain to a partner the skill for the I Can statement. I can use place-value strategies to place a decimal point when multiplying . . . the same way I would with whole numbers and then move the decimal point one place to the left in the product for each decimal place in the factors; or, I could use estimation to predict what the whole number should be and use that number to place the decimal. Exit Ticket Write a problem that includes multiplying decimals. Explain how you know where to place the decimal in the product. DIFFERENTIATED INSTRUCTION • Independent Activities Tabletop Flipchart Mini-lessons for reteaching to targeted small groups Games Reinforce math content and vocabulary Readers Supports key math skills and concepts in real-world situations. Activities Meaningful and fun math practice Chapter 7 • Lesson 2 258 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (tr) ©G. K. & Vikki Hart/Photodisc/Getty Images 258 Go Math! Grade 5 Problem Solving · Applications World Real 22. Juan has pet rabbits in an enclosure that has an area of 30.72 square feet. The enclosure Taylor is planning to build for his rabbits will be 2.2 times as large as Juan’s. How many more square feet will Taylor’s enclosure have than Juan’s enclosure? 23. A zoo is planning a new building for the penguin exhibit. First, they made a model that was 1.3 meters tall. Then, they made a more detailed model that was 1.5 times as tall as the first model. The building will be 2.5 times as tall as the height of the detailed model. What will be the height of the building? 24. MP Leslie and Ali both solve the multiplication problem 5.5 × 4.6. Leslie says the answer is 25.30. Ali says the answer is 25.3. Whose answer is correct? Explain your reasoning. Spot on the 25. For 25a–25d select True or False to indicate if the statement is correct. 25a. The product of 1.3 and 2.1 is 2.73. ● True ● False 25b. The product of 2.6 and 0.2 is 52. ● True ● False 25c. The product of 0.08 and 0.3 is 2.4. ● True ● False 25d. The product of 0.88 and 1.3 is 1.144. ● True ● False 36.864 more square feet 4.875 meters Both answers are correct; Possible explanation: Leslie’s answer shows 30 hundredths, which is the same as the 3 tenths used in Ali’s answer. gg CorrectionKey=NL-A 5_mnlese694762_c07l02.indd 258 5/27/2022 2:56:17 PM

1,160 1,392 13.92 232 2. 7.3 _ × 9.6 3. 46.3 × __ 0.8 4. 29.5 __ × 1.3 5. 3.76 ×__ 4.8 6. 9.07 ×__ 6.5 7. 0.42 × 75.3 8. 5.6 × 61.84 9. 7.5 × 18.74 10. 0.9 × 53.8 Problem Solving World Real 11. Aretha runs a marathon in 3.25 hours. Neal takes 1.6 times as long to run the same marathon. How many hours does it take Neal to run the marathon? 12. Tiffany catches a fish that weighs 12.3 pounds. Frank catches a fish that weighs 2.5 times as much as Tiffany’s fish. How many pounds does Frank’s fish weigh? 13. Write Math Write a problem that includes multiplying decimals. Explain how you know where to place the decimal in the product. 5.2 hours 30.75 pounds Check students’ problems and explanations. 70.08 31.626 346.304 38.35 18.048 37.04 140.55, or 140.550 48.42 58.955 gg CorrectionKey=NL-A 5_mnlese694762_c07p02.indd 259 5/27/2022 2:55:12 PM

(7 × ____ 1 1,000 ) 17. Taliya buys a sweater for $16.79 and a pair of pants for $28.49. She pays with a $50 bill. How much change should Taliya get back? 18. Elvira is playing a pattern game and has the following sequence. 2.75, _____, 3.25, 3.50, 3.75 What is the unknown term in the sequence? 19. What digit should go in the box to make the following statement true? 63.749 < 63. 2 2.1 yards 20.397 3 or 3.00 30.75 hours $4.72 Possible answers: 8 or 9 gg CorrectionKey=NL-A 5_mnlese694762_c07p02.indd 260 5/27/2022 2:55:13 PM

261A Go Math! Grade 5 LESSON 7.3 Lesson at a Glance Multiply Decimals with Zeros in the Product SNAPSHOT Mathematical Standards ● Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Mathematical Practices and Processes ● Attend to precision. ● Construct arguments and critique reasoning of others. ● Look for and make use of structure. ● Reason abstractly and quantitatively. I Can Objective I can understand the concept of having the correct number of decimal places in a product. Learning Goal Multiply decimals with zeros in the product. Language Objective Students show and tell how you know you have the correct number of decimal places in your product. MATERIALS • MathBoard ACROSS THE GRADES Before Grade 5 After Explore the addition and subtraction of multi-digit numbers with decimals to the hundredths. Multiply and divide a multi-digit number with decimals to the tenths by one-tenth and onehundredth with procedural reliability. Multiply and divide positive multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency. ABOUT THE MATH If Students Ask Why might I need to write zeros when multiplying decimals? The algorithm for multiplying is the same for whole numbers and decimals. However, when multiplying decimals, the additional step of placing the decimal point in the product may require writing zeros to ensure that each digit in the product is placed in its correct place-value position. Students who are proficient in the use of place value will find multiplying decimals to be a logical process, and they should understand that writing zeros in the product is a necessary step used to correctly show the value of each digit. A firm grasp of this concept will benefit all students as they encounter decimal multiplication in real-world situations. For more professional learning, go online to Teacher’s Corner.

0.05 • How many times as great is the value of a digit in the tenths place of a number than the value of the same digit in the hundredths place? 10 times as great Learning Activity Supporting All Learners On May Day, a day of celebration in many European countries, children celebrate with many festivities. One festivity is decorating a pole with ribbon. A neighbor is decorating a pole of their mailbox. One yard of ribbon costs $0.35. The pole of the mailbox is 0.2 yard tall. How much does 0.2 yard of ribbon cost? Connect the story to the problem. • What problem are you asked to find? how much 0.2 yard of ribbon will cost • What information are you given in the problem? the cost of one yard of ribbon and the amount of ribbon needed to decorate the pole on a mailbox • What operation can you use to solve the problem? multiplication • Why? Possible answer: because the neighbor is buying only a decimal part of one yard; the whole costs $0.35, and you want 0.2 of that whole. • What models can you use to represent 0.2 and 0.35? Possible answer: decimal squares

1, or 2 place values × 0.1 × 0.1 hundredths × 0.01 0.08 no Math Talk: Possible explanation: The whole number product does not always have enough digits to place the decimal point. So, I can write zeros to the left of the product when needed. Possible answer: I need to  nd 0.4 of 0.2 foot to determine the distance Jamie’s snail travels. See below. gg CorrectionKey=NL-A 5_mnlese694762_c07l03.indd 261 5/27/2022 2:55:14 PM

Examples Remind students that when dealing with money values given in dollars and cents, they should show the final product using place values to hundredths. • How can you show hundredths multiplied by tenths using decimal patterns? 0.1 × 0.01 • Why can the zero in the thousandths place be removed in Step 3? Possible answer: 6 hundredths and 60 thousandths have the same value. Try This! • What was the first step you took in finding the product? Possible answer: I found how many decimal places would be in the product. • Why is it helpful to find the number of decimal places in the product before multiplying? Possible answer: It makes it easier to see how many zeros I have to write between the decimal point and the product of the whole numbers. Construct arguments and critique reasoning of others. Math Talk Use Math Talk to focus on students’ understanding of why zeros to the right of the final digit in a decimal do not change the value of the number. • How many thousandths are in 1 hundredth? How do the two possible answers reflect this? There are 10 thousandths in 1 hundredth. Therefore, 10 thousandths = 1 hundredth, or 0.010 = 0.01. MP Common Errors Error When multiplying with whole numbers to find a decimal product, students use the incorrect whole numbers. Example In the Example, students may multiply 3 × 2 instead of 30 × 2. Springboard to Learning Make sure students understand that they are multiplying 30 hundredths, or 30 cents. Have students circle all digits to the right of the decimal point in each factor as they read aloud the decimals. Ready for More Visual Small Group • Have each student write a multiplication problem involving two decimal numbers, one of which involves hundredths. • Students should pass their papers to the next person in the group. Each student will then write the number of decimal places the product should have. • Ask students to pass their papers again. This time, each student solves the problem and writes the product, filling in zeros where needed. • Have students discuss whether each problem was completed correctly and state how many decimal places and zeros were in each product. Chapter 7 • Lesson 3 262 262 Go Math! Grade 5 Examples Multiply money. 0.2 ∙ $0.30 STEP 1 Multiply as with whole numbers. Think: The factors are 30 hundredths and 2 tenths. What are the whole numbers you will multiply? ___ $0.30 __ × 0.2 $0.060 STEP 2 Determine the position of the decimal point in the product. Since hundredths are being multiplied by tenths, the product will show ___. STEP 3 Place the decimal point. Write zeros to the left of the whole number product as needed. Since the problem involves dollars and cents, what place value should you use to show cents? ___ So, 0.2 × $0.30 is __. Try This! Find the product. 0.2 × 0.05 = ___ What steps did you take to find the product? Math Talk Construct arguments and critique reasoning of others. MP Explain why the answer to the Try This! can have a digit with a place value of hundredths or thousandths and still be correct. © Houghton Mifflin Harcourt Publishing Company© Houghton Mifflin Harcourt Publishing Company $0.06 30 ∙ 2 thousandths hundredths 0.010, or 0.01 Possible explanation: The answers 0.01 and 0.010 are equivalent. 10 thousandths can be renamed as 1 hundredth. Possible answer: First, I determined how many decimal places will be in the product. Then I multiplied as with whole numbers. Last, I placed the decimal point in the correct position. I had to write a zero to the left of the whole-number product to place the decimal point in the correct position. 30 ∙_ 2 60 0.05 ∙ 0.2 0.010 5 ∙ 2 10 gg CorrectionKey=NL-A gg CorrectionKey=NL-A 5_mnlese694762_c07l03.indd 262 5/27/2022 2:55:14 PM

decimal place decimal places 3 1 2 0.8 ×_ 0.1 8 0.04 ×_ 0.7 28 0.03 ×_ 0.3 9 $0.06 ×_ 0.5 0.09 ×_ 0.8 0.05 ×_ 0.7 0.0 0.0 0.00 35 © Houghton Mifflin Harcourt Publishing Company 3 ×_ 9 27 0.03 ×_ 0.9 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c07r03.indd 35 13/05/22 10:42 AM MTSS RtI1 Name LESSON 7.3 Enrich Multiply and Compare Write , or = in the circle to make each comparison statement true. 1 0.6 × 0.05 = 0.03 2 0.72 > 0.9 × 0.08 3 0.3 × 0.3 > 0.06 4 $0.20 = 0.4 × $0.50 5 0.8 × 0.06 0.07 × 0.6 9 0.3 × 0.12 = 0.4 × 0.09 10 0.2 × 0.19 < 0.8 × 0.05 11 Explain how you completed Exercise 10. Possible explanation: first I found the product 0.2 × 0.19, which is 0.038. Then I found the product 0.8 × 0.05, which is 0.040. Finally, I compared 0.038 and 0.040. Since 3 hundredths is less than 4 hundredths, I know that 0.038 < 0.040. 35 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c07e03.indd 35 13/05/22 10:38 AM

0.03 = 0.04 d. Show how you will solve the problem. e. Complete the sentence. The garden snail travels __ mile in 2 days. 16. In a science experiment, Tania uses 0.8 ounce of water to create a reaction. She wants the next reaction to be 0.1 times the size of the previous reaction. How much water should she use? 17.  e library is 0.5 mile from Celine’s house.  e dog park is 0.3 times as far from Celine’s house as the library. How far is the dog park from Celine’s house? Write an equation and solve. 0.08 ounce 0.5 × 0.3 = 0.15; 0.15 mile or 0.01 or 0.03 the distance traveled by the snail in two days The average distance traveled by the snail is 0.05 mile a day. The snail travels 0.2 times as far as the average distance on Day 1, and 0.6 times as far as the average distance on Day 2. Possible answer: I will use multiplication to  nd 0.2 × 0.05 and 0.6 × 0.05. Then I will add the two products to  nd the total distance. 0.04 0.05 __ × 0.2 0.010 0.05 __ × 0.6 0.030 gg CorrectionKey=NL-A 5_mnlese694762_c07l03.indd 264 5/27/2022 2:55:15 PM

