go math grade 5 practice and homework lesson 4.1

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Go Math Grade 5 Answer Key Pdf | Go Math 5th Grade Answer Key Pdf

Go Math Grade 5 Answer Key Pdf:  HMH 5th Grade Go Math Practice Books and Answer Key provide students comprehensive unlimited practice, real-time feedback, and also different question types and learning aids. As per the student’s understanding level only these Go Math Solution Key is designed and helping them to learn all primary mathematical concepts in a conceptual way.

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Go Math Answer Key Grade 5 | Go Math Grade 5 Teacher Edition Answers Pdf

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Grade 5 HMH Go Math – NEW

• 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

Grade 5 Math Common Core Tests

• Test 1 Session 1 (page 2)
• Test 2 Session 1 (page 3)
• Test 3 Session 1 (page 4)
• Test 3 Session 2 (page 5)
• Test 4 Session 1 (page 6)
• Test 4 Session 2 (page 7)

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Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals

Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals comes in handy while preparing for the exams. Go Math Grade 5 Chapter 4 Solution Key is given by the subject experts. We listed Go Math Grade 5 Answer Key covering the questions from Practice Test, Chapter Test, Cumulative Practice. Know how to solve various models of 5th Grade Go Math Ch 4 Multiply Decimals by referring to the Solutions Key Provided. The Best Part about or 5th Grade Ch 4 Multiply Decimals Answer Key is that we have given an elaborate explanation for all the Problems.

Go Math Grade 5 Chapter 4 Multiply Decimals Answer Key

Go Math Grade 5 Chapter 4 Multiply Decimals Solution Key covers Questions from basic to advanced level of difficulty. All the Problems are explained by subject experts and create an Interest in the Subject among the Students. If they have any difficulty in solving the Chapter 4 Lessons Problems they can cross check the detailed explanation provided below to resolve their doubts. Students can feel confident with the concepts by practicing from the 5th Grade Go Math Multiply Decimals Answer Key.

Lesson 1: Algebra • Multiplication Patterns with Decimals

• Multiplication Patterns with Decimals – Page No. 165
• Multiplication Patterns with Decimals Lesson Check – Page No. 166

Lesson 2: Investigate • Multiply Decimals and Whole Numbers

• Multiply Decimals and Whole Numbers – Page No. 167
• Multiply Decimals and Whole Numbers Lesson Check – Page No. 168

Lesson 3: Multiplication with Decimals and Whole Numbers

• Multiplication with Decimals and Whole Numbers – Page No. 171
• Multiplication with Decimals and Whole Numbers Lesson Check – Page No. 172

Lesson 4: Multiply Using Expanded Form

• Multiply Using Expanded Form – Page No. 175
• Multiply Using Expanded Form Lesson Check – Page No. 176

Lesson 5: Problem Solving • Multiply Money

• Multiply Money – Page No. 179
• Multiply Money Lesson Check – Page No. 180

Mid-Chapter Checkpoint

Mid-Chapter Checkpoint – Page No. 181

• Mid-Chapter Checkpoint Lesson Check – Page No. 182

Lesson 6: Investigate • Decimal Multiplication

• Decimal Multiplication – Page No. 185
• Decimal Multiplication Lesson Check – Page No. 186

Lesson 7: Multiply Decimals

• Multiply Decimals – Page No. 188
• Multiply Decimals Lesson Check – Page No. 189
• Multiply Decimals Lesson Check 1 – Page No. 190

Lesson 8: Zeros in the Product

• Zeros in the Product – Page No. 193
• Zeros in the Product Lesson Check – Page No. 194

Review/Test

• Review/Test – Page No. 195
• Review/Test – Page No. 196
• Review/Test – Page No. 197
• Review/Test – Page No. 198

Share and Show – Page No. 165

Complete the pattern.

Question 1. 10 0 × 17.04 = 17.04 10 1 × 17.04 = 17.04 10 2 × 17.04 = 17.04 10 3 × 17.04 = 17.04 _____

Answer: 10 0 × 17.04 = 17.04 10 1 × 17.04 = 170.4 10 2 × 17.04 = 1,704 10 3 × 17.04 =17,040

Explanation: As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side. 10 0 × 17.04 = 1 x 17.04 = 17.04 10 1 × 17.04 = 10 x 17.04 = 170.4 10 2 × 17.04 = 100 x 17.04 = 1,704 10 3 × 17.04 = 1000 x 17.04 = 17,040

Question 2. 1 × 3.19 = _____ 10 × 3.19 = _____ 100 × 3.19 = _____ 1,000 × 3.19 = _____

Answer: 1 × 3.19 = 3.19 10 × 3.19 = 31.9 100 × 3.19 = 319 1,000 × 3.19 = 3,190 As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.

Question 3. 45.6 × 10 0 = _____ 45.6 × 10 1 = _____ 45.6 × 10 2 = _____ 45.6 × 10 3 = _____

Answer: 45.6 × 10 0 = 45.6 45.6 × 10 1 = 456 45.6 × 10 2 = 4,560 45.6 × 10 3 = 45,600

Explanation: As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side. 45.6 × 10 0 = 45.6 x 1 = 45.6 45.6 × 10 1 = 45.6 x 10 = 456 45.6 × 10 2 = 45.6 x 100 = 4,560 45.6 × 10 3 = 45.6 x 1000 = 45,600

Question 4. 1 × 6,391 = _____ 0.1 × 6,391 = _____ 0.01 × 6,391 = _____

Answer: 1 × 6,391 = 6,391 0.1 × 6,391 = 639.1 0.01 × 6,391 = 63.91 As you multiply by decreasing powers of 10, the position of the decimal point moves towards the left side

On Your Own

Question 5. 1.06 × 1 = _____ 1.06 × 10 = _____ 1.06 × 100 = _____ 1.06 × 1,000 = _____

Answer: 1.06 × 1 = 1.06 1.06 × 10 = 10.6 1.06 × 100 = 106 1.06 × 1,000 = 1,060 As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side.

Question 6. 1 × 90 = _____ 0.1 × 90 = _____ 0.01 × 90 = _____

Answer: 1 × 90 = 90 0.1 × 90 = 9.0 = 9 0.01 × 90 = 0.9

Explanation: As you multiply by decreasing powers of 10, the position of the decimal point moves towards the left side 1 × 90 = 90 0.1 × 90 = 9.0 0.01 × 90 = 0.90

Question 7. 10 0 × $0.19 = $ _____ 10 1 × $0.19 = $ _____ 10 2 × $0.19 = $ _____ 10 3 × $0.19 = $ _____

Answer: 10 0 × $0.19 = $ 0.19 10 1 × $0.19 = $ 1.9 10 2 × $0.19 = $ 19 10 3 × $0.19 = $ 190

Explanation: As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side. 10 0 × $0.19 = $ 0.19 10 1 × $0.19 = $ 1.9 10 2 × $0.19 = $ 19 10 3 × $0.19 = $ 190

Question 8. 580 × 1 = _____ 580 × 0.1 = _____ 580 × 0.01 = _____

Answer: 580 × 1 = 580 580 × 0.1 = 58 580 × 0.01 = 5.8

Explanation: As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side. 580 × 1 = 580 580 × 0.1 = 58.0 = 58 580 × 0.01 = 5.8

Question 9. 10 0 × 80.72 = _____ 10 1 × 80.72 = _____ 10 2 × 80.72 = _____ 10 3 × 80.72 = _____

Answer: 10 0 × 80.72 = 80.72 10 1 × 80.72 = 807.2 10 2 × 80.72 = 8,072 10 3 × 80.72 = 80,720

Explanation: As you multiply by decreasing powers of 10, the position of the decimal point moves towards the left side 10 0 × 80.72 = 80.72 10 1 × 80.72 = 807.2 10 2 × 80.72 = 8,072 10 3 × 80.72 = 80,720

Question 10. 1 × 7,230 = _____ 0.1 × 7,230 = _____ 0.01 × 7,230 = _____

Answer: 1 × 7,230 = 7,230 0.1 × 7,230 = 723 0.01 × 7,230 = 72.3

Explanation: As you multiply by increasing powers of 10, then the position of the decimal point moves towards the right side. 1 × 7,230 = 7,230 0.1 × 7,230 = 723.0 = 723 0.01 × 7,230 = 72.3

Algebra Find the value

Question 11. n × $3.25 = $325.00 n = _____

Answer: n = 100

Explanation: n × $3.25 = $325.00 n × $3.25 = $325.00 n x $325 x $0.01 = $325.00 n x $325 x $1/100 = $325.00 n =  $325.00/$325 x 100 n = 1 x 100 = 100

Question 12. 0.1 × n = 89.5 n = _____

Answer: n = 895

Explanation: 0.1 × n = 89.5 1/10 x n = 895 x 0.1 n = 895 x 0.1 x 10 n = 895

Question 13. 10 3 × n = 630 n = _____

Answer: n = 0.63

Explanation: 10 3 × n = 630 1000 x n = 630 n = 630 x 1/1000 n = 630 x 0.001 n = 0.63

Problem Solving – Page No. 166

What’s the Error?

So, Kirsten needs ______ feet of cord to make 1,000 lanyards. Describe how Kirsten could have solved the problem without writing out the pattern needed. Type below: ________

Answer: Kirsten needs 1,750 feet of cord to make 1,000 lanyards. that decimal point moves one Noce M the right for each increasing power of 10. So, the answer is 1,750 feet.

Share and Show – Page No. 167

Use the decimal model to find the product.

Explanation: The picture shows that 5 groups of 6 hundredths. 0.06 = 6 hundredths Each square box shows 1/ 100. So, shade 6 boxes 5 times to get the product. Count the number of boxes shaded. There are 30 hundredths are shaded = 0.30 = 0.3 5 × 0.06 = 0.3

Question 2. 2 × 0.38 = _____

Explanation: The picture shows that 2 groups of 38 hundredths. 0.38 = 38 hundredths Each square box shows 1/ 100. So, shade 38 boxes 2 times to get the product. 38 hundredths + 38 hundredths = 76 hundredths = 0.76.

Question 3. 4 × 0.24 = _____

Explanation: 4 groups of 24 hundredths Each square box shows 1/ 100. So, shade 24 boxes 4 times to get the product. 24 hundredths + 24 hundredths + 24 hundredths + 24 hundredths = 96 hundredths = 0.96.

Find the product. Draw a quick picture.

Question 4. 4 × 0.6 = _____

Explanation: 4 × 0.6 4 groups of 6 tenths 0.6 + 0.6 + 0.6 + 0.6 = 2.4 4 × 0.6 = 2.4

Question 5. 2 × 0.67 = _____

Explanation: 2 × 0.67 2 groups of 67 hundredths 0.67 + 0.67 = 1.34 2 × 0.67 = 1.34

Question 6. 3 × 0.62 = _____

Explanation: 3 × 0.62 3 groups of 62 hundredths 0.62 + 0.62 + 0.62 = 1.86 3 × 0.62 = 1.86

Question 7. 4 × 0.32 = _____

Explanation: 4 × 0.32 4 groups of 32 hundredths 0.32 + 0.32 + 0.32 + 0.32 = 1.28 4 × 0.32 = 1.28

Question 8. Describe how you solved Exercise 7 using place value and renaming. Type below: ________

Answer: 4 × 0.32 4 groups of 32 hundredths There are 32 hundredths. 32 hundredths there are 30 tenths and 2 hundredths. Combine the tenths and rename. 2 + 2 + 2 + 2 = 8 Combine the tenths and rename. There are 3 tenths. 3 + 3 + 3 + 3 = 12; 2 tenths and 1 tens Cross out the tenths you renamed. Combine the ones and rename them. 0 + 0 + 0 + 0 + 1 = 1 1.28 4 × 0.32 = 1.28

Problem Solving – Page No. 168

Question 9. Each day a bobcat drinks about 3 times as much water as a Canada goose drinks. How much water can a bobcat drink in one day? _____ liter

Answer: 0.72 liters

Explanation: Each day a bobcat drinks about 3 times as much water as a Canada goose drinks. Canada goose = 0.24 liters bobcat drinks = 3 x 0.24 3 x 0.24 = 0.72 liters

Question 10. River otters drink about 5 times as much water as a bald eagle drinks in a day. How much water can a river otter drink in one day? _____ liter

Answer: 0.8 liter

Explanation: River otters drink about 5 times as much water as a bald eagle drinks in a day. bald eagle drinks 0.16 liters 5 times as 0.16 liters = 5 x 0.16 = 0.8 liter

Question 11. Explain how you could use a quick picture to find the amount of water that a cat drinks in 5 days. Type below: ________

Explanation: Cat drinks 0.15 liters of water in a day. In 5 days, 5 x 0.15 = 0.75

Question 12. Test Prep Jared has a parakeet that weighs 1.44 ounces. Susie has a Senegal parrot that weighs 3 times as much as Jared’s parakeet. How many ounces does Susie’s parrot weigh? Options: a. 0.32 ounce b. 0.43 ounce c. 4.32 ounces d. 43.2 ounces

Answer: c. 4.32 ounces

Explanation: Jared has a parakeet that weighs 1.44 ounces. Susie has a Senegal parrot that weighs 3 times as much as Jared’s parakeet. Susie’s parrot weigh 3 x 1.44 ounces = 4.32 ounces

Share and Show – Page No. 171

Place the decimal point in the product.

Question 1. 6.81 ×   7 ———- 4767 Think: The place value of the decimal factor is hundredths.