Practice and Homework Multiply Decimals with Zeros in the Product Use the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine students’ understanding of content for this lesson. PROFESSIONAL LEARNING MATH TALK IN ACTION Teacher: How can you check that the product in Problem 6 is reasonable? Sondra: I found the number of decimal places that should be in the product before I multiplied, so I just counted to be sure the product had two decimal places. Blake: I remembered that multiplying tenths by tenths should give me hundredths, so I made sure the answer was in hundredths. Teacher: Very good. Now Look at Problem 8. How is that product different from the product in Problem 6? Jason: In Problem 8, I have to multiply hundredths by tenths, instead of multiplying tenths by tenths. Teacher: Explain how this will change the product. Sondra: There should be three decimal places in the product, instead of two decimal places like in Problem 6. Blake: I used patterns again, so I knew that multiplying tenths by hundredths should give me thousandths. Teacher: Excellent reasoning, everyone. Using patterns or counting the decimal places in the factors will both give you the same results. 265 Go Math! Grade 5 Chapter 7 • Lesson 3 265 © Houghton Mifflin Harcourt Publishing Company LESSON 7.3 Practice and Homework Name Multiply Decimals with Zeros in the Product Find the product. 1. 0.07 ×__ 0.2 0.014 2. 0.3 __ × 0.1 3. 0.05 ×__ 0.8 4. 0.08 ×__ 0.3 5. 0.06 ×__ 0.7 6. 0.2 ×__ 0.4 7. 0.05 __ × 0.4 8. 0.08 ×__ 0.8 9. $0.90 ×__ 0.1 10. 0.02 ×__ 0.3 11. 0.09 ×__ 0.5 12. $0.05 ×__ 0.2 Problem Solving World Real 13. A beaker contains 0.5 liter of a solution. Jordan uses 0.08 of the solution for an experiment. How much solution does Jordan use? 14. A certain type of nuts is on sale at $0.35 per pound. Tamara buys 0.2 pound of nuts. How much will the nuts cost? 15. Write Math Explain how you write products when there are not enough digits in the product to place the decimal point. 7 ×_ 2 14 0.040 or 0.04 liter $0.07 0.03 0.042 0.064 0.04 or 0.040 0.024 0.08 0.020 or 0.02 $0.09 0.006 0.045 $0.01 Check students’ explanations. gg CorrectionKey=NL-A 5_mnlese694762_c07p03.indd 265 5/27/2022 2:54:07 PM

Continue to practice concepts and skills with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Chapter 7 • Lesson 3 266 266 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company Lesson Check 16. Liam multiplies 0.06 and 0.5. What product should he record? 17. What is the product of 0.4 and 0.09? Spiral Review 18. A florist makes 24 bouquets. She uses 16 flowers for each bouquet. Altogether, how many flowers does she use? 19. Pavel has 312 books in his bookcases. He has 11 times as many fiction books as nonfiction books. How many fiction books does Pavel have? 20. Dwayne buys a pumpkin that weighs 12.65 pounds. To the nearest tenth of a pound, how much does the pumpkin weigh? 21. What is the value of the digit 6 in the number 896,000? 0.03 or 0.030 384 flowers 12.7 pounds 0.036 286 fiction books 6,000 gg CorrectionKey=NL-A 5_mnlese694762_c07p03.indd 266 5/27/2022 2:54:07 PM

42 = 342. Make sure students distinguish the properties of addition from the properties of multiplication and that they understand the reasoning for each property. For more professional learning, go online to Teacher’s Corner.

Chapter 7 • Lesson 4 267B DAILY ROUTINES Problem of the Day 7.4 Jacob, Kylie, and Manuel each bought a sandwich and a drink. The total bill came to $21, and each drink cost $2. If each sandwich cost the same amount, what is the cost of one sandwich? $5 Vocabulary • Interactive Student Edition • Multilingual Glossary Fluency Builder Materials base-ten blocks Subtract 3-Digit Numbers Have students work in pairs. Ask each student to model a 3-digit number using baseten blocks. Then have students work together to find the difference between their numbers. Students may have to use regrouping to find the difference. Have student pairs repeat this exercise a few times using different 3-digit numbers. FOCUSING ON THE WHOLE STUDENT Social & Emotional Learning Self-Awareness Ask students to explain how they know when a concept is still unclear. Have you ever gotten the wrong answer but felt confident you knew how to solve the problem? Or maybe you’ve gotten the right answer by chance without really understanding someting? How do you know when something is still unclear, or when a concept does not yet make sense to you? Being able to identify when there is something you do not yet fully understand is an important aspect of your learning journey. 1 Engage with the Interactive Student Edition I Can Objective I can use properties of multiplication to solve problems. Making Connections Invite students to tell you what they know about multiplication of whole numbers. Ask the following questions. • What is the relationship between 10 and the product of 10 and 0? between 10 and the product of 10 and 1? between 10 and the product of 10 and 2? 10 × 0 = 0, and 10 > 0. 10 × 1 = 10, and 10 = 10. 10 × 2 = 20, and 10 < 20. • How can you check the product in a multiplication problem? Possible answer: Estimate the product using nearby numbers that are easy to multiply. Learning Activity Write the following numbers for students to see, then ask them the following questions. 4.5, 3.2, 2. • How many ways can you write multiplication expressions for these three numbers? What are the six ways? 4.5 × 3.2 × 2; 3.2 × 4.5 × 2; 4.5 × 2 × 3.2; 3.2 × 2 × 4.5; 2 × 4.5 × 3.2; 2 × 3.2 × 4.5 • Pick one of the orders that you think would be easier to multiply and one that would be harder to multiply. Explain why. Possible answer: 2 × 4.5 × 3.2 would be easier since I start by multiplying a decimal and a whole number. 4.5 × 3.2 × 2 would be harder since I start by multiplying two decimals.

5 to illustrate the Commutative Property of Addition. • How can you model the Commutative Property of Multiplication? Possible answer: Make a 3 × 2 array and a 2 × 3 array. Both products equal 6. Multilingual Support 267 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (br) ©Monkey Business/Adobe Stock Chapter 7 • Lesson 4 267 CHAPTER 7 Name Lesson 4 Apply Properties of Multiplication to Decimals I Can use properties of multiplication to solve problems. You can use the properties of multiplication to help you evaluate numerical expressions more easily. Properties of Multiplication Commutative Property of Multiplication If the order of factors changes, the product stays the same. 3.6 × 4.25 = 4.25 × 3.6 Associative Property of Multiplication If the grouping of factors changes, the product stays the same. 1.2 × (3 × 5.64) = (1.2 × 3) × 5.64 Identity Property of Multiplication The product of any number and 1 is that number. 7.982 × 1 = 7.982 Zero Property of Multiplication The product of any number and 0 is 0. 9.6 × 0 = 0 UNLOCK the Problem World Real Kalea purchases 1.5 rows of seats for the play. Each row has 8 seats. If every seat costs $6.25, how much did she pay? Use properties to find 8 × 6.25 × 1.5. 8 × 6.25 × 1.5 = 6.25 × _× 1.5 = 6.25 × (8 × _) = 6.25 × _ = _ Kalea pays $ _ for the seats. Use the ___ Property to reorder the factors. Use the ___ Property to group the factors. Use mental math to multiply. Math Talk Construct arguments and critique reasoning of others. MP Explain why grouping 8 and 1.5 makes the problem easier to solve. 8 1.5 Commutative Math Talk: Possible explanation: I can use mental math to multiply 1.5 and 8, and since the product is a whole number, it is easier to multiply by 6.25. Associative 12 75 75 gg CorrectionKey=NL-A 5_mnlese694762_c07l04.indd 267 5/27/2022 2:54:31 PM

_ = _ Write 3.6 as a sum of a whole number and a decimal. Use the Distributive Property. Use mental math to multiply. Use mental math to add. Another Way Use subtraction. 8 × 3.6 = 8 × (_− 0.4) = (_× 4) − (8 × _) = _− _ = _ Write 3.6 as a difference of a whole number and a decimal. Use the Distributive Property. Use mental math to multiply. Use mental math to subtract. Example 2 Complete the equation, and tell which property you used. A 5.843 × _= 5.843 Think: A number times 1 is equal to itself. Property: B 8.49 × 2.7 = 2.7 × _ Think: Changing the order of factors does not change the product. Property: Math Talk Look for and make use of structure. MP Explain how to use the Distributive Property to find the product 6 × 7.99. 3 8 24 4.8 4 8 32 3.2 28.8 1 8.49 Identity Property of Commutative Property of Multiplication Multiplication Math Talk: Possible explanation: Write 7.99 as 8 ∙ 0.01, and then use the Distributive Property. 6 ∙ (8 ∙ 0.01) ∙ (6 ∙ 8) ∙ (6 ∙ 0.01) ∙ 48 ∙ 0.06 ∙ 47.94 0.4 28.8 0.6 gg CorrectionKey=NL-A gg CorrectionKey=NL-A 5_mnlese694762_c07l04.indd 268 6/16/2022 12:18:05 PM

16 = 116 2 Explain how the Associative Property of Addition is similar to the Associative Property of Multiplication. With each property, you can change the grouping of either the addends or the factors and not change the sum or the product. LESSON 7.4 Enrich 36 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c07e04.indd 36 13/05/22 10:39 AM

TM and Version 2.0 Differentiated Centers Kit Grab Problem Solving Applications Problem 16 Students are required to analyze a problem and explain whether or not a student applied the properties correctly. Math on the Spot Use this video to help students model and solve this type of problem. World Real Problem 17 This problem assesses a student’s knowledge of the properties of multiplication. Remind students that the product of any number and 1 is that number. This is the Identity Property of Multiplication. Remind students that when two factors are multiplied together, the product is the same regardless of the order. This is the Commutative Property of Multiplication. The Associative Property of Multiplication deals with the grouping of factors. Remind students, if the grouping of factors changes, the product stays the same. 5 Evaluate Formative Assessment I Can Have students work in pairs to demonstrate and explain the skill for the I Can statement. I can use properties of multiplication to solve problems by . . . using the Associative, Commutative, Identity, and Distributive Properties to group numbers that are easier to multiply. Exit Ticket Explain how you could mentally find 8 × 4.5 by using the Distributive Property. DIFFERENTIATED INSTRUCTION • Independent Activities Tabletop Flipchart Mini-lessons for reteaching to targeted small groups Games Reinforce math content and vocabulary Readers Supports key math skills and concepts in real-world situations. Activities Meaningful and fun math practice Chapter 7 • Lesson 4 270 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (tr) ©tiero/Adobe Stock 270 Go Math! Grade 5 Problem Solving · Applications World Real 13. There are 11 rows of 24 boxes in the warehouse. Each box weighs 6.78 pounds. Use parentheses to write two different expressions to show the total weight of the boxes. Which property does your pair of expressions demonstrate? What is the total weight? 14. Apples cost $1.88 per pound. Use properties to determine how much 6.5 pounds would cost. 15. Sefina bought 8 tickets to a play. Each ticket costs $18.76. To find the total cost in dollars, she added the product 8 × 18 to the product 8 × 0.76, for a total of 150.08. Which property did Sefina use? 16. Omari wrote 1.8 × (3.4 − 2.1) = (1.8 × 3.4) − 2.1. Is Omari’s equation sense or nonsense? Did she apply the properties correctly? Explain. Spot on the 17. Find the property that each equation shows. 2.1 × (4.9 × 3.72) = (2.1 × 4.9) × 3.72 • 1 × 13.604 = 13.604 • 0.007 × 0.45 = 0.45 × 0.007 • 26.825 × 0 = 0 • • Zero Property of Multiplication • Commutative Property of Multiplication • Associative Property of Multiplication • Identity Property of Multiplication 1,789.92 pounds; Possible expressions: (11 x 24) x 6.68 and 11 x (24 x 6.78); Associative Property of Multiplication $12.22 Distributive Property nonsense; no; Possible answer: She used a combination of the Associative Property and the Distributive Property, but neither is correct. gg CorrectionKey=NL-A 5_mnlese694762_c07l04.indd 270 5/27/2022 2:54:33 PM

6 = 114 gg CorrectionKey=NL-A 5_mnlese694762_c07p04.indd 271 5/27/2022 2:53:08 PM

Continue to practice concepts and skills with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Chapter 7 • Lesson 4 272 272 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company Lesson Check 12. To find 1.9 × (3.1 × 5.7). Jean multiplied 1.9 and 3.1. Then he multiplied the product by 5.7. What property did he use? 13. Use the Distributive Property to show an expression that is equal to 5 × 9.8. Spiral Review 14. On average, Americans consume 1.31 pounds of honey every year. How many pounds of honey do they consume in 3 years? 15. A golden eagle flies a distance of 870 miles in 15 days. If the eagle flies the same distance each day of its journey, how far does the eagle fly per day? 16. What is the value of the underlined digit in the following number? 3.495 17. Write the decimal. thirty-two and six hundred five thousandths. Associative Property of Multiplication 3.93 pounds of honey 0.005 58 miles 32.605 (5 ∙ 10) ∙ (5 ∙ 0.2) gg CorrectionKey=NL-A 5_mnlese694762_c07p04.indd 272 5/27/2022 2:53:08 PM

MTSS RtI Waggle 273–274 Go Math! Grade 5 CHAPTER 7 Chapter Review Summative Assessment Use the Chapter Review to assess students’ progress in Chapter 7. Online, Data-Driven Decision Making Based on the results of the Chapter Review, use the following resources to review skills. Item Lesson Content Focus Intervene With 4, 15 7.1 Place the decimal point in decimal multiplication. Reteach 7.1, Waggle 1, 3, 6, 8A, 8B, 9, 10, 11, 12, 13C, 16, 17, 18, 19, 20A, 20B, 21 7.2 Place the decimal point in decimal multiplication. Reteach 7.2, Waggle 2, 22 7.3 Multiply decimals with zeros in the product. Reteach 7.3, Waggle 5, 7, 13A, 13B, 14 7.4 Use properties of operations to solve problems. Reteach 7.4, Waggle 274 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company© Houghton Mifflin Harcourt Publishing Company 5. Use properties to find 4 × 7.9 × 2.5. 7.9 × __ × 2.5 __ Property of Multiplication 7.9 × __ × __ __ Property of Multiplication 7.9 × __ __ 6. Which problems will have two decimal places in the product? Mark all that apply. A 3.4 × 6.7 B 7.4 × 10 C 9.85 × 1 D 8.4 × 9 E 7 × 2.96 7. Madeleine is trying to multiply 0.5 x 0.34 x 2. Explain how she can use the Identity Property of Multiplication to find the product. What is the product? 8. Maria worked 31.75 hours this week. Part A Last week, Maria worked 0.8 times as many hours. How many hours did she work last week? Show your work. hours Part B Next week, Maria is scheduled to work 1.2 times as many hours. Assuming she works whatever she is scheduled for, how many hours will she work next week? Show your work. hours 4 4 Commutative 2.5 Associative 10 79 0.34; Possible explanation: She can first use the Commutative Property to rewrite the expression as 0.5 × 2 × 0.34. Then, Check students’ work. Check students’ work. 25.4 38.1 0.5 × 2 = 1, and the Identity Property of Multiplication says that anything multiplied by 1 is itself. DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A DO NOT EDIT--Chan CorrectionKey=NL- 5_mnlese694762_c07cr.indd 274 5/27/2022 2:56:40 PM Chapter 7 273 © Houghton Mifflin Harcourt Publishing Company Chapter 7 Name Chapter Review 1. Patricio is making a scale model of his school. His school is 11.4 meters tall. If the model is 0.07 of the actual size of the school, how tall is the model? meters 2. For 2a–2d, choose Yes or No to indicate whether the product is correct. 2a. 0.3 × 0.4 = 1.2 ● Yes ● No 2b. 0.02 × 0.4 = 0.008 ● Yes ● No 2c. 0.05 × 0.3 = 0.015 ● Yes ● No 2d. 0.06 × 0.03 = 0.018 ● Yes ● No 3. Leona is working with a piece of string that is 5.5 feet long. She needs the string to be 2.7 times as long. How long will the string be? 4. Laurel models the product 0.9 × 0.6. Shade the correct amount of boxes that will show the product. Find the product. 0.9 × 0.6 = __ Go Online For more help 0.798 14.85 feet 0.54 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A 5_mnlese694762_c07cr.indd 273 5/27/2022 2:56:39 PM

  __3.91 10.71 2.3 ∙_1.7 161  ∙_____ 230 3.91 1.7 _ ∙ 4.7 6.8 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A 5_mnlese694762_c07cr.indd 276 5/27/2022 2:56:40 PM Chapter 7 275 © Houghton Mifflin Harcourt Publishing Company© Houghton Mifflin Harcourt Publishing Company Name 9. Arabella drives 17.8 miles a day. Yaya drives 1.6 times as far each day. How far does Yaya drive in 3 weeks? Show your work. Check students’ work. 598.08 miles 10. Elianna practices flute for 4.8 hours each week. Avery practices the oboe for 2.7 times as long each week. How many hours does Avery practice each week? 12.96 hours Check students’ work. 11. Use the numbers in the boxes to complete the number sentences. A number may be used more than once. 1,620 162 16.2 1.62 0.162 3.6 × 4.5 = 16.2 3.6 × 45 = 162 3.6 × 0.45 = 1.62 0.36 × 0.45 = 0.162 12. Beau spends 4 times as much as Jin on gear for the track season. Jin spent $12.89. How much did Beau spend? $ 51.56 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A 5_mnlese694762_c07cr.indd 275 5/27/2022 2:56:40 PM 278 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company 19. For 19a–19d select True or False for each statement. 19a. The product of 1.5 and 2.8 is 4.2. ● True ● False 19b. The product of 7.3 and 0.6 is 43.8. ● True ● False 19c. The product of 0.09 and 0.7 is 6.3. ● True ● False 19d. The product of 0.79 and 1.5 is 1.185. ● True ● False 20. A builder buys 24.5 acres of land to develop a new community of homes and parks. Part A The builder plans to use 0.25 of the land for a park. How many acres will he use for the park? acres Part B He buys a second property that has 0.62 times as many acres as the first property. How many acres of land does the second property have? Show your work. 24.5 __∙ 0.62 490 ∙__ 14700 15.190 The second property has 15.190 or 15.19 acres of land. 21. Joaquin lives 0.3 mile from Keith. Layla lives 0.4 times as far from Keith as Joaquin. How far does Layla live from Keith? Write an equation to solve. mile 22. Brianna is getting materials for a chemistry experiment. Her teacher gives her a container that has 0.15 liter of a liquid in it. Brianna needs to use 0.4 of this liquid for the experiment. How much liquid will Brianna use? liter 6.125 0.3 ∙ 0.4 ∙ 0.12 0.06 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A 5_mnlese694762_c07cr.indd 278 5/27/2022 2:56:41 PM Chapter 7 277 © Houghton Mifflin Harcourt Publishing Company© Houghton Mifflin Harcourt Publishing Company Name 15. Shade the model to show 0.5 × 0.3. Then find the product. 0.5 × 0.3 = 0.15 16. Genesis reports that 4.5 × 7.6 = 3.42. Is she correct? Explain your reasoning. No; Because 45 ∙ 76 ∙ 3420, the product of 4.5 ∙ 7.6 would be 34.20, or 34.2. She did not include the 0 as a decimal place since it did not have to be written. 17. Explain how an estimate helps you to place the decimal point when multiplying 3.9 × 5.3. Possible explanation: The estimate, 4 ∙ 5 ∙ 20, helps me know that the decimal point should be placed so that the answer is close to 20. 18. On Saturday, Ahmed walks his dog 0.7 mile. On the same day, Latisha walks her dog 0.4 times as far as Ahmed walks his dog. How far does Latisha walk her dog on Saturday? _0.28 mile(s) DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A 5_mnlese694762_c07cr.indd 277 5/27/2022 2:56:40 PM

278A Go Math! Grade 5 CHAPTER 7 Chapter Test Summative Assessment Use the Chapter Test to assess students’ progress in Chapter 7. Chapter Tests are found in the Assessment Guide. Test items are presented in formats consistent with high-stakes assessments. Grade 5 • Chapter 7 Test 43 © Houghton Mifflin Harcourt Publishing Company Name Chapter 7 Chapter Test 1 Maria wants to find 0.2 × 0.6. What model should Maria use to find the product? A B C D What is the product? 0.2 × 0.6 = 2 During a track meet, Calvin drinks 0.6 liter of water. Melinda drinks 0.8  times as much water as Calvin during the track meet. How much water does Melinda drink during the track meet? liter(s) 3 Place an X in the table to show if each sentence is true or false. True False The product of 1.3 and 2.1 is 2.73. The product of 4.8 and 0.4 is 12.2. The product of 0.08 and 0.7 is 5.6. The product of 0.21 and 1.8 is 0.378. 4 Bruce is getting materials for a chemistry experiment. His teacher gives him a container that has 0.25  liter of a liquid in it. Bruce needs to use 0.4 of this liquid for the experiment. How much liquid will Bruce use? A 100 liters B 1 liter C 0.1 liter D 0.001 liter 0.12 0.48 5_GMNLE_AS_1836710_CH07.indd 43 14/05/22 12:09 PM 44 © Houghton Mifflin Harcourt Publishing Company Name Chapter 7 Chapter Test 5 A builder buys 16.1 acres of land to develop a new set of walking trails and baseball fields. Part A The builder plans to use 0.25 of the land for baseball fields. How many acres will the builder use for the baseball fields? acres Part B The builder buys a second property that has 0.41 times as many acres as the first property. How many acres of land are in the second property? acres 6 Which equation is shown by the model? A 4 × 1.4 = 5.6 B 0.4 × 1.14 = 0.056 C 0.4 × 0.14 = 0.056 D 0.04 × 0.14 = 0.0056 7 What are the unknown numbers in the equation? 0.3 × 1.8 × 0.2 = (0.3 × ) × 1.8 = 8 Mr. O’Brien is paid $9.30 per hour for the first 40 hours he works in a week. He is paid 1.5 times that rate for each hour after that. Last week, Mr. O’Brien worked 44 hours. He says he earned $409.20 last week. Do you agree? Circle the words to correctly complete the sentence. I agree disagree because Mr. O’Brien made more than exactly less than $409.20 last week. 9 Gia multiplies 2.3 by 1.65. What is the place value of the decimal in the product? A thousandths B hundredths C tenths D ones 10 To solve 0.2 × 0.06, Pilar multiplies whole numbers. She writes 2 × 6 = 12. Which amount shows where Pilar should place the decimal point in the product? A 12.00 B 0.012 C 0.12 D 1.20 4.025 6.601 0.2 0.108 5_GMNLE_AS_1836710_CH07.indd 44 14/05/22 12:09 PM

Chapter 7 Test 278B Teacher Notes

TM and Version 2.0 Differentiated Centers Kit Grab CHAPTER 8 Chapter at a Glance Divide Decimals LESSON 8.1 • 1 Day LESSON 8.2 • 1 Day LESSON 8.3 • 1 Day Lesson at a Glance Understand Decimal Division Patterns . . . 281A Represent Division of Decimals by Whole Numbers . . . . . . . . . . 287A Estimate Quotients . . 293A I Can I can use patterns to help place the decimal point in a quotient. I can use a model to divide a decimal by a whole number. I can estimate decimal quotients. Learning Goal Use patterns to help place the decimal point in a quotient. Model division of decimals by whole numbers. Estimate decimal quotients. Vocabulary Multilingual Support Strategy: Identify Relationships Strategy: Model Concepts Strategy: Develop Meanings Practice and Fluency LESSON 8.1 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* LESSON 8.2 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* LESSON 8.3 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* MTSS RtI Intervention and Enrichment ■ Waggle ◆ ■ Reteach 8.1 ◆ ■ Tier 2 Intervention Skill S70 ◆ ■ Tier 3 Intervention Skill E70 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 8.1 ■ Waggle ◆ ■ Reteach 8.2 ◆ ■ Tier 2 Intervention Skill S55 ◆ ■ Tier 3 Intervention Skill E55 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 8.2 ■ Waggle ◆ ■ Reteach 8.3 ◆ ■ Tier 2 Intervention Skill S71 ◆ ■ Tier 3 Intervention Skill E71 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 8.3 See the Grab-and-Go!™ Centers Kit for more small-group activities. The kit provides literature, games, and activities for small-group learning. ◆ Print/Printable Resource ■ Interactive Resource 279A Go Math! Grade 5

Chapter Pacing Chart Introduction Instruction Assessment Total 1 day 7 days 2 days 10 days LESSON 8.4 • 1 Day LESSON 8.5 • 1 Day LESSON 8.6 • 1 Day Lesson at a Glance Divide Decimals by Whole Numbers . . . . 299A Represent Decimal Division . . . . . . . . . . . 305A Write Zeros in the Dividend . . . . . . . . . . 311A I Can I can divide decimals by whole numbers. I can use a model to divide by a decimal. I can determine when to write a zero in the dividend to find a quotient. Learning Goal Divide decimals by whole numbers. Model division by decimals. Write a zero in the dividend to find a quotient. Vocabulary Multilingual Support Strategy: Model Concepts Strategy: Scaffolding Language Strategy: Model Concepts Practice and Fluency LESSON 8.4 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* LESSON 8.5 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* LESSON 8.6 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* MTSS RtI Intervention and Enrichment ■ Waggle ◆ ■ Reteach 8.4 ◆ ■ Tier 2 Intervention Skill S71 ◆ ■ Tier 3 Intervention Skill E71 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 8.4 ■ Waggle ◆ ■ Reteach 8.5 ◆ ■ Tier 2 Intervention Skill S71 ◆ ■ Tier 3 Intervention Skill E71 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 8.5 ■ Waggle ◆ ■ Reteach 8.6 ◆ ■ Tier 2 Intervention Skill S55 ◆ ■ Tier 3 Intervention Skill E55 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 8.6 *For individual and class practice with counting automaticity and operational fluency, go to Achieving Facts Fluency pages located online. ◆ Print/Printable Resource ■ Interactive Resource Chapter 8 279B