Answer: 6.81 x 7 = 47.67

Explanation: 6.81 x 7 = 7 x 6.81 7 x (6 + 0.81) = (7 x 6) + (7 x 0.81) = 42 + 5.67 = 47.67

Question 2. 3.7 × 2 ———- 74 _____

Answer: 7.4

Explanation: 3.7 x 2 3.7 x 10 = 37 37 x 2 = 74 37 x 0.1 = 3.7 74 x 0.1 = 7.4

Question 3. 19.34 ×    5 ———- 9670 _____

Answer: 96.7

Explanation: 19.34 x 100 = 1934 1934 x 5 = 9670 1934 x 0.01 = 19.34 9670 x 0.01 = 96.7

Find the product.

Question 4. 6.32 ×  3 ———- _____

Answer: 18.96

Explanation: 6.32 x 100 = 632 632 x 3 = 1896 632 x 0.01 = 6.32 1896 x 0.01 = 18.96

Question 5. 4.5 × 8 ———- _____

Explanation: 4.5 x 10 = 45 45 x 8 = 360 45 x 0.1 = 4.5 360 x 0.1 = 36.0

Question 6. 40.7 ×  5 ———- _____

Answer: 203.5

Explanation: 40.7 x 10 = 407 407 x 5 = 2035 407 x 0.1 = 40.7 2035 x 0.1 = 203.5

Question 7. 4.93 ×   7 ———- _____

Answer: 34.51

Explanation: 7 x 3 = 21 hundredths; 2 tenths and 1 hundredths 7 x 9 = 63 tenths; 63 + 2 tenths = 65 tenths; 6 ones and 5 tenths 4 x 7 = 28; 28 + 6 = 34 ones; 34.51

Question 8. 8.2 × 6 ———- _____

Answer: 49.2

Explanation: 6 x 2 = 12 tenths; 1 ones and 2 tenths 6 x 8 = 48; 48 + 1 = 49 ones 49.2

Question 9. 0.49 ×   4 ———- _____

Answer: 1.96

Explanation: 9 x 4 = 36 hundredths; 3 tenths and 6 hundredths 4 x 4 = 16 tenths; 16 + 3 tenths = 19 tenths; 1 ones and 9 tenths 4 x 0 = 0; 0 + 1 = 1ones; 1.96

Question 10. 9.08 ×   9 ———- _____

Answer: 81.72

Explanation: 9 x 8 = 72 hundredths; 7 tenths and 2 hundredths 9 x 0 = 0 tenths; 0 + 7 tenths = 7 tenths; 7 tenths 9 x 9 = 81; 81 81.72

Question 11. 7.55 ×  8 ———- _____

Answer: 60.4

Explanation: 8 x 5 = 40 hundredths; 4 tenths and 0 hundredths 8 x 5 = 40 tenths; 40 + 4 tenths = 44 tenths; 4 ones and 4 tenths 8 x 7 = 56 ones; 56 + 4 = 60 ones 60.40 = 60.4

Question 12. 15.37 ×    5 ———- _____

Answer: 76.85

Explanation: 5 x 7 = 35 hundredths; 3 tenths and 5 hundredths 5 x 3 = 15 tenths; 15 + 3 tenths = 18 tenths; 1 ones and 8 tenths 5 x 5 = 25 ones; 25 + 1 = 26 ones; 2 hundreds and 6 ones 5 x 1 = 5 hundreds; 5 + 2 = 7 hundreds 76.85

Practice: Copy and Solve Find the product.

Question 13. 8 × 7.2 = _____

Answer: 8 × 7.2 = 57.6

Explanation: 8 × 7.2 = 8 x (7 + 0.2) = (8 x 7) + (8 x 0.2) = 56 + 1.6 = 57.6

Question 14. 3 × 1.45 = _____

Answer: 3 × 1.45 = 4.35

Explanation: 3 x 1.45 = 3 x (1 + 0.45) = (3 x 1) + (3 x 0.45) = 3 + 1.35 = 4.35

Question 15. 9 × 8.6 = _____

Answer: 9 × 8.6 = 77.4

Explanation: 9 × 8.6 = 9 x (8 + 0.6) = (9 x 8) + (9 x 0.6) = 72 + 5.4 = 77.4

Question 16. 6 × 0.79 = _____

Answer: 6 × 0.79 = 4.74

Explanation: 6 x 0.79 = 4.74

Question 17. 4 × 9.3 = _____

Answer: 4 × 9.3 = 37.2

Explanation: 4 × 9.3 = 4 x (9 + 0.3) = (4 x 9) + (4 x 0.3) = 36 + 1.2 = 37.2

Question 18. 7 × 0.81 = _____

Answer: 7 × 0.81 = 5.67

Explanation: 7 × 0.81 = 5.67

Question 19. 6 × 2.08 = _____

Answer: 6 × 2.08 = 12.48

Explanation: 6 × 2.08 = 6 x (2 + 0.08) = (6 x 2) + (6 x 0.08) = 12 + 0.48 = 12.48

Question 20. 5 × 23.66 = _____

Answer: 5 × 23.66 = 118.3

Explanation: 5 × 23.66 = 5 x (23 + 0.66) = (5 x 23) + (5 x 0.66) = 115 + 3.3 = 118.3

Problem Solving – Page No. 172

Question 21. Sari has a bag containing 6 half dollars. What is the weight of the half dollars in Sari’s bag? _____ grams

Answer: 68.04 grams

Explanation: Sari has a bag containing 6 half dollars. Half dollars = 11.34 grams 6 x 11.34 = 68.04 grams The weight of the half dollars in Sari’s bag is 68.04 grams.

Question 22. Felicia is running a game booth at a carnival. One of the games requires participants to guess the weight, in grams, of a bag of 9 dimes. What is the actual weight of the dimes in the bag? _____ grams

Answer: 20.43 grams

Explanation: Felicia is running a game booth at a carnival. One of the games requires participants to guess the weight, in grams, of a bag of 9 dimes. 9 x 2.27 grams = 20.43 grams

Question 23. Chance has $2 in quarters. Blake has $5 in dollar coins. Whose coins have the greatest weight? Explain. _________

Answer: Dollar coins has the greatest weight than quarters.

Explanation: $2 means 4 quarters = 4 x 5.67 = 22.68 $5 in dollar coins = 5 x 8.1 = 40.5 Dollar coins has the greatest weight than quarters.

Question 24. Julie multiplies 6.27 by 7 and claims the product is 438.9. Explain without multiplying how you know Julie’s answer is not correct. Find the correct answer. Type below: _________

Answer: 6.27 has two decimal digits 438.9 has one decimal digit Therefore, Julie’s answer is not correct. 6.27 x 7 = 43.89

Question 25. Test Prep Every day on his way to and from school, Milo walks a total of 3.65 miles. If he walks to school 5 days, how many miles will Milo have walked? _____ miles

Answer: 18.25 miles

Explanation: Milo walks a total of 3.65 miles. If he walks to school 5 days, 5 x 3.65 = 18.25 miles

Share and Show – Page No. 175

Draw a model to find the product.

Explanation: 19 × 0.75 19 = 10 + 9 0.75 = 0.7 + 0.05 10 x 0.7 = 7 10 x 0.05 = 0.5 9 x 0.7 = 6.3 9 x 0.05 = 0.45 7 + 0.5 + 6.3 + 0.45 = 14.25 19 × 0.75 = 14.25

Question 2. 27 × 8.3 = _____

Explanation: 27 × 8.3 = 224.1 27 = 20 + 7 8.3 = 8 + 0.3 20 x 8 = 160 20 x 0.3 = 6 7 x 8 = 56 7 x 0.3 = 2.1 160 + 6 + 56 + 2.1 = 224.1

Question 3. 18 × 8.7 = _____

Answer: 18 × 8.7 = 156.6

Explanation: 8.7 x 10 = 87 18 x 87 = 1566 87 x 0.1 = 8.7 1566 x 0.1 = 156.6

Question 4. 23 × 56.1 = _____

Answer: 1290.3

Explanation: 56.1 x 10 = 561 561 x 23 = 12,903 561 x 0.1 = 56.1 12,903 x 0.1 = 1290.3

Question 5. 47 × 5.92 = _____

Answer: 278.24

Explanation: 5.92 x 100 = 592 592 x 47 = 27,824 592 x 0.01 = 5.92 27,824 x 0.01 = 278.24

Question 6. 71 × 8.3 = _____

Explanation: 71 = 70 + 1 8.3 = 8 + 0.3 70 x 8 = 560 70 x 0.3 = 21 1 x 8 = 8 1 x 0.3 = 0.3 560 + 21 + 8 + 0.3 = 589.3

Question 7. 28 × 0.91 = _____

Explanation: 28 = 20 + 8 0.91 = 0.90 + 0.01 20 x 0.90 = 18 20 x 0.01 = 0.2 8 x 0.90 = 7.2 8 x 0.01 = 0.08 18 + 0.2 + 7.2 + 0.08 = 25.48

Question 8. 19 × 0.65 = _____

Answer: 19 × 0.65 = 12.35

Explanation: 0.65 x 100 = 65 65 x 19 = 1235 65 x 0.01 = 0.65 1235 x 0.01 = 12.35

Question 9. 34 × 98.3 = _____

Answer: 34 × 98.3 = 3342.2

Explanation: 98.3 x 10 = 983 983 x 34 = 33,422 983 x 0.1 = 98.3 33,422 x 0.1 = 3342.2

Question 10. 26 × 16.28 = _____

Answer: 26 × 16.28 = 423.28

Explanation: 16.28 x 100 = 1628 1628 x 26 = 42,328 1628 x 0.01 = 16.28 42,328 x 0.01 = 423.28

UNLOCK the Problem – Page No. 176

Answer: We need to find How many hours are in 2 weeks on Earth? 2 weeks x 23.93 hours per day?

Question 11. b. What information do you need to know to solve the problem? Type below: _________

Answer: Number of days in a week Hours per day

Question 11. c. Write an expression to represent the problem to be solved. Type below: _________

Answer: 2 weeks = 14 days 14 x 23.93 hours

Question 11. d. Show the steps you used to solve the problem. Type below: _________

Answer: 335.02 hours

Explanation: 23.93 = 23.93 x 100 = 2393 2393 x 14 = 33,502 2393 x 0.01 = 23.93 33502 x 0.01 = 335.02

Question 11. e. Complete the sentences. On Earth, there are about _____ hours in a day, _____ days in 1 week, and _____ days in two weeks. Since _____ × _____ = _____ , there are about _____ hours in 2 weeks on Earth. Type below: _________

Answer: On Earth, there are about 23.93 hours in a day,  7 days in 1 week, and 14 days in two weeks. Since 23.93 × 14 = 335.02, there are about 335.02 hours in 2 weeks on Earth.

Question 12. Michael’s favorite song is 3.19 minutes long. If he listens to the song 15 times on repeat, how long will he have listened to the same song? _____ minutes

Answer: 47.85 minutes

Explanation: Michael’s favorite song is 3.19 minutes long. If he listens to the song 15 times, 15 x 3.19 = 47.85 minutes

Question 13. Test Prep A car travels 56.7 miles in an hour. If it continues at the same speed, how far will the car travel in 12 hours? Options: a. 68.004 miles b. 680.04 miles c. 680.4 miles d. 6,804 miles

Answer: c. 680.4 miles

Explanation: A car travels 56.7 miles in an hour. In 12 hours, 12 x 56.7 = 680.4 hours

Share and Show – Page No. 179

Question 1. Manuel collects $45.18 for a fundraiser. Gerome collects $18.07 more than Manuel. Cindy collects 2 times as much as Gerome. How much money does Cindy collect for the fundraiser? First, draw a diagram to show the amount Manuel collects. Then, draw a diagram to show the amount Gerome collects. Next, draw a diagram to show the amount Cindy collects. Finally, find the amount each person collects. Cindy collects ______ for the fundraiser. Type below: _________

Question 2. What if Gerome collects $9.23 more than Manuel? If Cindy still collects 2 times as much as Gerome, how much money would Cindy collect? Type below: _________

Answer: Gerome collects $9.23 more than Manuel Manuel: $45.18 Gerome: $45.18 + $9.23 = $54.41 Cindy: 2 x $54.41 = $108.82

Question 3. It costs $5.15 to rent a kayak for 1 hour at a local state park. The price per hour stays the same for up to 5 hours of rental. After 5 hours, the cost is decreased to $3.75 per hour. How much would it cost to rent a kayak for 6 hours? $ ______

Answer: $29.5

Explanation: It costs $5.15 to rent a kayak for 1 hour at a local state park. The price per hour stays the same for up to 5 hours of rental. After 5 hours, the cost is decreased to $3.75 per hour. For first 5 hours, $5.15 Next hour after 5 hours, it decreased to $3.75 For 6 hours, 5 x $5.15 + 1 x $3.75 5 x $5.15 = $25.75 1 x $3.75 = $3.75 $25.75 + $3.75 = $29.5

Question 4. Jenn buys a pair of jeans for $24.99. Her friend Karen spends $3.50 more for the same pair of jeans. Vicki paid the same price as Karen for the jeans but bought 2 pairs. How much did Vicki spend? $ ______

Answer: $56.98

Explanation: Jenn buys a pair of jeans for $24.99. Karen: $24.99 + $3.50 = $28.49 Vicky: 2 x $28.49 = $56.98