CHAPTER LESSON 8.7 • 1 Day Lesson at a Glance Solve Multi-Step Decimal Problems . . . . . . . . . . 317A I Can I can work backward to solve a multi-step decimal problem. Learning Goal Solve multi-step decimal problems using the strategy work backward. Vocabulary Multilingual Support Strategy: Understanding Context Practice and Fluency LESSON 8.7 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* MTSS RtI Intervention and Enrichment ■ Waggle ◆ ■ Reteach 8.7 ◆ ■ Tier 2 Intervention Skill S84 ◆ ■ Tier 3 Intervention Skill E84 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 8.7 8 Chapter at a Glance Divide Decimals ◆ Print/Printable Resource ■ Interactive Resource 279C Go Math! Grade 5

Teacher Notes Chapter 8 279D

CHAPTER 8 Teaching for Depth Divide Decimals Decimals Divided by Whole Numbers Modeling operations helps students make sense of the procedures. • Dividing decimals by whole numbers is best modeled using sharing (partitive) division. This is where the total number (dividend) is shared among the given number of groups (divisor). • Students use decimal models to represent the dividend and then share them equally among the given number of groups, regrouping as necessary. • Contexts also support this process. The model below represents this problem. James bought 9.6 pounds of rice to share equally among 4 families. How much rice will he give to each family? Use Procedures to Divide Students make sense of procedures for dividing decimals by estimating the quotient using compatible numbers. This estimate can help the student place the decimal point after dividing. Exploring division with models and contexts and making sense of the placement of the decimal point after dividing will help students to understand how the decimal division algorithms work. From the Research “Students who worked on the contextualized problems improved their competence with decimals more than did a comparable group of students.” (Irwin, 2001, p. 415) Decimals Divided by Decimals Decimal models can be used to show how to divide decimals by decimals. • Students model dividing decimals by decimals using measurement (quotitive) division. In measurement division the total number (dividend) is known, as is the number in each group (divisor). • The quotient represents the number of groups. • Consider this problem: Latoya has 2 liters of milk to use to feed the kittens. How many servings of milk can she make if each serving is 0.4 liter? • To solve this problem, students would represent 2 liters with 2 flats and then exchange them for 20 longs to see how many groups of 4 longs they can make. Mathematical Practices and Processes Look for and make use of structure. Dividing decimals will provide students with opportunities to problem solve. Students use structure when they model decimal division. The modeling helps them develop procedures for determining quotients. Eventually, students solve multi-step problems involving decimal division. When they encounter difficult problems, they can use models to help them. For more professional learning, go online to Teacher’s Corner. 279E Go Math! Grade 5

TM and Version 2.0 Differentiated Centers Kit Grab Chapter 8 279F Instructional Journey While every classroom may look a little different, this instructional model provides a framework to organize small-group and whole-group learning for meaningful student learning. Whole Group Engage 5 minutes Readiness • Problem of the Day • Fluency Builder or Vocabulary Builder • Access Prior Knowledge Engagement • I Can • Making Connections • Learning Activity Small and Whole Group Explore 15–20 minutes Exploration • Investigate, Unlock the Problem • Multilingual Support and Strategy • Common Errors Small Group Explain 15–20 minutes Quick Check Share and Show Differentiated Instruction TM and Version 2.0 Grab Intervention • Waggle • Reteach • Tier 2 and Tier 3 MTSS • Tabletop Flipchart Mini Lessons Language Support • Vocabulary Activities • Language Routines • Multilingual Glossary Enrichment • Waggle Games • Ready for More • Enrich Whole Group Elaborate 5 minutes • Math on the Spot Videos • Higher-Order Thinking Problems Evaluate • I Can Reflection • Exit Ticket • Practice and Homework • Fluency Practice • Waggle Assessment Diagnostic Formative Summative • Show What You Know • Lesson Quick Check • Chapter Review • Chapter Test • Performance Assessment Task The kit provides literature, games, and activities for small-group learning.

CHAPTER 8 Strategies for Multilingual Learners Assessing your student’s understanding of mathematical concepts can be done by listening, speaking, reading, and writing. The level of support a student needs determines how best to assess that student’s understanding of mathematical concepts and will help meet the needs of all your students. Planning for Instruction Language Support Substantial (WIDA Level 1)* Moderate (WIDA Levels 2 & 3)* Light (WIDA Levels 4 & 5)* Student’s Use of Language • uses single words • uses common short phrases • heavily relies on visual supports and use of manipulatives • uses single words • uses some academic vocabulary • relies on visual supports and use of manipulatives • uses a variety of sentences • uses academic vocabulary • benefits from visual supports and manipulatives Ways to Assess Understanding Listening: points to pictures, words, or phrases to answer questions Speaking: answers yes/no questions Reading: matches symbols to math terms and concepts Writing: draws a visual representation of a problem Listening: matches, categorizes, or sequences information based on visuals Speaking: begins to explain reasoning, asks math questions, repeats explanations from peers Reading: identifies important information to solve a problem Writing: uses simple sentences and visual representations Listening: draws conclusions and makes connections based on what they heard Speaking: explains and justifies concepts and solutions Reading: understands information in math contexts Writing: completes sentences using some academic vocabulary * For more information on WIDA Standards, visit their website at: https://wida.wisc.edu/. • Look for strategies throughout the lesson to support multilingual learners. • Log on to ED to find additional multilingual activities and Vocabulary Cards. 279G Go Math! Grade 5

In This Chapter Key Academic Vocabulary Current Development • Vocabulary Using Language Routines to Develop Understanding Language routines provide opportunities for students to develop an understanding of mathematical language and concepts by listening, speaking, reading, and writing. More information on these language routines can be found on the Language Support Cards. Stronger and Clearer Each Time 1 Students show their thinking with math tools and visuals. 2 Students share their thinking and receive feedback with a partner or a group. 3 Students revoice feedback and revise their work. Language Support Substantial (WIDA Level 1)* Moderate (WIDA Levels 2 & 3)* Light (WIDA Levels 4 & 5)* Language Routine Differentiation 1 Students show their thinking using visuals and/ or manipulatives. 2 Students answer yes/no or single-word-answer questions about their reasoning. 3 Students revise their work. 1 Students show thinking using words and/or visuals. 2 Students communicate with their partner or group using visual representations. 3 Students repeat feedback and revise their work. 1 Students show thinking using words and visuals. 2 Students use academic vocabulary to communicate with their group. 3 Students revoice feedback and revise their work. Possible Student Work Solve. ___ 1.2 3 = Model 1.2 1 one 2 tenths Make 3 even groups. How many tenths in each group? 4 ___ 1.2 3 = .4 Solve. ____ 1.29 3 = ____ 1.29 3 = Estimate. 1.2 _____ 3 = .4 Show the steps. .43 3∙1.29 1.2 9 9 0 ____ 1.29 3 = .43 .43 3∙1.29 1.2 9 9 0 Does 3 go into 1? no Does 3 go into 12? yes How many times? 4 .4 × 3 = 1.2 .03 × 3 = .09 ____ 1.29 3 = .43 * For more information on WIDA Standards, visit their website at: https://wida.wisc.edu/. Chapter 8 279H

World MATH Real in the INTERVENE If NO...then INTERVENE If YES...then use INDEPENDENT ACTIVITIES TM and Version 2.0 Differentiated Centers Kit Grab CHAPTER 8 Assessing Prior Knowledge Use Show What You Know to determine if students need intensive or strategic intervention. In this activity, students are given a set of clues to find the solution of a multi-step division and addition problem. Discuss solution strategies, and then ask: • What does “one-tenth” mean? one of 10 equal parts • How can you use division to find onetenth of a number? I know that dividing a number by 10 is the same as multiplying a number by one-tenth. • What is one way to find Sora’s age? Possible answer: I can divide 3,000 by 10, divide the quotient by 10, and then divide that quotient again by 10. Finally, I add 10 to the final quotient. Show What You Know • Diagnostic Assessment Use to determine if students need intervention for the chapter’s prerequisite skills. Were students successful with Show What You Know? TIER 3 TIER 2 TIER 2 Skill Missed More Than Division Facts 1 Estimate with 1-Digit Divisors 1 Division 1 Intervene With Intensive Intervention Skill E53 Strategic Intervention Skill S56 Strategic Intervention Skill S61 Use the Reteach or Enrich Activities online or the independent activities in the Grab-and-Go 2.0™ Differentiated Centers Kit. 279 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (b) ©Christoph Weihs/Alamy Images; (inset) ©Powered by Light RF/Alamy Images Chapter 8 Chapter 8 279 Name Divide Decimals Show What You Know Division Facts Find the quotient. 1. 6 )‾24 = _ 2. 7 )‾56 = _ 3. 18 ÷ 9 = _ 4. 35 ÷ 5 = _ Estimate with 1-Digit Divisors Estimate the quotient. 5. 6 )‾253 6. 4 )‾1,165 7. 7 )‾1,504 Division Divide. 8. 34 )‾785 9. 27 ) 1,581 ‾ 10. 41 )‾4,592 MATH in the World Real Instead of telling Carmen her age, Sora gave her this clue. Find Sora’s age. Clue My age is 10 more than one-tenth of one-tenth of one-tenth of 3,000. 40 4 8 2 7 23 r3 Sora’s age is 13. 300 58 r15 200 112 Possible estimates are given. y 5_mnlese694762_c08co.indd 279 5/27/2022 2:52:53 PM

. Intervention Options MTSS RtI Response to Intervention TIER 1 TIER 2 TIER 3 ENRICHMENT On-Level Intervention Strategic Intervention Intensive Intervention Independent Activities TIER 1 TIER 2 TIER 3 ENRICHMENT On-Level Intervention Strategic Intervention Intensive Intervention Independent Activities TIER 1 TIER 2 TIER 3 ENRICHMENT On-Level Intervention Strategic Intervention Intensive Intervention Independent Activities TIER 1 TIER 2 TIER 3 ENRICHMENT On-Level Intervention Strategic Intervention Intensive Intervention Independent Activities TM and Version 2.0 Differentiated Centers Kit Grab Vocabulary Builder Have students complete the activities on this page by working alone or with partners. Visualize It The bubble map is a visual representation of concepts that are related. The word decimal is at the center. Other related words are placed in the bubbles around it. Understand Vocabulary Introduce the review words for the chapter. Students can enhance their understanding of key chapter vocabulary through the use of the VOCABULARY CARDS. Have students cut out the cards and create their own deck of terms. You can use these cards to reinforce knowledge and reading across the content areas. School-Home Letter is available in English and Spanish online, and in multiple other languages. Use Show What You Know, Lesson Quick Check, and Assessments to diagnose students’ intervention levels. For students who are generally at grade level but need early intervention with the lesson concepts, use: • Reteach • Tabletop Flipchart Mini Lesson • Waggle 1 2 3 Tier 1 Activity For students who need smallgroup instruction to review concepts and skills needed for the chapter, use: 1 2 3 Prerequisite Skills Activities 1 2 3 Tier 2 Activity For students who need one-on-one instruction to build foundational skills for the chapter, use: 1 2 3 Prerequisite Skills Activities 1 2 3 Tier 3 Activity For students who successfully complete lessons, use: • Waggle Practice and Games • Ready for More Activity for every lesson • Enrich Chapter 8 280 280 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (br) ©HMH Vocabulary Builder Go Online For more help Visualize It Complete the bubble map using review words. decimal decimal point hundredth tenth Connect to Vocabulary Review Words compatible numbers decimal decimal point dividend divisor equivalent fractions estimate exponent hundredth quotient remainder tenth Understand Vocabulary Complete the sentences using review words. 1. A ____ is a symbol used to separate the ones place from the tenths place in decimal numbers. 2. Numbers that are easy to compute with mentally are called ____. 3. A ____ is one of ten equal parts. 4. A number with one or more digits to the right of the decimal point is called a ____. 5. The ____ is the number that is to be divided in a division problem. 6. A ____ is one of one hundred equal parts. 7. You can ____ to find a number that is close to the exact amount. © Houghton Mifflin Harcourt Publishing Company • Image Credits: (br) ©HMH is the number that is to be is one of one hundred decimal point compatible numbers tenth decimal dividend hundredth estimate Check students’ maps. Possible answers shown. y 5_mnlese694762_c08co.indd 280 5/27/2022 2:52:56 PM

281A Go Math! Grade 5 LESSON 8.1 Lesson at a Glance Understand Decimal Division Patterns SNAPSHOT Mathematical Standards ● Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Mathematical Practices and Processes ● Attend to precision. ● Construct arguments and critique reasoning of others. ● Look for and make use of structure. ● Model with mathematics. I Can Objective I can use patterns to help place the decimal point in a quotient. Learning Goal Use patterns to help place the decimal point in a quotient. Language Objective Students express an opinion about how they think patterns help you place the decimal point in a quotient. MATERIALS • MathBoard ACROSS THE GRADES Before Grade 5 After Explore the multiplication and division of multi-digit whole numbers using estimation, rounding and place value. Explore the multiplication and division of multi-digit numbers with decimals to the hundredths using estimation, rounding and place value. Multiply and divide positive multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency. ABOUT THE MATH Teaching for Depth Students are already familiar with multiplying by 10 and 100 and by 0.1 and 0.01. In this lesson, students learn that the patterns for dividing are similar to the patterns for multiplying, where the position of the decimal point in the product moves one place to the left as the number of decimal digits increases in the decimal factor. 36 × 1 = 36 36 ÷ 1 = 36 36 × 0.1 = 3.6 36 ÷ 10 = 3.6 36 × 0.01 = 0.36 36 ÷ 100 = 0.36 It is helpful for students to see that dividing by 10 and 100 is the same as multiplying by 0.1 and 0.01 or finding __1 10 and ___1 100 of a number. Seeing connections helps deepen students’ understanding of math concepts. For more professional learning, go online to Teacher’s Corner.

Chapter 8 • Lesson 1 281B DAILY ROUTINES Problem of the Day 8.1 Tracy uses 1.5 cups of flour to make 1 loaf of banana bread. How many cups of flour does she need for 100 loaves of banana bread? 150 cups Vocabulary • Interactive Student Edition • Multilingual Glossary Vocabulary Builder The vocabulary in this lesson should be familiar to students. Briefly review the terms to make sure students understand the meanings: decimal, decimal point, dividend, divisor, and quotient. Write the following problem on the board, and read the vocabulary terms so students can identify each part of the problem. decimal point decimal 6.5 ÷ 10 ∙ 0.65 quotient dividend divisor FOCUSING ON THE WHOLE STUDENT Access Prior Knowledge Have students review multiplying by 10, 100, and 1,000 by solving the problems below. 3 × 1 = _____ 3 × 100 = _____ 3 × 10 = _____ 3 × 1,000 = _____ • How do 10, 100, and 1,000 compare? The number of zeros in each multiple of 10 increases by one each time, so it is 10 times as great as the previous multiple of 10. • How do the products compare? Possible answer: Each product is 10 times as great as the previous product. Social & Emotional Learning Self-Management When students cannot figure out how to proceed with a task, encourage them to consider using alternative strategies or approaches suggested by their classmates. What do you do when your strategy is not working for the problem situation? It is good to persevere, and sometimes that means recognizing what you are trying isn’t working like you thought it would and getting ideas from other people. What is your preferred way to gain a new perspective about a problem? Do you reach out to your classmates or try to figure it out on your own? 3 300 30 3,000 1 Engage with the Interactive Student Edition I Can Objective I can use patterns to help place the decimal point in a quotient. Making Connections Invite students to tell you what they know about growing plants. • Have you ever planted a seed in a flowerpot or in a garden? What kind of seed was it? Answers will vary. • Did your seed grow? Answers will vary. • What does a plant need to grow? water, sun, and soil • What are some foods that come from plants? Possible answer: beans, corn, tomatoes Learning Activity The height of a mailbox post is 103 centimeters and the mailbox post is as tall as 100 flowers stacked on top of one another. All the flowers have the same height. What is the height of each flower? • What is the relationship between the height of the flower and the height of the mailbox? The flower’s height is the height of the mailbox post divided by 100. • Will the height of the flower be greater than 103 centimeters or less than 103 centimeters? Possible answer: less than 103 centimeters because the flower is shorter than a mailbox post • How many hundreds are in 103? one hundred How might this answer help you solve the problem? Possible answer: Dividing 100 by 100 equals 1, so the height of each flower will be about 1 centimeter.

LESSON 8.1 2 Explore Unlock the Problem Read the problem, and have students identify the operation needed to solve it. One Way Look for and make use of structure. Have students look at the multiplication pattern. Point out that as the decimal point moves left in the decimal factor, the decimal point also moves left in the product. • Now look at the division pattern. What happens to the divisor each time? The divisor is 10 times as great as the previous divisor. • What fraction of 560 is 56? 56 is __1 10 of 560. • What happens to the quotient each time? Possible answer: The quotient is __1 10 the size of the previous quotient. Problem 1 Students must explain what they notice about the quotients. • What happens to the divisor each time? The number of zeros increases by one each time, so each divisor is 10 times as great as the previous divisor in the pattern. • What happens to the position of the decimal point in the quotient as the number of zeros in the divisor increases? Possible answer: The decimal point moves one place to the left as the number of zeros in the divisor increases by one. MP STRATEGY: Identify Relationships Have students write these problems on their MathBoards. 132 ÷ 1 = 132 132 ÷ 10 = 13.2 132 ÷ 100 = 1.32 132 ÷ 1,000 = 0.132 • Discuss the pattern. • Have students place their finger on the decimal point and move it one place to the left for each zero in the divisor. • Have students use the model to talk about dividing by 1,000. Multilingual Support 281 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©279photo Studio/Shutterstock Chapter 8 • Lesson 1 281 CHAPTER 8 Name Lesson 1 Understand Decimal Division Patterns I Can use patterns to help place the decimal point in a quotient. UNLOCK the Problem The Healthy Wheat Bakery uses 560 pounds of flour to make 1,000 loaves of bread. Each loaf contains the same amount of flour. How many pounds of flour does the bakery use in each loaf of bread? You can use place-value patterns to help you find quotients. Dividing by 10, 100, or 1,000 is the same as multiplying by 0.1, 0.01, or 0.001. 560 × 1 = 560 560 × 0.1 = 56.0 560 × 0.01 = 5.60 560 × 0.001 = 0.560 • Underline the sentence that tells you what you are trying to find. • Circle the numbers you need to use. One Way Use place-value patterns. Divide. 560 ÷ 1,000 Look for a pattern in these products and quotients. 560 ÷ 1 = 560 560 ÷ 10 = 56.0 560 ÷ 100 = 5.60 560 ÷ 1,000 = 0.560 560 ÷ 0.1 = 5,600 560 ÷ 0.01 = 56,000 So, _ pound of flour is used in each loaf of bread. 1. What do you notice about the quotients as you divide by 10, 100, and 1,000? 0.56 The decimal point moves one place to the left as the place value increases. gg CorrectionKey=NL-A 5_mnlese694762_c08l01.indd 281 5/27/2022 2:52:34 PM

Example Read and discuss the problem with students. • What number can you divide 25.5 by to find how many pounds of onions Liang used? Explain. 10. He used __1 10 as many pounds of onions as pounds of tomatoes; dividing by 10 is the same as finding __1 10 of a number. • What number can you divide 25.5 by to find how many pounds of green peppers Liang used? Explain. 100; Possible explanation: He used ___1 100 as many pounds of green peppers as pounds of tomatoes, and dividing by 100 is the same as finding ___1 100 of a number. Try This! Work through the problems and review the patterns with students. • Describe the patterns you see. Possible answers: Each quotient is __1 10 the size of the previous quotient. The decimal point moves one place to the left as the number of zeros in the divisor increases by one. Construct arguments and critique reasoning of others. Math Talk Use Math Talk to focus on students’ understanding of placing the decimal point in a quotient when dividing by different values. • Could you use the same method to divide a whole number by 10, 100, or 1,000? Yes. I can rewrite the whole number as a decimal, and then I can apply the same method to divide. MP 3 Explain Share and Show The first problem connects to the learning model. Have students use the MathBoard to explain their thinking. Math Board Common Errors Common Errors Error Students may move the decimal point to the right instead of to the left when dividing by 10, 100, and 1,000. Example 12.7 ∙ 1 ∙ 12.7 12.7 ∙ 10 ∙ 127 Springboard to Learning Remind students that when dividing by a whole number greater than 1, the quotient will be less than the dividend. Ready for More Visual Partners Materials index cards, scissors • Give each student four index cards. Have students cut the index cards in half. • Have students write four problems, each one on half of an index card. Each problem should show a number divided by 1, by 10, by 100, and by 1,000. Students should write each answer on the other half of the index card. • Students mix up their cards and trade them with a partner. Partners then match each problem with its answer. • Have partners trade their cards with another pair of students and do the activity again. 345 ÷ 100 = 3.45 Chapter 8 • Lesson 1 282 282 Go Math! Grade 5 CONNECT Dividing by 10 is the same as multiplying by 0.1 or finding __1 10 of a number. Example Liang used 25.5 pounds of tomatoes to make a large batch of salsa. He used one-tenth as many pounds of onions as pounds of tomatoes. He used one-hundredth as many pounds of green peppers as pounds of tomatoes. How many pounds of each ingredient did Liang use? Tomatoes: 25.5 pounds Onions: 25.5 pounds ÷ _ Think: 25.5 ÷ 1 = _ 25.5 ÷ 10 = _ Green Peppers: 25.5 pounds ÷ _ Think:_÷ 1 = _ _÷ 10 = _ _÷ 100 = _ So, Liang used 25.5 pounds of tomatoes, _ pounds of onions, and _ pound of green peppers. Try This! Complete the pattern. A 32.6 ÷ 1 = __ 32.6 ÷ 10 = __ 32.6 ÷ 100 = __ B 50.2 ÷ 1 = __ 50.2 ÷ 10 = __ 50.2 ÷ 100 = __ Math Talk Construct arguments and critique reasoning of others. MP How can you determine where to place the decimal point in the quotient 47.3 ÷ 100? Math Share and Show Board Complete the pattern. 1. 456 ÷ 1 = 456 456 ÷ 10 = 45.6 456 ÷ 100 = 4.56 456 ÷ 1,000 = _ Think: The dividend is being divided by increasing place values, so the decimal point will move to the _ 1 place for each increasing place value. © Houghton Mifflin Harcourt Publishing Company • Image Credits: (tc) ©comstock/Getty Images; (cl) ©Artville/Getty Images; (tr) ©Brand X Pictures/Getty Images© Houghton Mifflin Harcourt Publishing Company 10 100 25.5 25.5 2.55 0.255 25.5 25.5 25.5 2.55 0.255 2.55 32.6 50.2 3.26 5.02 0.326 0.502 left Math Talk: Possible explanation: I can use a place-value pattern. The decimal point will move 2 places to the left. 0.456 gg CorrectionKey=NL-A gg CorrectionKey=NL-A 5_mnlese694762_c08l01.indd 282 5/27/2022 2:52:34 PM