On Your Own – Page No. 180

Question 5. Austin shops at Surfer Joe’s Surf Shop before going to the beach. He buys 2 T-shirts, a pair of board shorts, and a towel. If he gives the cashier $60, how much change will Austin get back? $ ______

Answer: $2.86

Explanation: T-Shirt = $12.75 Board Shorts = $25.99 Sandals = $8.95 Towel = $5.65 Sunglasses = $15.50 Austin shops at Surfer Joe’s Surf Shop before going to the beach. He buys 2 T-shirts, a pair of board shorts, and a towel. (2 x $12.75) + ($25.99) + $5.65 = $25.5 + $31.64 = $57.14 $60 – $57.14 = $2.86

Question 6. Maria buys 3 T-shirts and 2 pairs of sandals at Surfer Joe’s Surf Shop. How much does Maria spend? $ ______

Answer: $56.15

Explanation: Maria buys 3 T-shirts and 2 pairs of sandals at Surfer Joe’s Surf Shop. 3 x $12.75 = $38.25 2 x $8.95 = $17.9 $38.25 + $17.9 = $56.15

Question 7. Nathan receives a coupon in the mail for $10 off of a purchase of $100 or more. If he buys 3 pairs of board shorts, 2 towels, and a pair of sunglasses, will he spend enough to use the coupon? How much will his purchase cost? Type below: _________

Answer: $94.77

Explanation: 3 pairs of board shorts, 2 towels, and a pair of sunglasses 3 x $25.99 = $77.97 2 x $5.65 = $11.3 Sunglasses = $15.50 $77.97 + $11.3 + $15.50 = $104.77 $10 off of a purchase of $100 or more $104.77 – $10 = $94.77

Question 8. Moya spends $33.90 on 3 different items. If she did not buy board shorts, which three items did Moya buy? Type below: _________

Answer: T-Shirt, Towel, and Sunglasses

Explanation: Moya spends $33.90 on 3 different items. If she did not buy board shorts, T-Shirt = $12.75 Towel = $5.65 Sunglasses = $15.50

Question 9. Test Prep At a donut shop in town, each donut costs $0.79. If Mr. Thomas buys a box of 8 donuts, how much will he pay for the donuts? Options: a. $6.32 b. $8.79 c. $63.20 d. $87.90

Answer: a. $6.32

Explanation: At a donut shop in town, each donut costs $0.79. If Mr. Thomas buys a box of 8 donuts, 8 x $0.79 = $6.32

Concepts and Skills

Question 1. Explain how you can use a quick picture to find 3 × 2.7. Type below: ________

Answer: 3 × 2.7 = 8.1; As there are 8 ones and 1 tenths, we can draw eight square boxes and 1 line to represent 1 tenth.

Question 2. 1 × 3.6 = _______ 10 × 3.6 = _______ 100 × 3.6 = _______ 1000 × 3.6 = _______

Answer: 1 × 3.6 = 3.6 10 × 3.6 = 36 100 × 3.6 = 360 1000 × 3.6 = 3,600

Question 3. 10 0 × 17.55 = _______ 10 1 × 17.55 = _______ 10 2 × 17.55 = _______ 10 3 × 17.55 = _______

Answer: 10 0 × 17.55 = 17.55 10 1 × 17.55 = 175.5 10 2 × 17.55 = 1755 10 3 × 17.55 = 17,550

Explanation: 10 0 × 17.55 = 1 x 17.55 = 17.55 10 1 × 17.55 = 10 x 17.55 = 175.5 10 2 × 17.55 = 100 x 17.55 = 1755 10 3 × 17.55 = 1000 x 17.55 = 17,550

Question 4. 1 × 29 = _______ 0.1 × 29 = _______ 0.01 × 29 = _______

Answer: 1 × 29 = 29 0.1 × 29 = 2.9 0.01 × 29 = 0.29

Question 5. 3.14 ×   8 ———– _____

Answer: 25.12

Explanation: 8 x (3.14) = 8 x (3 + 0.14) = (8 x 3) + (8 x 0.14) = 24 + 1.12 = 25.12

Question 6. 17 × 0.67 = _____

Answer: 11.39

Explanation: 0.67 x 100 = 67 67 x 17 = 1139 67 x 0.01 = 0.67 1139 x 0.01 = 11.39

Question 7. 29 × 7.3 = _____

Answer: 211.7

Explanation: 29 × 7.3 = 29 x (7 + 0.3) = (29 x 7) + (29 x 0.3) = 203 + 8.7 = 211.7

Draw a diagram to solve.

Question 8. Julie spends $5.62 at the store. Micah spends 5 times as much as Julie. Jeremy spends $6.72 more than Micah. How much money does each person spend? Julie: $ _______ Micah: $ _______ Jeremy: $ _______

Mid-Chapter Checkpoint – Page No. 182

Question 9. Sarah is cutting ribbons for a pep rally. The length of each ribbon needs to be 3.68 inches. If she needs 1,000 ribbons, what is the length of ribbon Sarah needs? _____ inches

Answer: 3680 inches

Explanation: Sarah is cutting ribbons for a pep rally. The length of each ribbon needs to be 3.68 inches. If she needs 1,000 ribbons, 3.68 x 1,000 = 3680 inches

Question 10. Adam is carrying books to the classroom for his teacher. Each books weighs 3.85 pounds. If he carries 4 books, how many pounds is Adam carrying? _____ pounds

Answer: 15.4 pounds

Explanation: Adam is carrying books to the classroom for his teacher. Each books weighs 3.85 pounds. If he carries 4 books, 4 x 3.85 = 15.4 pounds.

Question 11. A car travels 54.9 miles in an hour. If the car continues at the same speed for 12 hours, how many miles will it travel? _____ miles

Answer: 658.8 miles

Explanation: A car travels 54.9 miles in an hour. If the car continues at the same speed for 12 hours, 12 x 54.9 = 658.8 miles

Question 12. Charlie saves $21.45 each month for 6 months. In the seventh month, he only saves $10.60. How much money will Charlie have saved after 7 months? $ __________

Answer: $139.3

Explanation: Charlie saves $21.45 each month for 6 months. In the seventh month, he only saves $10.60. 6 x $21.45 + $10.60 = $128.7 + $10.60 = $139.3

Share and Show – Page No. 185

Multiply. Use the decimal model.

Explanation: The shaded and crossed parts represent the product. 32 hundredths = 0.32

Explanation: Count the number of overlapped boxes to find the product. 7 tenths = 0.7

Explanation: Count the red line crossed boxes to get the product. 4 x 16 = 64 0.1 x 0.1 = 0.01 64 x 0.01 = 0.64

Explanation: 3 x 4 = 12 0.1 x 0.1 = 0.01 12 x 0.01 = 0.12

Explanation: 9 x 6 = 54 0.1 x 0.1 = 0.01 54 x 0.01 = 0.54

Explanation: Count the red line crossed boxes to get the product. 5 x 12 = 60 0.1 x 0.1 = 0.01 60 x 0.01 = 0.60

Explanation: 8 x 9 = 72 0.1 x 0.1 = 0.01 72 x 0.01 = 0.72

Explanation: 5 x 3 = 15 0.1 x 0.1 = 0.01 15 x 0.01 = 0.15

Explanation: Count the red line crossed boxes to get the product. 5 x 15 = 75 0.1 x 0.1 = 0.01 75 x 0.01 = 0.75

Question 10. Explain why when you multiply and find one tenth of one tenth, it is equal to one hundredth. Type below: _________

Answer: When you do one-tenth of one-tenth, it is one-tenth over 10 —-> (1/10) /10 So, you can consider it as (1/10) / (10/1). This is only for simplicity. Now, you have to multiply the denominator of the fraction in the numerator with the numerator of fraction in denominator i.e., 10 with 10 and this comes in denominator only. and numerator of fraction in the numerator with the denominator of the fraction in denominator i.e., 1 with 1. So, you get, (1*1) / (10*10) = 1/100 This is again the 10th part of one-tenth OR 100th part of 1 = one hundredth

Problem Solving – Page No. 186

Sense or Nonsense?

Answer: Randy’s Model is correct. Stacy’s Model makes nonsense. Because Stacy’s Model is showing 0.10 x 0.8 which is not equal to 0.3 x 0.5

Explanation: Randy and Stacy used models to find 0.3 of 0.5 0.3 x 0.5 = 0.15

Share and Show – Page No. 188

Question 1. 3.62 × 1.4 ———-

5068 Think: A hundredth is being multiplied by a tenth. Use the pattern 0.01 × 0.1. ___

Answer: 5.068

Explanation: 3.62 x 100 = 362 = 362 x 0.01 1.4 x 10 = 14 = 14 x 0.1 362 x 14 = 5068 0.01 x 0.1 = 0.001 5068 x 0.001 = 5.068

Question 2. 6.8 ×1.2 ———- 816 _____

Answer: 8.16

Explanation: 6.8 x 10 = 68 = 68 x 0.1 1.2 x 10 = 12 = 12 x 0.1 68 x 12 = 816 0.1 x 0.1 = 0.01 816 x 0.01 = 8.16

Question 3. 0.9 × 0.8 ———- _____

Answer: 0.72

Explanation: 0.9 x 10 = 9 = 9 x 0.1 0.8 x 10 = 8 = 8 x 0.1 9 x 8 = 72 0.1 x 0.1 = 0.01 72 x 0.01 = 0.72

Question 4. 84.5 ×  5.5 ———- _____

Answer: 464.75

Explanation: 84.5 x 10 = 845 = 845 x 0.1 5.5 x 10 = 55 = 55 x 0.1 845 x 55 = 46475 0.1 x 0.1 = 0.01 46475 x 0.01 = 464.75

Question 5. 2.39 ×2.7 ———- _____

Answer: 6.453

Explanation: 2.39 x 100 = 239 = 239 x 0.01 2.7 x 10 = 27 = 27 x 0.1 239 x 27 = 6453 0.01 x 0.1 = 0.001 6453 x 0.001 = 6.453

On Your Own – Page No. 189

Question 6. 7.9 × 3.4 ———- _____

Answer: 26.86

Explanation: 7.9 x 10 = 79 = 79 x 0.1 3.4 x 10 = 34 = 34 x 0.1 79 x 34 = 2686 0.1 x 0.1 = 0.01 2686 x 0.01 = 26.86

Question 7. 9.2 ×5.6 ———- _____

Answer: 51.52

Explanation: 9.2 x 10 = 92 = 92 x 0.1 5.6 x 10 = 56 = 56 x 0.1 92 x 56 = 5152 0.1 x 0.1 = 0.01 5152 x 0.01 = 51.52

Question 8. 3.45 × 9.7 ———- _____

Answer: 33.465

Explanation: 3.45 x 100 = 345 = 345 x 0.01 9.7 x 10 = 97 = 97 x 0.1 345 x 97 = 33465 0.01 x 0.1 = 0.001 33465 x 0.001 = 33.465

Question 9. 45.3 × 0.8 ———- _____

Answer: 36.24

Explanation: 45.3 x 10 = 453 = 453 x 0.1 0.8 x 10 = 8 = 8 x 0.1 453 x 8 = 3624 0.1 x 0.1 = 0.01 3624 x 0.01 = 36.24

Question 10. 6.98 × 2.5 ———- _____

Answer: 17.450

Explanation: 6.98 x 100 = 698 = 698 x 0.01 2.5 x 10 = 25 = 25 x 0.1 698 x 25 = 17,450 0.01 x 0.1 = 0.001 17450 x 0.001 = 17.450

Question 11. 7.02 ×3.4 ———- _____

Answer: 23.868

Explanation: 7.02 x 100 = 702 = 702 x 0.01 3.4 x 10 = 34 = 34 x 0.1 702 x 34 = 23868 0.01 x 0.1 = 0.001 23868 x 0.001 = 23.868

Question 12. 14.9 ×0.35 ———- _____

Answer: 5.215

Explanation: 14.9 x 10 = 149 = 149 x 0.1 0.35 x 100 = 35 = 35 x 0.01 149 x 35 = 5215 0.1 x 0.01 = 0.001 5215 x 0.001 = 5.215

Question 13. 50.99 ×  3.7 ———- _____

Answer: 188.663

Explanation: 50.99 x 100 = 5099 = 5099 x 0.01 3.7 x 10 = 37 = 37 x 0.1 5099 x 37 = 188663 0.01 x 0.1 = 0.001 188663 x 0.001 = 188.663

Question 14. 18.43 ×  1.9 ———- _____

Answer: 35.017

Explanation: 18.43 x 100 = 1843 = 1843 x 0.01 1.9 x 10 = 19 = 19 x 0.1 1843 x 19 = 35017 0.01 x 0.1 = 0.001 35017 x 0.001 = 35.017

Question 15. 3.4 × 5.2 = _____

Answer: 17.68

Explanation: 3.4 × 5.2 34 x 52 = 1768 0.1 x 0.1 = 0.01 1768 x 0.01 = 17.68

Question 16. 0.9 × 2.46 = _____

Answer: 2.214

Explanation: 9 x 246 = 2214 0.1 x 0.01 = 0.001 2214 x 0.001 = 2.214

Question 17. 9.1 × 5.7 = ____

Answer: 51.87

Explanation: 91 x 57 = 5187 0.1 x 0.1 = 0.01 5187 x 0.01 = 51.87

Question 18. 4.8 × 6.01 = _____

Answer: 28.848

Explanation: 48 x 601 = 28848 0.1 x 0.01 = 0.001 28848 x 0.001 = 28.848

Question 20. 7.6 × 18.7 = _____

Answer: 142.12

Explanation: 76 x 187 = 14212 0.1 x 0.1 = 0.01 14212 x 0.01 = 142.12

Question 21. 0.77 × 14.9 = _____

Answer: 114.73

Explanation: 77 x 149 = 11473 0.01 x 0.1 = 0.01 11473 x 0.01 = 114.73

Question 22. 3.3 × 58.14 = _____

Answer: 191.862

Explanation: 33 x 5814 = 191862 0.1 x 0.01 = 0.001 191862 x 0.001 = 191.862

Problem Solving – Page No. 190

Question 23. Charlie has an adult Netherlands dwarf rabbit that weighs 1.2 kilograms. Cliff’s adult Angora rabbit weighs 2.9 times as much as Charlie’s rabbit. How much does Cliff’s rabbit weigh? _____ kilograms

Answer: 3.48 kilograms

Explanation: Charlie has an adult Netherlands dwarf rabbit that weighs 1.2 kilograms. Cliff’s adult Angora rabbit weighs 2.9 times as much as Charlie’s rabbit. 1.2 x 2.9 = 3.48 kilograms

Question 24. John 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 John’s. What will be the area of the enclosure Taylor is planning to build? _____ square feet

Answer: 67.584 square feet

Explanation: John 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 John’s. 30.72 x 2.2 = 67.584 square feet

Question 25. 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? _____ meters

Answer: 4.875 meters

Explanation: 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. 1.3 x 1.5 = 1.95 The building will be 2.5 times as tall as the height of the detailed model. 2.5 x 1.95 = 4.875 meters

Question 26. Leslie and Paul both solve the multiplication problem 5.5 x 4.6. Leslie says the answer is 25.30. Paul says the answer is 25.3. Whose answer is correct? Explain your reasoning. Type below: _________

Answer: Both answers are correct. Because 25.30 = 25.3. The zeros have no value after the decimal point of a number.