3 Explain Use the checked problems for Quick Check. Students should show their answers for the Quick Check on the MathBoard. Quick Check If MTSS RtI If MTSS RtI Then a student misses the checked problems Differentiate Instruction with • Reteach 8.1 • Waggle Look for and make use of structure. Math Talk Use Math Talk to focus on students’ understanding of place value. • As the divisor increases in value, what happens to the quotient? It decreases. MP 4 Elaborate On Your Own If students complete the checked problems correctly, they may continue with the remaining problems. Attend to precision. Problems 11–13 Students are required to use higher-order thinking skills as they apply what they learned to find the value of n. • How can you find the value of n in Problem 11? Possible answer: If I compare the dividend and the quotient, I can see the decimal place has moved three places to the left. This means the divisor n must be 1,000. • How can you find the value of n in Problem 12? Possible answer: If I divide by 100, the decimal place would move two places to the left. So, if I move the decimal place in the quotient two places to the right, I would get the dividend n. MP Meeting Individual Needs Reteach 8.1 Enrich 8.1 283 Go Math! Grade 5 Chapter 8 • Lesson 1 283 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (tc) ©comstock/Getty Images; (cl) ©Artville/Getty Images; (tr) ©Brand X Pictures/Getty Images© Houghton Mifflin Harcourt Publishing Company Name Complete the pattern. 2. 225 ÷ 1 = _ 225 ÷ 10 = _ 225 ÷ 100 = _ 225 ÷ 1,000 = _ 3. 605 ÷ 1 = _ 605 ÷ 10 = _ 605 ÷ 100 = _ 605 ÷ 1,000 = _ 4. 74.3 ÷ 1 = _ 74.3 ÷ 10 = _ 74.3 ÷ 100 = _ Math Talk Look for and make use of structure. MP What happens to the value of a number when you divide by 10, 100, or 1,000? On Your Own Complete the pattern. 5. 156 ÷ 1 = _ 156 ÷ 10 = _ 156 ÷ 100 = _ 156 ÷ 1,000 = _ 6. 32 ÷ 1 = _ 32 ÷ 10 = _ 32 ÷ 100 = _ 32 ÷ 1,000 = _ 7. 23 ÷ 1 = _ 23 ÷ 10 = _ 23 ÷ 100 = _ 23 ÷ 1,000 = _ 8. 12.7 ÷ 1 = _ 12.7 ÷ 10 = _ 12.7 ÷ 100 = _ 9. 92.5 ÷ 1 = _ 92.5 ÷ 10 = _ 92.5 ÷ 100 = _ 10. 86.3 ÷ 1 = _ 86.3 ÷ 10 = _ 86.3 ÷ 100 = _ MP Find the value of n. 11. 268 ÷ n = 0.268 n = ___ 12. n ÷ 100 = 0.123 n = ___ 13. n ÷ 10 = 4.6 n = ___ 14. Loretta is trying to build the largest taco in the world. She uses 2,000 pounds of ground beef, one-tenth as many pounds of cheese as beef, and one-hundredth as many pounds of lettuce as beef. How many pounds of lettuce and cheese combined did she use? 225 23 86.3 605 74.3 22.5 2.3 8.63 60.5 7.43 2.25 0.23 0.863 6.05 0.743 0.225 0.023 156 12.7 32 92.5 15.6 1.27 3.2 9.25 1.56 0.127 1,000 12.3 46 0.32 0.925 0.156 0.032 0.605 Possible answer: The value of the number is one tenth of, one hundredth of, or one thousandth of that number. 220 pounds gg CorrectionKey=NL-A 5_mnlese694762_c08l01.indd 283 6/16/2022 11:37:07 AM Name LESSON 8.1 Reteach Understand Decimal Division Patterns To divide a number by 10, 100, or 1,000, use the number of zeros in the divisor to determine how the position of the decimal point changes in the quotient. Number of zeros: Move decimal point: 147 ÷ 1 = 0 0 places to the left 147 ÷ 10 = 1 1 place to the left 147 ÷ 100 = 2 2 places to the left 147 ÷ 1,000 = 3 3 places to the left 147 14.7 1.47 0.147 Dividing by 10, 100, or 1,000 is the same as multiplying by 0.1, 0.01, or 0.001. Number of zeros: Move decimal point: 972 × 1 = 0 0 places to the left 972 × 0.1 = 1 1 place to the left 972 × 0.01 = 2 2 places to the left 9.72 × 0.001 = 3 3 places to the left 972 97.2 9.72 0.972 Complete the pattern. 1 358 × 1 = 358 × 0.1 = 358 × 0.01 = 358 × 0.001 = 2 102 ÷ 1 = 102 ÷ 10 = 102 ÷ 100 = 102 ÷ 1,000 = 3 99.5 ÷ 1 = 99.5 ÷ 10 = 99.5 ÷ 100 = 358 35.8 3.58 0.358 102 10.2 1.02 0.102 99.5 9.95 0.995 37 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c08r01.indd 37 13/05/22 10:43 AM MTSS RtI1 Name Deals on Office Supplies Christina buys paper and paper clips at an office supply store. Use the information in the picture for 1–7. 1 What is the cost of one sheet of paper if Christina buys the smaller pack (100 sheets)? $0.036 2 What is the cost of one sheet of paper if Christina buys the larger pack (1,000 sheets)? $0.032 3 Which pack of paper offers a better deal? Explain. Possible answer: The larger pack offers a better deal. Each sheet of paper in the larger pack costs $0.004 less than each sheet of paper in the smaller pack. 4 What is the cost of one paper clip if Christina buys one pack of 100 paper clips? $0.015 5 What is the cost of one paper clip if Christina buys 1,000 paper clips? $0.009 6 To buy 1,000 paper clips, a customer is actually buying 10 smaller boxes with 100 paper clips in each. What is the cost of one of the smaller boxes? $0.90 7 How much cheaper is each box of 100 paper clips if Christina buys a pack of 10 boxes instead of 10 individual boxes? $0.60 LESSON 8.1 Enrich 37 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c08e01.indd 37 13/05/22 10:40 AM

TM and Version 2.0 Differentiated Centers Kit Grab Problem Solving Applications Problems 15–17 Students will use information from a table to solve problems. Problem 16 Students are required to divide 66.7 by 1,000 and round to the nearest thousandth. Math on the Spot Use this video to help students model and solve this type of problem. World Real Model with mathematics. Problem 17 Students are required to find the amount of sugar per muffin and then multiply by 100 to find the total amount of sugar needed for 100 muffins. Problem 19 This problem assesses a student’s ability to correctly place a decimal point in a division problem. Students who place the decimal point incorrectly may not understand the place value of decimals. Review place value and the fact that each place to the right is one-tenth the value of the place to its left. MP 5 Evaluate Formative Assessment I Can Have students express an opinion to demonstrate the skill for the I Can statement. I can use patterns to help place the decimal point in a quotient by . . . using a pattern with divisors of 10, 100, and 1,000. The decimal point moves one place to the left as the number of zeros in the divisor increases by one. Exit Ticket Explain how to use a pattern to find 35.6 ÷ 100. DIFFERENTIATED INSTRUCTION • Independent Activities Tabletop Flipchart Mini-lessons for reteaching to targeted small groups Games Reinforce math content and vocabulary Readers Supports key math skills and concepts in real-world situations. Activities Meaningful and fun math practice Chapter 8 • Lesson 1 284 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (tr) ©Judith Collins/Alamy Images 284 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company Problem Solving · Applications World Real Use the table to solve Problems 15–17. 15. How much more cornmeal than flour does each muffin contain? cornmeal flour sugar baking powder salt Ingredient Dry Ingredients for 1,000 Corn Muffins 150 110 66.7 10 4.17 Number of kilograms 16. If each muffin contains the same amount of sugar, how many kilograms of sugar, to the nearest thousandth, are in each corn muffin? 17. MP The bakery decides to make only 100 corn muffins on Tuesday. How many kilograms of sugar will be needed? 18. Write Math Explain how you know that the quotient 47.3 ÷ 10 is equal to the product 47.3 × 0.1, 19. Use the numbers on the tiles to complete each number sentence. 62.4 ÷ 1 = _ 62.4 ÷ 10 = _ 62.4 ÷ 100 = _ . 0 2 4 6 Spot on the 0.04 kilogram of cornmeal 0.067 kilogram of sugar 6.67 kilograms of sugar Possible explanation: When I divide by 10, the decimal point moves one place to the left. When I multiply by 0.1, the decimal point moves one place to the left. So, both equal 4.73. 62.4 6.24 0.624 gg CorrectionKey=NL-A 5_mnlese694762_c08l01.indd 284 5/27/2022 2:52:35 PM

Practice and Homework Understand Decimal Division Patterns Use the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine students’ understanding of content for this lesson. PROFESSIONAL LEARNING MATH TALK IN ACTION This Math Talk in Action is an example of dialogue for Problem 6. Teacher: How did you find 16 ÷ 1? Heidi: Any number divided by 1 is that number. So, 16 ÷ 1 is 16. Teacher: How did you find 16 ÷ 10? Manuel: The number of zeros in the divisor increased by 1, so I moved the decimal point one place to the left and got 1.6. Teacher: How did you find 16 ÷ 100? Manuel: The same way. The divisor has two zeros, so I moved the decimal point two places left to get 0.16. Teacher: What did you do for 16 ÷ 1,000? Wes: I did like Manuel. The divisor has three zeros, so I moved the decimal point three places left to get 0.016. Teacher: Why did you write a zero before the 1? Wes: There wasn’t another digit, so I had to write a zero in the tenths place to show 16 thousandths. Teacher: How would you find 16 ÷ 100,000? Wes: I would extend the pattern, moving the decimal point 1 more place left each time the number of zeros increased by 1. Manuel: I think you can just look at the number of zeros in the divisor. It tells me how many places to move the decimal point to the left. So, I could move the decimal point 6 places left and write zeros as needed. It’s 0.000016. 285 Go Math! Grade 5 Chapter 8 • Lesson 1 285 © Houghton Mifflin Harcourt Publishing Company LESSON 8.1 Practice and Homework Name Understand Decimal Division Patterns Complete the pattern. 1. 78.3 ÷ 1 = __78.3 78.3 ÷ 10 = __7.83 78.3 ÷ 100 = __0.783 2. 179 ÷ 1 = __ 179 ÷ 10 = __ 179 ÷ 100 = __ 179 ÷ 1,000 = __ 3. 87.5 ÷ 1 = __ 87.5 ÷ 10 = __ 87.5 ÷ 100 = __ 4. 124 ÷ 1 = __ 124 ÷ 10 = __ 124 ÷ 100 = __ 124 ÷ 1,000 = __ 5. 18 ÷ 1 = __ 18 ÷ 10 = __ 18 ÷ 100 = __ 18 ÷ 1,000 = __ 6. 16 ÷ 1 = __ 16 ÷ 10 = __ 16 ÷ 100 = __ 16 ÷ 1,000 = __ 7. 51.8 ÷ 1 = __ 51.8 ÷ 10 = __ 51.8 ÷ 100 = __ 8. 49.3 ÷ 1 = __ 49.3 ÷ 10 = __ 49.3 ÷ 100 = __ 9. 32.4 ÷ 1 = __ 32.4 ÷ 10 = __ 32.4 ÷ 100 = __ Problem Solving World Real 10. The local café uses 510 cups of mixed vegetables to make 1,000 quarts of beef barley soup. Each quart of soup contains the same amount of vegetables. How many cups of vegetables are in each quart of soup? 11. The same café uses 18.5 cups of flour to make 100 servings of pancakes. How many cups of flour are in one serving of pancakes? 12. Write Math Explain how to use a pattern to find 35.6 ÷ 100. 179 87.5 8.75 0.875 17.9 1.79 0.179 18 49.3 124 51.8 16 32.4 1.8 4.93 12.4 5.18 1.6 3.24 0.18 0.493 1.24 0.518 0.51 cup 0.185 cup 0.16 0.324 0.124 0.018 0.016 Check students’ explanations. gg CorrectionKey=NL-A 5_mnlese694762_c08p01.indd 285 5/27/2022 2:50:11 PM

Continue to practice concepts and skills with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Chapter 8 • Lesson 1 286 286 Go Math! Grade 5 Lesson Check © Houghton Mifflin Harcourt Publishing Company 13. The Statue of Liberty is 305.5 feet tall from the foundation of its pedestal to the top of its torch. Isla is building a model of the statue. The model will be one-hundredth times as tall as the actual statue. How tall will the model be? 14. Sue’s teacher asked her to find 42.6 ÷ 100. How many places and in what direction should Sue move the decimal point to get the correct quotient? Spiral Review 15. In the number 956,783,529, how does the value of the digit 5 in the ten millions place compare to the digit 5 in the hundreds place? 16. Calista has $97.23 in her checking account. She uses her debit card to spend $29.74 and then deposits $118.08 into her account. What is Calista’s new balance? 17. At the bank, Josiah exchanges $50 in bills for 50 one-dollar coins. The total mass of the coins is 405 grams. Estimate the mass of 1 one-dollar coin. 18. A commercial jetliner has 245 passenger seats. The seats are arranged in 49 equal rows. How many seats are in each row? 3.055 feet 8 grams 2 places to the left 100,000 times as much as $185.57 5 seats gg CorrectionKey=NL-A 5_mnlese694762_c08p01.indd 286 5/27/2022 2:50:12 PM

287A Go Math! Grade 5 LESSON 8.2 Lesson at a Glance Represent Division of Decimals by Whole Numbers SNAPSHOT Mathematical Standards ● Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Mathematical Practices and Processes ● Attend to precision. ● Construct arguments and critique reasoning of others. ● Reason abstractly and quantitatively. ● Model with mathematics. ● Look for and make use of structure. I Can Objective I can use a model to divide a decimal by a whole number. Learning Goal Model division of decimals by whole numbers. Language Objective Students give an example of how you can use a model to divide a decimal by a whole number. MATERIALS • MathBoard • Decimal Models • color pencils • base-ten blocks ACROSS THE GRADES Before Grade 5 After Explore the multiplication and division of multi-digit whole numbers using estimation, rounding and place value. Explore the multiplication and division of multi-digit numbers with decimals to the hundredths using estimation, rounding and place value. Multiply and divide positive multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency. ABOUT THE MATH Modeling Division of Decimals In this lesson, students use models to divide decimals by whole numbers. Students should already be able to use base-ten blocks to model whole-number division. Connect their understanding of division of a whole number by a whole number to division of a decimal by a whole number. In each case, the blocks are used to show the dividend and students share the blocks to form equal groups. The number of blocks in each group is the quotient. The difference between the two types of division problems is what the blocks represent. In whole-number division, a flat represents 100, a long represents 10, and a small cube represents 1. In division of a decimal by a whole number, a flat represents 1, a long represents __1 10, and a small cube represents ___1100. 4.24 ÷ 4 = 1.06 For more professional learning, go online to Teacher’s Corner.