Explanation: 5.5 x 4.6 55 x 46 = 2530 0.1 x 0.1 = 0.01 2530 x 0.01 = 25.30 = 25.3

Question 27. Test Prep A vine in Mr. Jackson’s garden is 3.6 feet long. When it is measured again, it is 2.1 times as long. How long is the vine? Options: a. 5.7 feet b. 6.6 feet c. 7.5 feet d. 7.56 feet

Answer: a. 5.7 feet

Explanation: A vine in Mr. Jackson’s garden is 3.6 feet long. When it is measured again, it is 2.1 times as long. 3.6 + 2.1 = 5.7 feet

Share and Show – Page No. 193

Write zeros in the product.

Question 1. 0.05 × 0.7 ———-

Explanation:

□35 Think: Hundredths are multiplied by tenths. What should be the place value of the product? _____

Answer: 0.035

Explanation: 5 x 7 = 35 0.01 x 0.1 = 0.001 35 x 0.001 = 0.035

Question 2. 0.2 × 0.3 ———- _____

Answer: 0.06

Explanation: 2 x 3 = 6 0.1 x 0.1 = 0.01 6 x 0.01 = 0.06

Question 3. 0.02 × 0.2 ———- _____

Answer: 0.004

Explanation: 2 x 2 = 4 0.01 x 0.1 = 0.001 4 x 0.001 = 0.004

Question 4. $0.05 × 0.8 ———- $ _____

Answer: $0.04

Explanation: 5 x 8 = 40 0.01 x 0.1 = 0.001 40 x 0.001 = 0.040 = 0.04

Question 5. 0.09 × 0.7 ———- _____

Answer: 0.063

Explanation: 9 x 7 = 63 0.01 x 0.1 = 0.001 63 x 0.001 = 0.063

Question 6. 0.2 × 0.1 ———- _____

Answer: 0.02

Explanation: 2 x 1 = 2 0.1 x 0.1 = 0.01 2 x 0.01 = 0.02

Question 7. 0.3 × 0.3 ———- _____

Answer: 0.09

Explanation: 3 x 3 = 9 0.1 x 0.1 = 0.01 9 x 0.01 = 0.09

Question 8. 0.05 × 0.3 ———- _____

Answer: 0.015

Explanation: 5 x 3 = 15 0.01 x 0.1 = 0.001 15 x 0.001 = 0.015

Question 9. 0.02 × 0.4 ———- _____

Answer: 0.008

Explanation: 2 x 4 = 8 0.01 x 0.1 = 0.001 8 x 0.001 = 0.008

Question 10. $0.40 × 0.1 ———- $ _____

Explanation: 40 x 1 = 40 0.10 x 0.1 = 0.010 40 x 0.010 = 0.04

Question 11. 0.09 × 0.2 ———- _____

Answer: 0.018

Explanation: 9 x 2 = 18 0.01 x 0.1 = 0.001 18 x 0.001 = 0.018

Question 12. $ 0.05 × 0.6 ———- _____

Answer: $0.3

Explanation: 5 x 6 = 30 0.01 x 0.1 = 0.001 30 x 0.001 = 0.30 = 0.3

Question 13. 0.04 × 0.5 ———- _____

Answer: 0.020

Explanation: 4 x 5 = 20 0.01 x 0.1 = 0.001 20 x 0.001 = 0.020

Question 14. 0.06 × 0.8 ———- _____

Answer: 0.048

Explanation: 6 x 8 = 48 0.01 x 0.1 = 0.001 48 x 0.001 = 0.048

Algebra Find the value of n.

Question 15. 0.03 × 0.6 = n n = _____

Answer: n = 0.018

Explanation: 0.03 × 0.6 = n 0.018 = n n = 0.018

Question 16. n × 0.2 = 0.08 n = _____

Answer: n = 0.4

Explanation: n × 0.2 = 0.08 n = 0.08/0.2 n = 0.4

Question 17. 0.09 × n = 0.063 n = _____

Answer: n = 0.7

Explanation: 0.09 × n = 0.063 n = 0.063/0.09 n = 0.7

Page No. 194

Answer: We need to find how far snail travels on 0.2 times as far as the average distance in a day?

Question 18. b. What information will you use to solve the problem? Type below: _________

Answer: On an average day, a garden snail can travel about 0.05 miles. 0.2 times as far as the average distance in a day

Question 18. c. How will you use multiplication and place value to solve the problem? Type below: _________

Answer: 0.2 x 0.05

Question 18. d. Show how you will solve the problem. Type below: _________

Answer: 2 x 5 = 10 0.1 x 0.01 = 0.001 10 x 0.001 = 0.010 = 0.01

Question 18. e. Fill in the bubble for the correct answer choice above. Options: a. 0.7 mile b. 0.25 mile c. 0.1 mile d. 0.01 mile

Answer: d. 0.01 mile

Question 19. 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? Options: a. 0.08 ounce b. 0.09 ounce c. 0.8 ounce d. 0.9 ounce

Answer: a. 0.08 ounce

Explanation: 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. 0.8 x 0.1 = 0.08 ounce

Question 20. Michael multiplies 0.2 by a number. He records the product as 0.008. What number did Michael use? Options: a. 0.016 b. 0.04 c. 0.28 d. 0.4

Answer: b. 0.04

Explanation: Michael multiplies 0.2 by a number. He records the product as 0.008. 0.2 x n = 0.008 n = 0.008/0.2 n = 0.04 Michael use 0.04

Chapter Review/Test – Page No. 195

Check Concepts

Question 1. Explain how estimation helps you to place the decimal point when multiplying 3.9 × 5.3. Type below: _________

Answer: 3.9 × 5.3 39 x 53 = 2067 0.1 x 0.1 = 0.01 2067 x 0.01 = 20.67

Question 2. 1 × 7.45 = _______ 10 × 7.45 = _______ 100 × 7.45 = _______ 1,000 × 7.45 = _______

Answer: 1 × 7.45 = 7.45 10 × 7.45 = 74.5 100 × 7.45 = 745 1,000 × 7.45 = 7,450

Question 3. 10 0 × 376.2 = _______ 10 1 × 376.2 = _______ 10 2 × 376.2 = _______ 10 3 × 376.2 = _______

Answer: 10 0 × 376.2 = 376.2 10 1 × 376.2 = 3,762 10 2 × 376.2 = 37,620 10 3 × 376.2 = 376,200

Explanation: 10 0 × 376.2 = 1 x 376.2 = 376.2 10 1 × 376.2 = 10 x 376.2 = 3,762 10 2 × 376.2 = 100 x 376.2 =  37,620 10 3 × 376.2 = 1000 x 376.2 = 376,200

Question 4. 1 × 191 = _______ 0.1 × 191 = _______ 0.01 × 191 = _______

Answer: 1 × 191 = 191 0.1 × 191 = 19.1 0.01 × 191 = 1.91_

Question 5. 5 × 0.89 = _____

Answer: 4.45

Explanation: 5 × 0.89 5 x 9 = 45 hundredths; 4 tenths and 5 hundredths 5 x 8 = 40 tenths; 40 + 4 tenths = 44 tenths; 4 ones and 4 tenths 5 x 0 = 0; 0 + 4 = 4 ones 4.45

Question 6. 9 × 2.35 = _____

Answer: 21.15

Explanation: 9 × 2.35 9 x 5 = 45 hundredths; 4 tenths and 5 hundredths 9 x 3 = 27 tenths; 27 + 4 tenths = 31 tenths; 3 ones and 1 tenth 9 x 2 = 18; 18 + 3 = 21 ones 21.15

Question 7. 23 × 8.6 = _____

Answer: 197.8

Explanation: 23 x 8.6 23 x 6 = 138 tenths; 13 ones and 8 tenths 23 x 8 = 184 ones; 184 + 13 = 197 ones 197.8

Question 8. 7.3 × 0.6 = _____

Answer: 4.38

Explanation: 73 x 6 = 438 0.1 x 0.1 = 0.01 438 x 0.01 = 4.38

Question 9. 0.09 × 0.7 = _____

Question 10. 0.8 × $0.40 = $ _____

Answer: $0.32

Explanation: 8 x 4 = 32 0.1 x 0.1 = 0.01 32 x 0.01 = 0.32

Question 11. In January, Dawn earns $9.25 allowance. She earns 3 times as much in February. If during March, she earns $5.75 more than she did in February, how much allowance does Dawn earn in March? $ _________

Answer: $33.5

Explanation: In January, Dawn earns $9.25 allowance. February: 3 x $9.25 = $27.75 March: $27.75 + $5.75 = $33.5

Chapter Review/Test – Page No. 196

Fill in the bubble completely to show your answer.

Question 12. Janet hikes a trail at a local forest each day. The trail is 3.6 miles long, and she has hiked 5 days in the past week. How many miles has Janet hiked in the past week? Options: A. 18 miles B. 15.3 miles C. 11 miles D. 8.6 miles

Answer: A. 18 miles

Explanation: Janet hikes a trail at a local forest each day. The trail is 3.6 miles long, and she has hiked 5 days in the past week. 3.6 x 5 = 18 miles

Question 13. To earn money for his vacation, Grayson works at a local shop on weekends. His job is to cut bricks of fudge into 0.25 pound squares. If he cuts 36 equal-sized squares on Saturday, how many pounds of fudge has Grayson cut? Options: A. 7.25 pounds B. 9 pounds C. 90 pounds D. 72.5 pounds

Answer: B. 9 pounds

Explanation: To earn money for his vacation, Grayson works at a local shop on weekends. His job is to cut bricks of fudge into 0.25 pound squares. If he cuts 36 equal-sized squares on Saturday, 0.25 x 36 = 9 pounds

Question 14. James is making a scale model of his bedroom. The model is 0.6 feet wide. If the actual room is 17.5 times as wide as the model, what is the width of James’s room? Options: A. 18.1 feet B. 17.11 feet C. 16.9 feet D. 10.5 feet

Answer: D. 10.5 feet

Explanation: James is making a scale model of his bedroom. The model is 0.6 feet wide. If the actual room is 17.5 times as wide as the model, 0.6 x 17.5 = 10.5 feet

Question 15. The cost of admission to the matinee showing at a movie theater is $6.75. If 7 friends want to see the matinee showing of their favorite movie, how much will it cost? Options: A. $11.25 B. $14.75 C. $42.75 D. $47.25

Answer: D. $47.25

Explanation: The cost of admission to the matinee showing at a movie theater is $6.75. If 7 friends want to see the matinee showing of their favorite movie, 7 x $6.75 = $47.25

Chapter Review/Test – Page No. 197

Question 16. On Friday, Gail talks for 38.4 minutes on her cell phone. On Saturday, she uses 5.5 times as many minutes as she did on Friday. How long does Gail talk on her cell phone on Saturday? Options: A. 2.112 minutes B. 21.12 minutes C. 211.2 minutes D. 2,112 minutes

Answer: C. 211.2 minutes

Explanation: On Friday, Gail talks for 38.4 minutes on her cell phone. On Saturday, she uses 5.5 times as many minutes as she did on Friday. 38.4 x 5.5 = 211.2 minutes

Question 17. Harry walks to a produce market to buy bananas. If a pound of bananas costs $0.49, how much will Harry pay for 3 pounds of bananas? Options: A. $1.47 B. $3.49 C. $5.49 D. $10.47

Answer: A. $1.47

Explanation: Harry walks to a produce market to buy bananas. If a pound of bananas costs $0.49, For 3 pound, 3 x $0.49 = $1.47