184,722 = 471,215 FOCUSING ON THE WHOLE STUDENT Access Prior Knowledge Have students model the following numbers: 2.5, 3.6, 4.12, and 3.04. Remind students that when representing decimals, a flat represents 1 whole, a long represents 1 tenth, and 1 small cube represents 1 hundredth. • How can you model 3.04? 3 flats and 4 small cubes to represent 3 ones and 4 hundredths • Why did you not use any longs? There are 0 tenths. • How did you know which blocks to use? Possible answer: The place value told me which type of block to use, and the digit in that place value told me how many of those blocks to use. Supporting All Learners Diwali is an Indian festival and five-day celebration that occurs each fall season to celebrate things that make happiness in the world, such as knowledge and good deeds. Diwali takes up about 0.7 of a week and is filled with food, lanterns, dancing, decorations, and more. Using base-ten blocks, 7 longs can represent 0.7 of a week. Ask students to share their knowledge of festivals. 1 Engage with the Interactive Student Edition I Can Objective I can use a model to divide a decimal by a whole number. Making Connections Invite students to tell you what they know about decimals. Ask the following questions. • What is a whole number? one of the numbers 0, 1, 2, 3, 4, . . . • What is a decimal? a number with one or more digits to the right of the decimal point • What are the names of the first three decimal places in a place-value chart? tenths, hundredths, and thousandths Learning Activity Three neighbors placed 9.75 pounds of herbs from the farmers’ market in 3 baskets equally. If each neighbor gets a basket to take home, how many pounds of herbs does each neighbor get? • How many pounds of herbs were picked for the farmers’ market? 9.75 pounds • Why did the neighbors need to divide 9.75 by 3? All three baskets had an equal amount of herbs. • What models could you use to visualize what’s happening in this problem? Possible answer: I could draw a picture; I could use a number line; I could use base-ten blocks.

0.6. If the product or sum equals 2.4, then the answer is correct. MP STRATEGY: Model Concepts Use base-ten blocks to model 4.11 ∙ 3. • Pair students of mixed English proficiency. Have the more fluent English partner model first, explaining each step in the process. • Then have the English Learner model the same problem, reciting the steps in the process. • What is the quotient? 1.37 • Have partners work through another problem, modeling and verbalizing the steps to find the quotient. Multilingual Support 287 Go Math! Grade 5 Chapter 8 • Lesson 2 287 © Houghton Mifflin Harcourt Publishing Company CHAPTER 8 Name Lesson 2 Represent Division of Decimals by Whole Numbers I Can use a model to divide a decimal by a whole number. Investigate Materials ■ decimal models ■ color pencils Angela has enough wood to make a picture frame with a perimeter of 2.4 meters. She wants the frame to be a square. What will be the length of each side of the frame? A. Shade decimal models to show 2.4. B. You need to share your model among _ equal groups. C. Since 2 wholes cannot be shared among 4 groups without regrouping, cut your model apart to show the tenths. There are _ tenths in 2.4. Share the tenths equally among the 4 groups. There are _ ones and _ tenths in each group. Write a decimal for the amount in each group. _ D. Use your visual model to complete the number sentence. 2.4 ÷ 4 = _ So, the length of each side of the frame will be _ meter. Draw Conclusions 1. MP Explain why you needed to cut apart the model in Step C. 2. Explain how your model would be different if the perimeter were 4.8 meters. 24 4 0 6 0.6 0.6 0.6 Possible answer: I could not share the 2 wholes among the four groups, but I could regroup and share the 24 tenths. Possible answer: I would not need to cut the 4 wholes into 40 tenths, so each of the four groups would contain 1 whole and 2 tenths. gg CorrectionKey=NL-A 5_mnlese694762_c08l02.indd 287 5/27/2022 2:50:50 PM

Make Connections Discuss how to use base-ten blocks to model 3.21 ÷ 3. • In Step 2, why are you sharing equally among 3 groups? Possible answer: I am dividing 3.21 by 3, so I am sharing 3.21 equally among 3 groups to find how many are in each group. • In Step 3, how do you know how many hundredths are the same as 2 tenths and 1 hundredth? Possible answer: 1 tenth is the same as 10 hundredths, so 2 tenths is 20 hundredths. 20 hundredths plus 1 hundredth is 21 hundredths. • Compare using base-ten blocks to divide a decimal by a whole number to using base-ten blocks to divide a whole number by a whole number. Possible answer: In both cases, you use blocks to show the dividend and then share the blocks, regrouping when needed, to make equal groups. The blocks have different values, though. For whole numbers, the flat represents 100, the long 10, and the small cube 1. For decimals, a flat represents 1, a long represents 1 tenth, and a small cube represents 1 hundredth. Construct arguments and critique reasoning of others. Math Talk Use Math Talk to check that students can explain the reasonableness of their answers. If students are having difficulty explaining why their answer makes sense, suggest that they use estimation. • How does the model help you avoid putting the decimal point in the wrong place? I can see in the model that there are not enough blocks to have an answer of 10.7 and there are too many blocks to have an answer of 0.107. MP Common Errors Common Errors Error Students may not remember to regroup leftover blocks. Example 3.14 ∙ 2 ∙ 1.07 Springboard to Learning Remind students to place any leftover blocks with the remaining blocks to be shared so that they remember to regroup. Ready for More Visual / Kinesthetic Partners Materials base-ten blocks • Have each student think of a division problem similar to those in the lesson. Students should write their problem on a piece of paper without letting their partner see it. • Then have partners take turns modeling their problem using base-ten blocks. The other student should try to identify the problem being modeled and its answer. • Students should remain silent as they slowly model their problem. Partners can check what they think the problem and answer is with what is written down on paper. • Partners can try again with different division problems. Chapter 8 • Lesson 2 288 © Houghton Mifflin Harcourt Publishing Company© Houghton Mifflin Harcourt Publishing Company 288 Go Math! Grade 5 Make Connections You can also use base-ten blocks to model division of a decimal by a whole number. Materials ■ base-ten blocks Kyle has a roll of ribbon 3.21 yards long. He cuts the ribbon into 3 equal lengths. How long is each piece of ribbon? Divide. 3.21 ÷ 3 STEP 1 Use base-ten blocks to show 3.21. Remember that a flat represents one, a long represents one tenth, and a small cube represents one hundredth. There are _ one(s), _ tenth(s), and _ hundredth(s). STEP 2 Share the ones. Share the ones equally among 3 groups. There is _ one(s) shared in each group and _ one(s) left over. STEP 3 Share the tenths. Two tenths cannot be shared among 3 groups without regrouping. Regroup the tenths by replacing them with hundredths. There are _ tenth(s) shared in each group and _ tenth(s) left over. There are now _ hundredth(s). STEP 4 Share the hundredths. Share the 21 hundredths equally among the 3 groups. There are _ hundredth(s) shared in each group and _ hundredth(s) left over. So, each piece of ribbon is__yards long. Math Talk Construct arguments and critique reasoning of others. MP Explain why your answer makes sense. 3 1 0 0 1.07 2 0 21 7 0 1 Possible answer: 3.21 is about 3, and 3 ÷ 3 = 1. Since 1.07 is about 1, my answer makes sense. gg CorrectionKey=NL-A gg CorrectionKey=NL-A 5_mnlese694762_c08l02.indd 288 5/27/2022 2:50:50 PM

3 Explain Share and Show The first problems connect to the learning model. Have students use the MathBoard to explain their thinking. Use the checked problems for Quick Check. Students should show their answers for the Quick Check on the MathBoard. Math Board Quick Check If MTSS RtI If MTSS RtI Then a student misses the checked problems Differentiate Instruction with • Reteach 8.2 • Waggle Reason abstractly and quantitatively. • Can you use base-ten blocks to find 4.02 ∙ 4? Explain. Possible explanation: Yes. I can use the large cube to represent ones, flats for tenths, and longs for hundredths. Then I would show 4 large cubes and 2 longs. I would place 1 large cube in each of the 4 groups. Since 2 longs cannot be shared among 4 groups, I would trade the 2 longs for 20 small cubes. Then I would place 5 small cubes in each of the 4 groups. 1.005 Look for and make use of structure. Math Talk Use Math Talk to focus on students’ understanding of how to use multiplication to find an answer to a division problem. MP MP Meeting Individual Needs Reteach 8.2 Enrich 8.2 289 Go Math! Grade 5 Model with mathematics. • Can you use base-ten blocks to find 2.4 ∙ 4? Yes, I can use 2 flats and 4 longs. I can then regroup the blocks into 24 longs and divide them into 4 equal groups. Each group will have 6 longs, which is equal to 0.6. MP © Houghton Mifflin Harcourt Publishing Company© Houghton Mifflin Harcourt Publishing Company Chapter 8 • Lesson 2 289 Name Math Share and Show Board Use the model to complete the number sentence. 1. 1.6 ÷ 4 = __ 2. 3.42 ÷ 3 = __ Divide. Use base-ten blocks. 3. 1.8 ÷ 3 = __ 4. 3.6 ÷ 4 = __ 5. 2.5 ÷ 5 = __ 6. 2.4 ÷ 8 = __ 7. 3.78 ÷ 3 = __ 8. 1.33 ÷ 7 = __ 9. 4.72 ÷ 4 = __ 10. 2.52 ÷ 9 = __ 11. 6.25 ÷ 5 = __ Math Talk Look for and make use of structure. MP Explain how you can use inverse operations to find 2.4 ÷ 4. 0.4 1.14 0.6 0.3 1.18 0.9 1.26 0.28 0.5 0.19 1.25 Possible explanation: I can use multiplication and think 4 × □ = 2.4. I know that 4 × 6 tenths = 24 tenths or 2.4. So, 2.4 divided by 4 is equal to 0.6. gg CorrectionKey=NL-A 5_mnlese694762_c08l02.indd 289 6/16/2022 11:39:09 AM Name LESSON 8.2 Reteach Represent Division of Decimals by Whole Numbers You can draw a quick picture to help you divide a decimal by a whole number. In a decimal model, each large square represents one, or 1. Each bar represents one-tenth, or 0.1. Divide. 1.2 ÷ 3 Step 1 Draw a quick picture to represent the dividend, . 1.2 Step 2 Draw 3 circles to represent the divisor, . 3 Step 3 You cannot evenly divide 1 into 3 groups. Regroup 1 as 10 tenths. There are tenths in 1.2. 12 Step 4 Share the tenths equally among 3 groups. Each group contains ones and tenths. 0 4 So, 1.2 ÷ 3 = . 0.4 Divide. Draw a quick picture. 1 2.7 ÷ 9 = 2 4.8 ÷ 8 = 3 2.8 ÷ 7 = 4 7.25 ÷ 5 = 5 3.78 ÷ 3 = 6 8.52 ÷ 4 = 0.3 0.6 0.4 1.45 1.26 2.13 Check students’ drawings. 38 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c08r02.indd 38 13/05/22 10:45 AM MTSS RtI1 Name Write Division Equations In the models below, a large square represents 1, a bar represents 1 tenth, and a small square represents 1 hundredth. All divisors are whole numbers. Write the division equation each model represents. 1 1.5 ÷ 5 = 0.3 2 0.6 ÷ 3 = 0.2 3 4.56 ÷ 4 = 1.14 4 3.96 ÷ 3 = 1.32 5 Explain how you found the division equation the model in Exercise 1 represents. Possible explanation: There are 3 tenths in each circle, so I know the quotient is 0.3. The tenths are divided equally into 5 groups, so I know the divisor is 5. There are 15 tenths in all, or 1.5. This represents the dividend. So, the division equation is 1.5 ÷ 5 = 0.3. LESSON 8.2 Enrich 38 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c08e02.indd 38 13/05/22 10:33 AM