Question 18. At Anne’s Fabric Emporium, a yard of chiffon fabric costs $7.85. Lee plans to purchase 0.8 yard for a craft project. How much money will Lee spend on chiffon fabric? Options: A. $0.63 B. $6.28 C. $7.05 D. $8.65

Answer: B. $6.28

Explanation: At Anne’s Fabric Emporium, a yard of chiffon fabric costs $7.85. Lee plans to purchase 0.8 yard for a craft project. 0.8 x $7.85 = $6.28

Question 19. Mitchell has $18.79 in his savings account. Jeremy has 3 times as much as Mitchell. Maritza has $4.57 more than Jeremy. How much money does Maritza have in her savings account? Options: A. $13.71 B. $32.50 C. $56.37 D. $60.94

Answer: D. $60.94

Explanation: Mitchell: $18.79 Jeremy: 3 x $18.79 = $56.37 Maritza: $56.37 + $4.57 = $60.94

Chapter Review/Test – Page No. 198

Constructed Response

Question 20. A river otter eats about 0.15 times its weight in food each day. At the Baytown Zoo, the male river otter weighs 5 pounds. About how much food will the otter at the zoo consume each day? Explain how you found your answer. _____ pounds

Answer: 0.75 pounds

Explanation: A river otter eats about 0.15 times its weight in food each day. At the Baytown Zoo, the male river otter weighs 5 pounds. 0.15 x 5 = 0.75 pounds

Performance Task

Answer: $39.75

Explanation: Senior Citizen = $10.50 Adult = $15.75 Child = $8.25 A family of 2 adults and 1 child plans to spend the day at the Baytown Zoo. (2 x $15.75) + $8.25 $31.5 + $8.25 = $39.75

Question 21. B. Describe another way you could solve the problem. Type below: ________

Answer: (2 x $15.75) + $8.25 $15.75 + $15.75 + $8.25 = $39.75

Question 21. C. What if 2 more tickets for admission are purchased? If the two additional tickets cost $16.50, determine what type of tickets the family purchases. Explain how you can determine the answer without calculating. Options: a. Senior tickets b. Adult tickets c. Child tickets

Answer: c. Child tickets

Explanation: if 2 more tickets for admission are purchased? If the two additional tickets cost $16.50, $39.75 + $16.50 = $56.25 Two additional children’s tickets are purchased. Since senior citizen tickets cost about $10 each, then 2 tickets would cost about $20, which is too much. Adult tickets cost about $16 each, so 2 adult tickets would cost about $32, which is too much. Children’s tickets cost about $8, and 2 tickets would be about $16 which is correct.

Download Go Math Grade 5 Answer Key Chapter 4 Multiply Decimals for free of cost and take your preparation to the next level. Every Step included while solving the Problems of Multiply Decimals makes it easy for you to grasp the concepts. Keep in touch with our site to avail the latest updates on Class Specific Go Math Answer Keys in no time.

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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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Multiply Decimals

Lesson(s): 4.1, 4.3, 4.4, 4.7, 4.8

Understand the place value system. MAFS.5.NBT.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Lesson(s): 4.2–4.8

Perform operations with multi-digit whole numbers and with decimals to hundredths. MAFS.5.NBT.2.7 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.

Student Workbook Chapter 4

Enrich chapter 4, reteach chapter 4, student textbook chapter 4.

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Go Math! Grade 5 Teacher Edition

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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 4 • Lesson 5 150 150 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company Lesson Check 16. Ms. Ari buys and sells diamonds. She has a diamond that weighs 1.825 carats. What is the weight of Ms. Ari’s diamond rounded to the nearest hundredth? 17. A machinist uses a special tool to measure the diameter of a small pipe. The measurement tool reads 0.276 inch. What is this measure rounded to the nearest tenth? Spiral Review 18. Four ice skaters participate in an ice skating competition. The table shows their scores. Who has the highest score? Name Points Natasha 75.03 Taylor 75.39 Rowena 74.98 Suki 75.3 19. Write a decimal that is __1 10of 0.9. 20. Sam types 44 words per minutes. How long does it take Sam to type 1,232 words? 21. Joseph needs to find the quotient of 3,216 ÷ 8. In what place is the first digit in the quotient? 1.83 carats Taylor 28 minutes 0.3 inch 0.09 hundreds gg CorrectionKey=NL-A 5_mnlese694762_c04p05.indd 150 5/26/2022 1:23:48 PM

_ thousandths Go Online For more help Check student’s work. 5 8 2 6 4 16 3 52 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A 5_mnlese694762_c04cr.indd 151 5/26/2022 1:19:54 PM

Chapter 4 153–156 Performance Assessment Task See the Performance Tasks to assesses students’ understanding of the content. For each task, you will find sample student work for each of the response levels in the task scoring rubric. Performance Assessment Tasks may be used for portfolios. 154 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company© Houghton Mifflin Harcourt Publishing Company 12. Complete the table. Decimal 10 times as much as 1 10 of 0.08 0.2 0.6 0.05 13. Rafael bought 2.15 pounds of potato salad and 4.2 pounds of macaroni salad to bring to a picnic. For 13a–13c, select Yes or No to indicate whether each statement is true. 13a. Rounded to the nearest whole number, ● Yes ● No Rafael bought 2 pounds of potato salad. 13b. Rounded to the nearest whole number, ● Yes ● No Rafael bought 4 pounds of macaroni salad. 13c. Rounded to the nearest tenth, Rafael ● Yes ● No bought 2.1 pounds of potato salad. 14. The four highest scores on the floor exercise at a gymnastics meet were 9.675, 9.25, 9.325, and 9.5 points. Choose the numbers that make the statement true. The lowest of these four scores was 9.675 9.25 9.325 9.5 points. The highest of these four scores was 9.675 9.25 9.325 9.5 points. 0.8 0.5 6.0 2.0 0.008 0.005 0.06 0.02 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_c04cr.indd 154 5/26/2022 1:19:54 PM 156 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company 18. 0.4 is __ times as much as __. So, 4 tenths = __ thousandths. 19. Choose the value that makes the statement true. In the number 1.025, the value of the digit 2 is 2 ones tenths hundredths thousandths , and the value of the digit 5 is 5 ones tenths hundredths thousandths . 20. A rounded number for the weight of a puppy is 15.87 pounds. What are the least and greatest weights to the thousandths that could round to 15.87 pounds? Explain. Sample answer: The least weight is 15.865 pounds, and the greatest weight is 15.874 pounds. Possible explanation: Any number greater than 15.874 would round to 15.88 pounds. Any number less than 15.865 would round to 15.86 pounds. 21. 0.84 is 10 times as much as 0.084 0.84 8.4 84 and __1 10 of 0.084 0.84 8.4 84 . 400 100 0.004 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A 5_mnlese694762_c04cr.indd 156 5/26/2022 1:19:55 PM Chapter 4 153 © Houghton Mifflin Harcourt Publishing Company© Houghton Mifflin Harcourt Publishing Company Name 8. Round 25.999 to the nearest hundredth. Explain. 26.00; Sample answer: Since there is a 9 in the thousandth place, the number of hundredths will increase by 1 to 10, and a 0 will go in the hundredths place. The digit in the tenths place will increase by 1 to 10, so a 0 will go in the tenths place and the digit in the ones place will increase to 6. 9. What number is composed of 7 ones, 11 tenths, 12 hundredths and 41 thousandths? __ 10. Write the number 0.783 in two other forms. word form: _______ expanded form: _______ 11. The price of hand soap at the grocery store is $0.649. For 11a-11c, select True or False for each statement. 11a. Rounded to the nearest whole number, ● True ● False the price is $1 per ounce. 11b. Rounded to the nearest tenth, ● True ● False the price is $0.7 per ounce. 11c. Rounded to the nearest hundredth, ● True ● False the price is $0.65 per ounce. seven hundred eighty-three thousandths 8.261 (7 ∙ 1 10 ) ∙ (8 ∙ 1 100) ∙ (3 ∙ 1 1,000) DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A 5_mnlese694762_c04cr.indd 153 5/26/2022 1:19:54 PM Chapter 4 155 © Houghton Mifflin Harcourt Publishing Company© Houghton Mifflin Harcourt Publishing Company Name 15. Michelle records the value of 1 euro in U.S. dollars each day for her social studies project. The table shows the data she has recorded so far. Day Value of 1 Euro (in U.S. dollars) Monday 1.448 Tuesday 1.443 Wednesday 1.452 Thursday 1.458 On which two days was the value of 1 euro the same when rounded to the nearest hundredth of a dollar? Monday and Wednesday 16. Estee, Sarai, and Kurry each chose a number. Estee’s number is __1 10 of Sarai’s. Kurry’s number is 10 times as much as Sarai’s. Sarai's number is 0.09. What number did each person choose? Sarai: 0.09; Kurry: 0.9; Estee: 0.009 17. Karis has plants that are 16.407 centimeters, 16.427 centimeters tall, and 16.413 centimeters tall. Part A To compare the heights of the plants, which is the place value that you will consider? Explain. Possible answer: I will look at the digit in the hundredths place because it is the greatest place value where the digits differ. Part B Order the heights of the plants from tallest to shortest. 16.427 cm, 16.413 cm, 16.407 cm DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A 5_mnlese694762_c04cr.indd 155 5/26/2022 1:19:55 PM

2  thousandths 8 The four highest scores at a diving meet were 9.08, 9.1, 9.15, and 9.06  points. Write the decimals from the list to correctly complete the sentences. The lowest of these four scores was points. The highest of these four scores was points. 9.08 9.1 9.15 9.06 9 Which decimal has the same value as 1.616 when both are rounded to the nearest hundredth? A 1.519 B 1.598 C 1.614 D 1.623 10 Write the decimals from the list to correctly complete the sentence. The number 0.92 is 10 times as much as and ___1 10 of . 0.0092 0.092 0.92 9.2 92 9.15 9.06 0.092 9.2 DO NOT EDIT--Changes must be made through “File info” CorrectionKey=FL-B 5_MFLE_AS_1822128_Ch03.indd 36 12/10/21 3:51 PM

Chapter 4 Test 156B Teacher Notes

Launch Activity 2 Launch Activity Decimals and Fractions SNAPSHOT Mathematical Standards ● Preskill: Explore the addition and subtraction of multi-digit numbers with decimals to the hundredths. ● Preskill: Add and subtract fractions with like denominators, including mixed numbers and fractions greater than one, with procedural reliability. ● Preskill: Extend previous understanding of multiplication to explore the multiplication of a fraction by a whole number or a whole number by a fraction. Mathematical Practices and Processes ● Model with mathematics. ● Attend to precision. ● Look for and make use of structure. Learning Goal Use real-world context to understand and solve a problem involving the addition of fractions and decimals. Language Objective Students can describe how to use different strategies to solve the problem. MATERIALS • MathBoard ACROSS THE GRADES Before Grade 5 After • Students will explore how to add and subtract numbers with decimals to the hundredths. • Add and subtract fractions and mixed numbers with like denominators. • Students will multiply a whole number by a fraction. • Students will add and subtract numbers with decimals to the thousandths. • Explore how to multiply and divide numbers with decimals to the hundredths. • Add and subtract fractions and mixed numbers with unlike denominators, as well as extend their understanding of fraction multiplication and division. • Students will apply and extend their previous understanding of operations with decimals and fractions to multiplication and division with procedural fluency. • Solve multi-step real-world problems involving decimals and fractions. 157A Go Math! Grade 5

Go Online to Teacher’s Corner Common Errors Professional Learning PROFESSIONAL DEVELOPMENT IN THE CLASSROOM Formats for Classroom Discourse Social & Emotional Learning Whole-Class Discussions are led by the teacher, who helps the class focus on higher-level concepts, mathematical reasoning, and making sense of new ideas. The teacher should clear up widely held misconceptions and tie past concepts to new thinking. Small Groups of three to six students discuss ideas for solving the problem as a group and then with the teacher. This is a crucial time for the teacher to look for both conceptual and procedural errors. The teacher challenges group members to explain their strategies, whether correct or incorrect, for solving the problem. Partners respond to each other’s statements so that both partners put their thoughts into words. They practice contributing to the discussion and try to answer each other’s questions. The teacher asks for clarification of their thinking and asks directional questions, focusing on identifying and helping the students resolve their own errors. Working with partners and in groups is a key component of learning mathematics. These questions are designed specifically to support learning in a collaborative math classroom. • Why might they say that? (for students who are struggling, to help them understand correct answers) • How can you help them out? (for students who are on-target, to help students who are struggling) • What can you add to what they’re saying? (for incomplete answers) • Do you think their answer is reasonable? • What can you add to help them? (for incorrect answers) • How can you repeat what they said using your own words? (to help students consider the reasoning of others) • Can you reread the problem out loud? (when a student is disengaged, disruptive, or both) with Decimals and Fractions Within this lesson: • Students may not align place values correctly. • Students may forget to add the whole numbers because they do not include the whole number parts of the mixed numbers when they write equivalent fractions with like denominators. In other lessons with decimals and fractions: • Students may round decimals to the wrong place value. • Students may place the decimal point incorrectly in the product or quotient. • Students may multiply only the denominator of a fraction to find an equivalent fraction. • Students may multiply the whole numbers and then multiply the fractions. For further information and tips on helping students understand and correct common errors, see individual lessons. Launch Activity • Decimals and Fractions 157B