TM and Version 2.0 Differentiated Centers Kit Grab 4 Elaborate On Your Own Attend to precision. Problem 12 Students are required to identify the regrouping error Aida made and then solve the problem correctly. • How might Aida avoid this error next time? Answers will vary. Math on the Spot Use this video to help students model and solve this type of problem. MP Problem 15 This problem assesses a student’s ability to use a model to divide a decimal by a whole number. Students who are able to write the correct quotient but are not able to draw a model may understand the underlying algorithm for dividing but may not understand the true concept of what it means to divide. 5 Evaluate Formative Assessment I Can Have students give an example to demonstrate the skill for the I Can statement. I can use a model to divide a decimal by a whole number by . . . using base-ten blocks or other decimal models to show the dividend. Then I can share the blocks equally among the number of groups shown by the divisor. I may need to regroup sometimes in order to share equally. The number in each group is the quotient. Exit Ticket Explain how you can use base-ten blocks or other decimal models to find 3.15 ∙ 3. Include pictures to support your explanation. DIFFERENTIATED INSTRUCTION • Independent Activities Tabletop Flipchart Mini-lessons for reteaching to targeted small groups Games Reinforce math content and vocabulary Readers Supports key math skills and concepts in real-world situations. Activities Meaningful and fun math practice Chapter 8 • Lesson 2 290 290 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company On Your Own 12. Aida is making banners from a roll of paper that is 4.05 meters long. She will cut the paper into 3 equal lengths. She uses base-ten blocks to model how long each piece will be. Describe Aida’s error. 13. Sam can ride a bike 4.5 kilometers in 9 minutes, and Amanda can ride a bike 3.6 kilometers in 6 minutes. Which rider might go farther in 1 minute? 14. MP Explain how you can use inverse operations to find 1.8 ÷ 3. 15. Draw a model to show 4.8 ÷ 4 and solve. 4.8 ÷ 4 = __ Spot on the Possible description: Aida regrouped the leftover one as 10 hundredths instead of 10 tenths. She should have put 3 tenths in each of the groups and regrouped the leftover tenth to get 15 hundredths. 4.05 ÷ 3 = 1.35 Amanda; 4.5 ÷ 9 = 0.5, 3.6 ÷ 6 = 0.6; 0.6 > 0.5 Possible explanation: I can use multiplication and think 3 × □ = 1.8. I know that 3 × 6 tenths = 18 tenths or 1.8. So, 1.8 divided by 3 is equal to 0.6. 1.2 gg CorrectionKey=NL-A 5_mnlese694762_c08l02.indd 290 5/27/2022 2:50:51 PM

Practice and Homework Represent Division of Decimals by Whole Numbers Use the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine students’ understanding of content for this lesson. 291 Go Math! Grade 5 Chapter 8 • Lesson 2 291 © Houghton Mifflin Harcourt Publishing Company LESSON 8.2 Practice and Homework Name Represent Division of Decimals by Whole Numbers Use the model to complete the number sentence. 1. 1.2 ÷ 4 = __0.3 2. 3.69 ÷ 3 = __ Divide. Use base-ten blocks. 3. 4.9 ÷ 7 = __ 4. 3.6 ÷ 9 = __ 5. 2.4 ÷ 8 = __ 6. 6.48 ÷ 4 = __ 7. 3.01 ÷ 7 = __ 8. 4.26 ÷ 3 = __ Problem Solving World Real 9. In PE class, Carl runs a distance of 1.17 miles in 9 minutes. At that rate, how far does Carl run in one minute? 10. Marianne spends $9.45 on 5 greeting cards. Each card costs the same amount. What is the cost of one greeting card? 11. Write Math Explain how you can use base-ten blocks or other decimal models to find 3.15 ÷ 3. Include pictures to support your explanation. 1.23 0.7 1.62 0.4 0.43 0.3 1.42 0.13 mile $1.89 Check students’ explanations and drawings. gg CorrectionKey=NL-A 5_mnlese694762_c08p02.indd 291 5/27/2022 2:50:28 PM

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• Chapter 1 Represent, Count, and Write Numbers 0 to 5
• Chapter 2 Compare Numbers to 5
• Chapter 3 Represent, Count, and Write Numbers 6 to 9
• Chapter 4 Represent and Compare Numbers to 10
• Chapter 5 Addition
• Chapter 6 Subtraction
• Chapter 7 Represent, Count, and Write 11 to 19
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• Chapter 9 Identify and Describe Two-Dimensional Shapes
• Chapter 10 Identify and Describe Three-Dimensional Shapes
• Chapter 11 Measurement
• Chapter 12 Classify and Sort Data
• Chapter 1 Addition Concepts
• Chapter 2 Subtraction Concepts
• Chapter 3 Addition Strategies
• Chapter 4 Subtraction Strategies
• Chapter 5 Addition and Subtraction Relationships
• Chapter 6 Count and Model Numbers
• Chapter 7 Compare Numbers
• Chapter 8 Two-Digit Addition and Subtraction
• Chapter 9 Measurement
• Chapter 10 Represent Data
• Chapter 11 Three-Dimensional Geometry
• Chapter 12 Two-Dimensional Geometry
• Chapter 1 Number Concepts
• Chapter 2 Numbers to 1,000
• Chapter 3 Basic Facts and Relationships
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• Chapter 7: Division Facts and Strategies Extra Practice
• Chapter 8: Understand Fractions Extra Practice
• Chapter 9: Compare Fractions Extra Practice
• Chapter 10: Time, Length, Liquid Volume, and Mass Extra Practice
• Chapter 11: Perimeter and Area Extra Practice
• Chapter 12: Two-Dimensional Shapes Extra Practice

Common Core Grade 4 HMH Go Math – Answer Keys

• Chapter 1 Place Value, Addition, and Subtraction to One Million
• Chapter 2 Multiply by 1-Digit Numbers
• Chapter 3 Multiply 2-Digit Numbers
• Chapter 4 Divide by 1-Digit Numbers
• Chapter 5 Factors, Multiples, and Patterns
• Chapter 6 Fraction Equivalence and Comparison
• Chapter 7 Add and Subtract Fractions
• Chapter 8 Multiply Fractions by Whole Numbers
• Chapter 9 Relate Fractions and Decimals
• Chapter 10 Two-Dimensional Figures
• Chapter 11 Angles
• Chapter 12Relative Sizes of Measurement Units
• Chapter 13 Algebra: Perimeter and Area

Grade 4 Homework Practice FL.

Common Core – Grade 4 – Practice Book

• Chapter 1 Place Value, Addition, and Subtraction to One Million  (Pages 1- 20)
• Chapter 2 Multiply by 1-Digit Numbers  (Pages 21 – 47)
• Chapter 3 Multiply 2-Digit Numbers  (Pages 49- 65)
• Chapter 4 Divide by 1-Digit Numbers  (Pages 67 – 93)
• Chapter 5 Factors, Multiples, and Patterns  (Pages 95 – 109)
• Chapter 6 Fraction Equivalence and Comparison  (Pages 111 – 129)
• Chapter 7 Add and Subtract Fractions  (Pages 131 – 153)
• Chapter 8 Multiply Fractions by Whole Numbers  (Pages 155- 167)
• Chapter 9 Relate Fractions and Decimals  (Pages 169- 185)
• Chapter 10 Two-Dimensional Figures  (Pages 187- 204)
• Chapter 11 Angles  (Pages 205- 217)
• Chapter 12 Relative Sizes of Measurement Units  (Pages 219- 244)
• Chapter 13 Algebra: Perimeter and Area  (Pages 245- 258)

Grade 4 Homework FL. – Answer Keys

• Chapter 2 Multiply by 1-Digit Numbers Review/Test
• Chapter 3 Multiply 2-Digit Numbers Review/Test
• Chapter 4 Divide by 1-Digit Numbers Review/Test
• Chapter 5 Factors, Multiples, and Patterns Review/Test
• Chapter 6 Fraction Equivalence and Comparison Review/Test
• Chapter 7 Add and Subtract Fractions Review/Test
• Chapter 8 Multiply Fractions by Whole Numbers Review/Test
• Chapter 9 Relate Fractions and Decimals Review/Test
• Chapter 10 Two-Dimensional Figures Review/Test
• Chapter 11 Angles Review/Test
• Chapter 12 Relative Sizes of Measurement Units Review/Test
• Chapter 13 Algebra: Perimeter and Area Review/Test
• Chapter 1: Place Value, Multiplication, and Expressions
• Chapter 2: Divide Whole Numbers
• Chapter 3: Add and Subtract Decimals
• Chapter 4: Multiply Decimals
• Chapter 5: Divide Decimals
• Chapter 6: Add and Subtract Fractions with Unlike Denominators
• Chapter 7: Multiply Fractions
• Chapter 8: Divide Fractions
• Chapter 9: Algebra: Patterns and Graphing
• Chapter 10: Convert Units of Measure
• Chapter 11: Geometry and Volume
• Chapter 1: Divide Multi-Digit Numbers
• Chapter 2: Fractions and Decimals
• Chapter 3: Understand Positive and Negative Numbers
• Chapter 4: Model Ratios
• Chapter 5: Model Percents
• Chapter 6: Convert Units of Length
• Chapter 7: Exponents
• Chapter 8: Solutions of Equations
• Chapter 9: Independent and Dependent Variables
• Chapter 10: Area of Parallelograms
• Chapter 11: Surface Area and Volume
• Chapter 12: Data Displays and Measures of Center
• Chapter 13: Variability and Data Distributions

Go Math Answer Key for Grade 7

• Chapter 1: Adding and Subtracting Integers
• Chapter 2: Multiplying and Dividing Integers
• Chapter 3: Rational Numbers
• Chapter 4: Rates and Proportionality
• Chapter 5: Percent Increase and Decrease
• Chapter 6: Algebraic Expressions
• Chapter 7: Writing and Solving One-Step Inequalities
• Chapter 8: Modeling Geometric Figures
• Chapter 9: Circumference, Area, and Volume
• Chapter 10: Random Samples and Populations
• Chapter 11: Analyzing and Comparing Data
• Chapter 12: Experimental Probability
• Chapter 13: Theoretical Probability and Simulations
• Chapter 1 Real Numbers
• Chapter 2 Exponents and Scientific Notation
• Chapter 3 Proportional Relationships
• Chapter 4 Nonproportional Relationships
• Chapter 5 Writing Linear Equations
• Chapter 6 Functions
• Chapter 7 Solving Linear Equations
• Chapter 8 Solving Systems of Linear Equations
• Chapter 9 Transformations and Congruence
• Chapter 10 Transformations and Similarity
• Chapter 11 Angle Relationships in Parallel Lines and Triangles
• Chapter 12 The Pythagorean Theorem
• Chapter 13 Volume
• Chapter 14 Scatter Plots
• Chapter 15 Two-Way Tables

Give your kid the right amount of knowledge he needs as a part of your preparation by taking the help of our HMH Go Math Answer Key for Grades K-8. Resolve all your queries and assess your preparation standard using the Common Core Go Math Solution Key.

Practicing from the Go Math Answer Key for Grades K to 8 will provide a grade by grade roadmap and prepares students for College Readiness. Gradewise HMH Go Math Answer Key provided will develop problem-solving skills among students thereby helping them to Think, Explore and Grow. The Diverse Opportunities provided helps Kids to master the content with engaging activities.

Characteristics of Go Math Answer Key for Grades K to 8

Go through the below-listed features of referring to the HMH Go Math Anwer Key for Grades K to 8. They are outlined as follows

• All the Go Math Answer Key for Grades K to 8 are easy to download and we don’t charge any penny from you.
• Step by Step Solutions provided in the HMH Go Math Practice Key is aligned as per the College and Career Expectations.
• Solving from the Math 101 Practice Key helps you inculcate Higher Order Thinking Skills and you can answer any Question from your Homework, Assessment, or Review Test.
• More Rigorous Content made available meets the Common Core State Standards Initiative.
• You can gain a deeper knowledge of mathematical concepts and find solutions to all the Questions from Go Math Textbooks for Grades K, 1, 2, 3, 4, 5, 6, 7, 8

FAQs on Common Core HMH Go Math Answer Key

1. When Can I use the Go Math Answer Key for Grades K-8?

You can use the HMH Go Math Answer Key for Grades K to 8 while practicing the Go Math Textbook Questions as a part of your Homework or Assessment and make the most out of them.

2. Is there any site that provides the Common Core Go Math Solutions Key for Grades K, 1, 2, 3, 4, 5, 6, 7, 8?

Yes, you can find Go Math Answer Key for Grades K, 1, 2, 3, 4, 5, 6, 7, 8 all in one place i.e. ccssmathanswers.com a trusted and reliable portal.

3. Can I download HMH Go Math Answer Key PDF for free?

Yes, you can download the HMH Math 101 Practice Key for free on our page via quick links available and we don’t charge any amount for it.

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