Launch Activity 2 Launch Activity Decimals and Fractions River of Grass Everglades National Park is located on the southern tip of Florida. It is the largest subtropical wilderness in the United States and covers 7,800 square miles with nine distinct ecosystems. The Everglades is really a slow-moving river. It is called the River of Grass because the sedge grass growing in the swamps looks like a rippling field of grass. Over 360 types of birds and 50 types of reptiles live in the Everglades, including the American alligator and the American crocodile. One way to see the Everglades is by airboat. Airboats glide on top of the grass, and you can see the different wonders of this swampy grassland. What would you like to see on the River of Grass? More About the Everglades • There are 39 endangered or threatened species in the Everglades, including the Florida panther and the West Indian manatee. • American crocodiles live in the salty waters of the Everglades. Alligators have U-shaped snouts. Crocodiles have V-shaped snouts and look like they are smiling. • Nearly 8 million people rely on the Everglades for drinking water. Three Reads First, read to understand the situation. Next, read to understand the math. Then, read to ask what mathematical questions could be asked about the problem. Tavi takes an airboat tour near the Everglades. The airboat captain stops the boat at different scenic points. The airboat travels 1.2 miles, 1—1 2 miles, 2.1 miles, and then 2—1 5 miles back to the starting point of the tour. © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©ocudrone/Adobe Stock, (b) ©LarsSchmidtEisenlohr/Adobe Stock Launch Activity • Decimals and Fractions 157 gg CorrectionKey=NL-A 5_mnlese694762_li02.indd 157 5/26/2022 1:25:23 PM Launch Activity 2 Launch Activity Decimals and Fractions Introducing Decimals and Fractions This Launch Activity lesson challenges students to solve a problem using strategies that build upon their knowledge of operations with fractions and decimals. Students can use multiple representations to determine their solution. For example, they may use standard algorithms, drawings, or models. Engage Students Begin by discussing the opening topic. Invite students to participate by sharing what they know about the Everglades or other topics that relate to the lesson, such as boat rides or other types of tours that can be taken. Students show an increased aptitude for learning if they are actively engaged in some part of the subject matter. Questions might include: • Have you ever visited the Everglades or another national park? • How did you tour or travel in the park? • Have you ever been on an airboat? Have students work in mixed-ability groups. Give each student a task that they can do well. For instance, in groups of learners with varying abilities, assign each student a specific task, such as leading the group discussion, recording or drawing the work, presenting (but not explaining) the solution, and explaining the models and methods used by the group to solve the problem. First Read The teacher reads the situation aloud. The students listen to understand the situation. • What is the situation about? • Can you describe the situation using your own words? Second Read The students read the situation as a class or with partners. The students read to understand the math. • What quantities are used in the situation? • What are the connections between the quantities? Third Read Each student reads the situation on their own. The student reads to think about possible math problems. • What mathematical question could you ask about the situation? • Can this question be answered using the information given? Three Reads Language Routine 157 Go Math! Grade 5

for the Interactive lesson Go Online For the interactive lesson Go Online Read the final question. Make a plan to solve the problem. Tavi takes an airboat tour near the Everglades. The airboat captain stops the boat at different scenic points. The airboat travels 1.2 miles, 1—1 2 miles, 2.1 miles, and then 2—1 5 miles back to the starting point of the tour. What is the total distance Tavi travels by airboat? Write, model, or draw to solve the problem. Discuss with a partner or in a group. How did you find the total distance of the airboat ride? Is there another way to solve the problem? Compare how you solved the problem with the way other students in your class solved the problem. Math Talk 158 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company • Image Credit: ©Martina/Adobe Stock See possible answers in the margin. Students’ modeling will vary. See the Teacher Edition for more in-depth explanations. DO NOT EDITChanges must be made through File info CorrectionKey=NL-A 5_mnlese694762_li02.indd 158 5/26/2022 1:25:23 PM Prompts for Productive Perseverance For Launch Activity lessons, the exploration of math concepts is more critical than finding a solution. Students should be encouraged to think about new math ideas in an atmosphere that is conducive to learning, with minimal pressure. They learn to solve the problem in different ways and are able to choose the method that works well for them. What if students can’t start working or can’t enter into the conversation for this lesson? Use one or more of these opening prompts: • What information do you know about the problem? • Can you draw a picture that represents what you know? • What numbers are in the problem? • What is given in the problem that might help you answer the question? How can I help students who are frustrated? Ask these leading questions: • Think about a starting point. How can you enter into this problem? • What information do you have? • What are you working on? What have you done so far? • What comes next? What are you solving for? • What information do you need to get unstuck? Talk to your partner (or group). To increase students’ understanding of their own thinking, ask: • How can you convert or change the fraction into a decimal? ANSWERS Main problem: The students should arrive at solution of 7 miles. The student may have first combined the numbers that were decimals and found 3.3 miles. They then may have combined the fractions for a value of 3 __7 10 or 3.7. They then combined 3.3 and 3.7 to get 7. Students may have drawn models or other representations. Math Talk: Students may have drawn models or other representations. Launch Activity • Decimals and Fractions 158

TM and Version 2.0 Differentiated Centers Kit Grab CHAPTER 5 Chapter at a Glance Add and Subtract Decimals LESSON 5.1 • 1 Day LESSON 5.2 • 1 Day LESSON 5.3 • 1 Day Lesson at a Glance Decimal Addition . . . 161A Decimal Subtraction . . . . . . . . 167A Add Decimals . . . . . . 173A I Can I can use base-ten blocks to model decimal addition. I can use base-ten blocks to model decimal subtraction. I can solve real-world decimal problems using addition. Learning Goal Model decimal addition using base-ten blocks. Model decimal subtraction using base-ten blocks. Solve real-world decimal problems using addition. Vocabulary Multilingual Support Strategy: Understand Context Strategy: Scaffold Language Strategy: Model Concepts Practice and Fluency LESSON 5.1 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* LESSON 5.2 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* LESSON 5.3 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* MTSS RtI Intervention and Enrichment ■ Waggle ◆ ■ Reteach 5.1 ◆ ■ Tier 2 Intervention Skill S63 ◆ ■ Tier 3 Intervention Skill E63 ◆ ■ Enrich 5.1 ■ Waggle ◆ ■ Reteach 5.2 ◆ ■ Tier 2 Intervention Skill S65 ◆ ■ Tier 3 Intervention Skill E65 ◆ ■ Enrich 5.2 ■ Waggle ◆ ■ Reteach 5.3 ◆ ■ Tier 2 Intervention Skill S64 ◆ ■ Tier 3 Intervention Skill E64 ◆ ■ Enrich 5.3 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 159A Go Math! Grade 5 ICNt

Chapter Pacing Chart Introduction Instruction Assessment Total 1 day 7 days 2 days 10 days LESSON 5.4 • 1 Day LESSON 5.5 • 1 Day LESSON 5.6 • 1 Day Lesson at a Glance Subtract Decimals . . 179A Solve a Decimal Sequence . . . . . . . . . 185A Add and Subtract Decimals Through Thousandths . . . . . . . 191A I Can I can solve real-world decimal problems using subtraction. I can use addition or subtraction to describe a pattern or create a sequence with decimals. I can add and subtract multi-digit numbers with decimals to the thousandths. Learning Goal Solve real-world decimal problems using subtraction. Identify, describe, and create numeric patterns with decimals. Add and subtract multi-digit numbers with decimals to the thousandths. Vocabulary sequence, term inverse operations Multilingual Support Strategy: Creative Grouping Strategy: Cooperative Grouping Strategy: Describe Practice and Fluency LESSON 5.4 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* LESSON 5.5 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* LESSON 5.6 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* MTSS RtI Intervention and Enrichment ■ Waggle ◆ ■ Reteach 5.4 ◆ ■ Tier 2 Intervention Skill S66 ◆ ■ Tier 3 Intervention Skill E66 ◆ ■ Enrich 5.4 ■ Waggle ◆ ■ Reteach 5.5 ◆ ■ Tier 2 Intervention Skill S86 ◆ ■ Tier 3 Intervention Skill E86 ◆ ■ Enrich 5.5 ■ Waggle ◆ ■ Reteach 5.6 ◆ ■ Tier 2 Intervention Skill S64/S66 ◆ ■ Tier 3 Intervention Skill E64/E66 ◆ ■ Enrich 5.6 *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 5 159B ICNt

CHAPTER 5 Chapter at a Glance Add and Subtract Decimals LESSON 5.7 • 1 Day Lesson at a Glance Add and Subtract Money . . . . . . . . . . . . 197A I Can I can solve multi-step real-world problems involving addition and subtraction of money using decimal notation. Learning Goal Solve problems using the strategy make a table. Vocabulary Multilingual Support Strategy: Model Concepts Practice and Fluency LESSON 5.7 ◆ ■ Practice and Homework ■ ■ Waggle ◆ ■ Achieving Facts Fluency* MTSS RtI Intervention and Enrichment ■ Waggle ◆ ■ Reteach 5.7 ◆ ■ Tier 2 Intervention Skill S64/S66 ◆ ■ Tier 3 Intervention Skill E64/E66 ◆ ■ Tabletop Flipchart ◆ ■ Enrich 5.7 ◆ Print/Printable Resource ■ Interactive Resource 159C Go Math! Grade 5 ICNt

Teacher Notes Chapter 5 159D ICNt

0.3 = ? is 0.7, which is given by 68% of sixth graders and 51% of fifth and seventh graders. … [T]he errors show that many students have learned rules for manipulating symbols without understanding what those symbols mean or why the rules work.” (NRC, 2001, p. 234) For more professional learning, go online to Teacher’s Corner. 159E Go Math! Grade 5

TM and Version 2.0 Differentiated Centers Kit Grab Chapter 5 159F 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 Lesson 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 5 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. 159G Go Math! Grade 5

2.50 = 14.25 0 0 0 * For more information on WIDA Standards, visit their website at: https://wida.wisc.edu/. Chapter 5 159H

26 ones = _ __7 10 0.06 ___ 39100 0.4 ___ 20 100 or __210 0.53 43 64 50 55 57 46 5,000 4,000 400 1,400 10 7 2 5 5,556 Sample answers shown. gg CorrectionKey=NL-A 5_mnlese694762_c05co.indd 159 5/26/2022 1:26:17 PM ICNt

. 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 Chapter 5 160 Vocabulary Builder Have students complete the activities on this page by working alone or with partners. Visualize It A tree map helps show how words are related. This tree map starts with the main idea, pattern, at the top. Then branches down to two words that need to be filled in that connect patterns with numbers. At the bottom are add and subtract, two operations that are used to find rules for number patterns. By completing this tree map, it will demonstrate how these words are related to each other. Understand Vocabulary Introduce the new words for the chapter and have students fill in the blanks to each sentence that best describe the VOCABULARY WORD. Students can enhance their understanding of key chapter vocabulary through the use of a vocabulary chart. Have students complete a chart describing and illustrating the chapter vocabulary. You can use this chart to reinforce knowledge and reading across the content area. 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 Vocabulary Builder Go Online For more help Visualize It Use the ✓ words to complete the tree map. Pattern sequence term add subtract Connect to Vocabulary Review Words hundredth pattern tenth thousandth Preview Words inverse operation ✓ sequence ✓ term Understand Vocabulary Read the description. Which word do you think is described? 1. The place value of the second digit to the right of the decimal point 2. An ordered set of numbers ___ 3. The place value of the digit immediately to the right of the decimal point 4. The place value of the third digit to the right of the decimal point 6. Each of the numbers in a sequence ___ The place value of the digit immediately to the right of the decimal point 160 Go Math! Grade 5 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (br) ©HMH hundredth tenth sequence thousandth term gg CorrectionKey=NL-A 5_mnlese694762_c05co.indd 160 5/26/2022 1:26:19 PM ICNt

161A Go Math! Grade 5 LESSON 5.1 Lesson at a Glance Decimal Addition 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 ● Model with mathematics. ● Construct arguments and critique reasoning of others. I Can Objective I can use base-ten blocks to model decimal addition. Learning Goal Model decimal addition using base-ten blocks. Language Objective Students explain, using a response frame, You use base-ten blocks to model decimal addition by _____________________. MATERIALS • MathBoard • base-ten blocks ACROSS THE GRADES Before Grade 4 After Compose and decompose four-digit numbers in multiple ways using thousands, hundreds, tens and ones. Demonstrate each composition or decomposition using objects, drawings and expressions or equations. Explore the addition and subtraction of multi-digit numbers with decimals to the hundredths. Add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency. ABOUT THE MATH • In this lesson, the base-ten blocks will be used to model decimal place values. As shown, we will use flats to model ones, longs to model tenths, and small cubes to model hundredths. For example, the model at the right represents 1.25, a decimal number in hundredths. Ones Tenths Hundredths For more professional learning, go online to Teacher’s Corner.

27 Have students explain and demonstrate the regrouping that is needed to complete the addition problem. 1 Engage with the Interactive Student Edition I Can Objective I can use base-ten blocks to model decimal addition. Making Connections Ask students to tell what they know about decimals to hundredths. • In 4.93, what is the place value of each digit? 4 is in the ones place, 9 is in the tenths place, and 3 is in the hundredths place. • How could you write the value of each digit in 4.93 as a separate number? 4, 0.9, 0.03 • If we use base-ten flats to represent ones, longs to represent tenths, and cubes to represent hundredths, how could we model the number 4.93? Use 4 flats, 9 longs, and 3 cubes. Learning Activity Tanya, Maya, and Kelsey want to buy a hat for their friend. Tanya has $3.23, Maya has $4.11, and Kelsey has $5.19. How much money do the three girls have together? What is the problem the students are trying to solve? Ask the following questions. • What is the important information in the problem? Tanya has $3.23, Maya has $4.11, and Kelsey has $5.19. • How could you use a model to help you solve the problem? I can use flats to model dollars, and longs and small cubes to model cents. • How is this problem similar to other problems you have solved? How is it different? It is similar to other problems I have solved since it involves finding a total or sum; It is different since it involves adding decimals.

0.5 = 1.0, adding together two decimals greater than 0.5 will give you a sum greater than 1.0. 4 hundredths = 11 hundredths, which is greater 1 regrouped tenth = 6 tenths. than 9 hundredths. 10 hundredths for 1 tenth and then adding the regrouped tenth to the combined tenths. CorrectionKey=NL-A 5_mnlese694762_c05l01.indd 161 7/2/2022 1:54:39 PM

1.85 = __ Math Talk Construct arguments and critique reasoning of others. MP Explain how you know where to write the decimal point in the sum. yes 5.3 Math Talk: Possible explanation: I know that the decimal point is placed between the ones and tenths places. 3.22 CorrectionKey=NL-A CorrectionKey=NL-A 5_mnlese694762_c05l01.indd 162 5/26/2022 1:27:58 PM

0.19 = 0.61 Possible answer: I used a model. I added the first 2 addends and then added the third addend to the sum of the first two. 0.34 0.54 0.98 0.80 0.91 0.36 0.66 21 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c05e01.indd 21 13/05/22 10:34 AM

2.73 = 4.58 Does Jim’s work make sense? Explain your reasoning. 8. MP Explain how you would help Robyn understand that regrouping is important when adding decimals. 9. Write a decimal addition problem that requires regrouping the hundredths. Explain how you know you will need to regroup. Possible answer: 0.37 ∙ 0.48 ∙ 0.85; Possible explanation: The sum of the hundredths is greater than 9. Possible explanation: I would explain that regrouping is important because place value is based on groups of 10. So, when you have 10 you regroup. No, Robyn’s work does not make sense. Possible explanation: She didn’t regroup 10 tenths as 1 one, so she wrote 158 after the decimal point. Yes. Jim’s work makes sense. Possible explanation: He regrouped 10 tenths as 1 one and then added it to the other whole numbers. CorrectionKey=NL-A 5_mnlese694762_c05l01.indd 164 5/26/2022 1:28:00 PM

0.28 = _ Problem Solving World Real 7. Draco bought 0.6 pound of bananas and 0.9 pound of grapes at the farmers’ market. What is the total weight of the fruit? 8. Alma biked 2.65 miles in the morning and 3.19 miles in the afternoon. What total distance did she bike? 9. Write Math Explain why drawing a quick picture is helpful when adding decimals. 1.5 pounds 5.84 miles 0.51 0.66 1.5 0.79 Check students’ drawings. 0.99 Check students’ explanations. CorrectionKey=NL-A 5_mnlese694762_c05p01.indd 165 5/26/2022 1:26:53 PM

Chapter 5 • Lesson 1 166 Continue to practice concepts and skills with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. © Houghton Mifflin Harcourt Publishing Company 166 Go Math! Grade 5 Lesson Check 10. What is the sum of 2.5 and 1.9? 11. Keisha walked 0.65 hour in the morning and 0.31 hour in the evening. How many hours did she walk altogether? Spiral Review 12. Jodi walks 35 minutes a day. If she walks for 240 days, how many minutes altogether does Jodi walk? 13. The Speeders soccer team charged $6 to wash each car at a fundraiser car wash. The team collected a total of $672 by the end of the day. How many cars did the team wash? 14. Celesto records the number of visitors to the snake exhibit each day for 6 days. His data are shown in the table. If admission is $7 per person, how much money did the snake exhibit make over the 6 days? Visitors to the Snake Exhibit 30 25 44 12 25 32 15. Write an inequality to compare 4_ 6 and 12__16. 8,400 minutes $1,176 4.4 112 cars _4 6 < __1216 0.96 hour CorrectionKey=NL-A 5_mnlese694762_c05p01.indd 166 5/26/2022 1:26:54 PM

167A Go Math! Grade 5 LESSON 5.2 Lesson at a Glance Decimal Subtraction 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 ● Use appropriate tools strategically. ● Construct arguments and critique reasoning of others. ● Model with mathematics. I Can Objective I can use base-ten blocks to model decimal subtraction. Learning Goal Model decimal subtraction using base-ten blocks. Language Objective Students write, I have learned that place value helps you subtract decimals by _______. MATERIALS • MathBoard • base-ten blocks ACROSS THE GRADES Before Grade 4 After Compose and decompose four-digit numbers in multiple ways using thousands, hundreds, tens and ones. Demonstrate each composition or decomposition using objects, drawings and expressions or equations. Explore the addition and subtraction of multi-digit numbers with decimals to the hundredths. Add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency. ABOUT THE MATH Teaching for Depth Frequently throughout this lesson and chapter, remind students that when you subtract decimal numbers, you regroup the same way you regroup whole numbers. For example, if there are not enough tens to subtract, you regroup 1 hundred as 10 tens. In the same way, if there are not enough hundredths to subtract, you regroup 1 tenth as 10 hundredths. In other words, for both decimal and whole numbers, you regroup 1 of the greater unit as 10 of the lesser unit. Throughout our base-ten number system, 1 of a larger unit is equivalent to 10 of the next smaller unit, and this equivalent relationship forms the foundation of regrouping. For more professional learning, go online to Teacher’s Corner.

(9 ÷ 9) Distributive Property Vocabulary • Interactive Student Edition • Multilingual Glossary Fluency Builder Skills Practice Have students find the following differences. 1. 84 − 56 28 2. 282 − 147 135 3. 56 − 32 24 4. 62 − 18 44 5. 11 − 4 7 6. 264 − 148 116 7. 341 − 174 167 8. 84 − 57 27 9. 93 − 38 55 10. 271 − 134 137 11. 405 − 161 244 12. 137 − 52 85 FOCUSING ON THE WHOLE STUDENT Access Prior Knowledge On the board, write the subtraction problem shown below. 500 −__ 249 Have students explain and demonstrate the regroupings that must occur to complete the subtraction. 1 Engage with the Interactive Student Edition I Can Objective I can use base-ten blocks to model decimal subtraction. Making Connections Ask students to tell what they know about subtracting three-digit whole numbers. • How could you use base-ten blocks to subtract 327 – 153? Model each number using flats, longs, and cubes, subtract starting from the place value position on the right, and regroup if necessary. • Why must we regroup to subtract the tens? How can we regroup? There are only 2 tens in the first number and we need to subtract 5 tens. We need to regroup 1 hundred as 10 tens in the first number to subtract. Learning Activity What is the problem the students are trying to solve? Mei has $9.78. She wants to buy a souvenir that costs $6.51. How much money will she have left after buying the souvenir? Ask the following questions. • What is the important information in this problem? How do you know? How much money Mei has and how much the souvenir costs; The question is how much money she has left after buying the souvenir, so you need to know how much she started with and how much she will spend. • How could thinking about place value help you solve this problem? By thinking about place value, I can align the digits to make sure I subtract correctly. • What is the first step toward solving this problem? Align the digits and subtract the hundredths.

167 Go Math! Grade 5 LESSON 5.2 2 Explore Investigate Materials base-ten blocks After students complete the activity, ask them to formulate generalizations that describe when and how to regroup during decimal subtraction. Possible answer: I need to regroup whenever the value of the digit being subtracted is greater than the value of the digit I am subtracting from. Regroup 1 tenth as 10 hundredths and 1 one as 10 tenths. Use appropriate tools strategically. • What is another model you could use to show subtraction of 0.84 ∙ 0.56? Explain. Possible answer: I could shade squares of a hundred grid; I would shade 84 squares to represent 84 hundredths. Then I would cross out 56 squares to represent subtracting 56 hundredths. Draw Conclusions Construct arguments and critique reasoning of others. Problem 2 There are different ways to conclude that the difference of the numbers will be less than 1. Invite a variety of explanations. MP MP STRATEGY: Scaffold Language Sentence frames scaffold language to develop students’ skills to discuss mathematics. • Model how students can regroup by trading in a flat (1) for ten longs (0.1). = • To regroup, I will need to trade in ___ flat for ___ longs. • Have pairs discuss how to find 2.35 − 1.42 and 1.39 − 0.55 using the sentence frame to trade in base-ten blocks. Multilingual Support © Houghton Mifflin Harcourt Publishing Company • Image Credits (r) ©Houghton Mifflin Harcourt Chapter 5 • Lesson 2 167 © Houghton Mifflin Harcourt Publishing Company CHAPTER 5 Name Lesson 2 Decimal Subtraction I Can use base-ten blocks to model decimal subtraction. 0.1 one tenth 1 one 0.01 one hundredth Investigate Materials ■ base-ten blocks A. Use base-ten blocks to find 0.84 − 0.56. Model 0.84. B. Subtract 0.56. Start by removing 6 hundredths. Do you need to regroup to subtract? Explain. C. Subtract the tenths. Remove 5 tenths. D. Record the difference. 0.84 − 0.56 = __ Draw Conclusions 1. What if you remove the tenths first and then the hundredths? Explain how you would regroup. 2. MP If two decimals are both less than 1.0, what do you know about the difference between them? Explain. Yes.; Possible explanation: I need to regroup 1 tenth as 10 hundredths to subtract. 0.28 Possible explanation: I would still regroup by exchanging 1 tenth for 10 hundredths. Possible explanation: Since 0.99 – 0.01 = 0.98 and is the greatest possible difference, I know that if both decimals are less than 1.0, the difference will also be less than 1.0. CorrectionKey=NL-A 5_mnlese694762_c05l02.indd 167 5/26/2022 1:29:12 PM

Chapter 5 • Lesson 2 168 Make Connections Step 1 Ask students to describe the regrouping needed to subtract the hundredths. One tenth was regrouped as 10 hundredths. Step 2 Ask students to explain why there is no need to regroup to subtract the tenths. There are enough tenths to subtract. Step 3 Ask students to tell what place value each part of their picture represents. The squares represents ones, the sticks represent tenths, and the circles represent hundredths. Construct arguments and critique reasoning of others. Math Talk Use Math Talk to focus on students’ understanding of regrouping in decimal subtraction. Make sure students understand that they have to regroup because there aren’t enough hundredths to subtract 7 hundredths from 2 hundredths. After the steps of the activity have been completed, challenge students to discuss, and then state, a general rule that describes where to place the decimal point in any answer that is found by subtracting two decimal numbers. MP Common Errors Common Errors Error When finding the difference, students place the decimal point incorrectly. Example After Step 3, students write 13.5 or 0.135 for the answer. Springboard to Learning A quick picture for the subtraction involves drawing a square, sticks, and circles. Remind students to write a decimal point after drawing the square and before drawing the sticks and circles. Ready for More Visual Partners • Have one student in each pair write a decimal number (less than 5) to the hundredths place, while the other student writes a decimal number (less than 5) to the tenths place. • Have partners find the sums of their decimals and then find the difference of their decimals using quick pictures. • Have partners subtract their sum from 10.55 and their difference from 5.5. 1.23 2.2 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (tr) ©Photodisc/Getty Images© Houghton Mifflin Harcourt Publishing Company 168 Go Math! Grade 5 Make Connections You can use quick pictures to subtract decimals that need to be regrouped. STEP 1 • Use a quick picture to model 2.82 − 1.47. • Subtract the hundredths. • Are there enough hundredths to remove? _ If there are not enough hundredths, regroup. STEP 2 • Subtract the tenths. • Are there enough tenths to remove? _ If there are not enough tenths, regroup. • Subtract the ones. STEP 3 Draw a quick picture of your answer. Then record the answer. 2.82 − 1.47 = __ Math Talk Construct arguments and critique reasoning of others. MP Explain why you have to regroup in Step 1. no Math Talk: Possible explanation: I had to regroup in Step 1 because I did not have enough hundredths to remove 7 hundredths. 1.35 yes CorrectionKey=NL-A CorrectionKey=NL-A 5_mnlese694762_c05l02.indd 168 5/26/2022 1:29:13 PM

169 Go Math! Grade 5 3 Explain Share and Show Math Board The first problem connects 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. Quick Check If MTSS RtI Quick Check If MTSS RtI Then a student misses the checked exercises Differentiate Instruction with • Reteach 5.2 • Waggle 4 Elaborate On Your Own Model with mathematics. Math Talk Use Math Talk to focus on students’ understanding of using quick pictures to model decimal subtraction. Make sure the explanations include the idea that you have to regroup 1 tenth as 10 hundredths when there aren’t enough hundredths to subtract. Higher-Order Thinking Write 4.15 − 2.79 on the board. How will you know the number of regroupings that will be needed to find this answer? Possible answer: Since 9 hundredths is greater than 5 hundredths and 7 tenths is greater than 1 tenth, two regroupings will be needed. MP Meeting Individual Needs Reteach 5.2 Enrich 5.2 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (tr) ©Photodisc/Getty Images Chapter 5 • Lesson 2 169 © Houghton Mifflin Harcourt Publishing Company icture to model 2.82 − 1.47. hundredths. ough hundredths to remove? _ ot enough hundredths, regroup. Name Math Share and Show Board Complete the quick picture to find the difference. 1. 0.62 − 0.18 = __ Subtract. Draw a quick picture. 2. 3.41 − 1.74 = __ 3. 0.84 − 0.57 = __ 4. 4.05 − 1.61 = __ 5. 1.37 − 0.52 = __ On Your Own 6. Write a decimal subtraction equation that requires regrouping from the tenths. Explain how you know you will need to regroup. Math Talk MP Model with mathematics. Explain how you can use a quick picture to find 0.81 − 0.46. Math Talk: Possible explanation: I can draw 0.81 using 8 lines for tenths and 1 small circle for hundredths. I would regroup 1 tenth as 10 hundredths. Then, I would subtract 6 hundredths from 11 hundredths. Last, I would subtract 4 tenths from the remaining 7 tenths. My answer is 0.35. 2.44 0.85 1.67 0.27 For 2–7, check students’ drawings. 0.44 Possible answer: 2.37 – 1.49 = 0.88; Possible explanation: I know I will need to regroup 1 tenth as 10 hundredths because the number of hundredths I am subtracting is greater than the number of hundredths I am subtracting from. CorrectionKey=NL-A 5_mnlese694762_c05l02.indd 169 6/16/2022 12:26:03 PM Name Decimal Subtraction You can use decimal models to help you subtract decimals. Subtract. 1.85 − 0.65 Step 1 Shade squares to represent 1.85. Remember: By circling and crossing out shaded squares, you can see how many squares are taken away, or subtracted. Step 2 Circle and cross out 65 of the shaded squares to represent subtracting 0.65. Step 3 Count the shaded squares that are not crossed out. Altogether, 1 whole square and 20 one-hundredths squares, or 1.20 wholes, are NOT crossed out. So, 1.85 − 0.65 = 1.20. Subtract. Use decimal models. Draw a picture to show your work. 1 1.4 − 0.61 2 1.6 − 1.08 3 0.84 − 0.17 4 1.39 − 1.14 LESSON 5.2 Reteach Check students’ drawings. 0.25 0.52 0.67 0.79 22 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c05r02.indd 22 13/05/22 10:43 AM MTSS RtI1 Name Model Building Subtract 0.25 from each decimal represented by the models below. Then write the difference on the line provided. 1 Stretch Your Thinking Without subtracting, how can you tell which decimal modeled above will have the least difference when you subtract 0.25 from it? 2 Write a decimal subtraction sentence whose difference is greater than the greatest difference you found above. Shade the model to show the difference. LESSON 5.2 Enrich Possible answer: 0.99 − 0.25 = 0.74 Possible answer: the model with the least number of shaded squares, 0.27, will have the least difference. Check students’ work. 0.02 0.63 0.14 0.36 0.68 0.20 22 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c05e02.indd 22 13/05/22 10:39 AM

TM and Version 2.0 Differentiated Centers Kit Grab Chapter 5 • Lesson 2 170 Problem 7 Students must understand what the quick picture represents. • What decimal number does the black portion of the quick picture represent? Explain your answer. 3.67; Each square represents 1 one, each stick represents 1 tenth, and each circle represents 1 hundredth. • What does the portion marked with gray ovals and Xs represent? 2.42 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 8 This problem assesses a student’s ability to subtract decimals and explain their method through base-ten blocks and quick pictures. If students get the right answer but cannot explain how, they may not understand the value of each digit. Review place value and regrouping with students. MP 5 Evaluate Formative Assessment I Can Have students write to explain how to demonstrate the skill for the I Can statement. I can use base-ten blocks to model decimal subtraction by . . . modeling the first number using flats, longs, and small cubes. Then model the number being subtracted by removing small cubes, longs, and then flats that represent the number. Regroup as needed. Exit Ticket Describe a problem involving decimals that you would use a quick picture to solve. Then solve the problem. 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 © Houghton Mifflin Harcourt Publishing Company 170 Go Math! Grade 5 7. Antonio left his MathBoard on his desk during lunch. The quick picture below shows the problem he was working on when he left. Spot on the Write a word problem that can be solved using the quick picture above. Pose a problem. Solve your problem. • MP Describe how you can change the problem by changing the quick picture. 8. The price of a box of markers at a retail store is $4.65. The price of a box of markers at the school bookstore is $3.90. How much more do the markers cost at the retail store? Explain how you can use a quick picture to solve the problem. Possible problem: Shana had 3.67 decimeters of string. She cut off 2.42 decimeters. How much string did Shana have left? Possible description: I can change the quick picture by subtracting 1.73. The picture will change because I will need to regroup 1 one as 10 tenths before subtracting. The problem will change to Shana cutting off 1.73 decimeters of string. 3.67 ∙ 1.73 ∙ 1.94 $0.75; Possible explanation: I can draw 4.65 using 4 squares for ones, 6 lines for tenths, and 5 circles for hundredths. I would subtract 0 hundredths from 5 hundredths. I would regroup 1 one as 10 tenths. Then I would subtract 9 tenths from 16 tenths. Possible solution: 3.67 ∙ 2.42 ∙ 1.25 decimeters CorrectionKey=NL-A 5_mnlese694762_c05l02.indd 170 5/26/2022 1:29:15 PM

Practice and Homework Decimal Subtraction 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. 171 Go Math! Grade 5 Chapter 5 • Lesson 2 171 © Houghton Mifflin Harcourt Publishing Company LESSON 5.2 Practice and Homework Name Decimal Subtraction Subtract. Draw a quick picture. 1. 0.7 − 0.2 = _ 0.5 2. 0.45 − 0.24 = _ 3. 0.92 − 0.51 = _ 4. 4.1 − 2.7 = _ 5. 3.12− 2.52 = 6. 3.6 − 1.8 = _ Problem Solving World Real 7. Yelina made a training plan to run 5.6 miles per day. So far, she has run 3.1 miles today. How much farther does she have to run to meet her goal for today? 8. Wen cut a 2.3-foot length of pipe from a pipe that was 4.1 feet long. How long is the remaining piece of pipe? 9. Write Math Describe a problem involving decimals that you would use a quick picture to solve. Then solve the problem. 2.5 miles 1.8 feet 0.21 0.41 Check students’ drawings. 1.4 0.60, or 0.6 1.8 Check students’ answers. CorrectionKey=NL-A 5_mnlese694762_c05p02.indd 171 5/28/2022 10:01:27 AM

_× 48 15. In the past two weeks, Yu earned $513 at her part-time job. She worked a total of 54 hours. About how much did Sue earn per hour? 1.62 miles 700,000 0.7 million About $10 700 48 6 4 CorrectionKey=NL-A 5_mnlese694762_c05p02.indd 172 5/28/2022 10:01:28 AM

27.4, you would line up the ones and tens places, and also now the tenths place. For more professional learning, go online to Teacher’s Corner.

84 496 FOCUSING ON THE WHOLE STUDENT Access Prior Knowledge Choose one or both of the following activities. • Ask the students why it might be important to use decimals to hundredths when weighing something. Where have they seen items weighed or measured to the tenths place? The hundredths place? • Have students work in pairs to create a story that involves going to a store and buying two items. The story should include the name and exact price of each item. 1 Engage with the Interactive Student Edition I Can Objective I can solve real-world decimal problems using addition. Making Connections Lead the students in a conversation about using different units to weigh objects. • Have you ever seen really small or really big rocks before? Answers will vary. • How do the rocks compare with your pencil? Your desk? An apple? A shoe? Possible answers: The rock weighs more than my pencil or it weighs less than my pencil. Learning Activity Have students compare the weight 1 gram with the weight of a real-life object. Ask students what might have weights similar to different kinds of rocks. Then tell the students the following story. Dwayne is starting a rock collection. He weighs the first two rocks in his collection. The smaller rock weighs 9.24 grams and the larger rock weighs 25.57 grams. What is the combined weight of the two rocks? • What question are you asked to answer? What is the combined, or total, weight of the two rocks? • What are the weights of the larger rock and the smaller rock? 25.57 grams; 9.24 grams • Why do you think that grams are the units used to express the weight of little rocks? Possible answer: because these are small and a gram is a unit that is often used to measure small weights

__1.82 1 4.17 7 11 4 Possible explanation: I know that I need to regroup when I have more than 9 hundredths or 9 tenths. 4.17 4.17 CorrectionKey=NL-A 5_mnlese694762_c05l03.indd 173 5/26/2022 1:29:57 PM

1 3. 7 6 34.16 34 Yes; Possible explanation: because it is close to my estimate of 34 Possible estimates are given. 8 15 10 7.1 15.18 9.92 10 2 10.14 1.23 Math Talk: Possible explanation: If I don’t line up the place values correctly, I could add or subtract the wrong place values in the numbers. CorrectionKey=NL-A CorrectionKey=NL-A 5_mnlese694762_c05l03.indd 174 5/26/2022 1:29:57 PM

23 © Houghton Mifflin Harcourt Publishing Company 49.78 49 40.66 12 41 1 3 23 11.86 1.54 2.73 23.50 or 23.5 Possible estimates are given. DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c05r03.indd 23 13/05/22 10:43 AM MTSS RtI1 LESSON 5.3 Enrich Name Sum Match-Up Find the sum of the decimals shown on each cube. Then match each sum to the square with the correct sum. 1 78.95 23.09 127.86 418.08 2 234.98 77.09 36.75 229.9 3 239.05 117.67 61.36 1,147.87 4 167.89 902.13 77.85 348.82 5 Tell how you found the sum in Exercise 2. 6 Stretch Your Thinking Tell how you can check your answer for Exercise 4. Possible answer: I can subtract 902.13 and 77.85 from the sum and see if the difference matches 167.89. 1,147.87 2 902.13 2 77.85 5 167.89 Possible answer: I found the sum of 77.09 and 36.75, or 113.84. Then I found the sum of 113.84 and 234.98, or 348.82. 418.08 1,147.87 229.9 348.82 23 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c05e03.indd 23 13/05/22 10:40 AM

TM and Version 2.0 Differentiated Centers Kit Grab Chapter 5 • Lesson 3 176 Problem Solving Applications Attend to precision. Problem 11 Work with a partner to write an addition problem for this real-world problem. MP 5 Evaluate Formative Assessment I Can Have students write an addition problem and then explain to a partner in their own words how to demonstrate the skill for the I Can statement. I can solve real-world decimal problems using addition by . . . aligning the place values of decimal addends, which helps me add hundredths to hundredths, tenths to tenths, ones to ones, and so on. Exit Ticket Explain how to write an addition problem for a real-world problem. 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 © Houghton Mifflin Harcourt Publishing Company 176 Go Math! Grade 5 Problem Solving · Applications Fill in the bubble completely to show your answer. 9. A king’s crown has a ruby that is 4.9 carats and a sapphire that is 5.32 carats. What is the total number of carats on the king’s crown? A 9.41 carats B 9.22 carats C 10.22 carats D 11.12 carats 10. Vern bought 1.75 pounds of apples and 2.4 pounds of oranges. How many pounds of apples and oranges did he buy in all? A 2.15 pounds B 4.15 pounds C 1.99 pounds D 3.75 pounds 11. Sean runs 2.62 miles. Lisa runs 3.02 miles. Shannon runs 2.78 miles. Serge runs 3.8 miles. Which two people run for a total of 5.4 miles? A Sean and Shannon C Lisa and Shannon B Lisa and Serge D Sean and Serge 12. When Lupe got a puppy, it weighed three and eighty-five hundredths pounds. After a month, it weighed ninety-five hundredths more than when she got it. How much did the puppy weigh at the end of the month? A 480 pounds C 4.80 pounds B 4.70 pounds D 3.70 pounds CorrectionKey=NL-A 5_mnlese694762_c05l03.indd 176 5/26/2022 1:29:58 PM

2.49 = _ 11. Find one-tenth more than the number. a. 5.74? _ b. 8.9? _ 12. Find one-hundredth more than the number. a. 4.28? _ b. 3.6? _ Problem Solving World Real 13. Monique’s dog weighs 10.6 pounds. Her cat weighs 8.4 pounds. What is the combined total weight of Monique’s pets? 14. Monique spent $8.49 on dog food and $7.99 on cat food. What is the total amount Monique spent on food for her pets? 6 Possible estimates are given. 12 12 12 12.07 12.24 10.76 5.84 4.29 6 6.79 9.0 3.61 11 19 pounds $16.48 15 9 8 10 8.56 9.98 gg CorrectionKey=NL-A 5_mnlese694762_c05p03.indd 177 5/26/2022 1:28:24 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 5 • Lesson 3 178 © Houghton Mifflin Harcourt Publishing Company 178 Go Math! Grade 5 Lesson Check Fill in the bubble completely to show your answer. 15. Ulises ran 3.75 miles around the track. After resting, Ulises ran an additional 2.9 miles. What is the total distance Ulises ran? A 3.94 miles B 6.65 miles C 4.04 miles D 5.65 miles 16. On the first day of school, Cassandra measured 1.37 meters tall. During the school year, Cassandra grew 0.06 meters. How tall was Cassandra at the end of the school year? A 1.33 meters B 1.31 meters C 1.43 meters D 1.42 meters 17. Rufus measured the growth of a plant for his science project. At the end of the first week, the plant was 9.54 centimeters tall. During the second week, the plant grew 2.68 centimeters. How tall was Rufus’s plant at the end of the second week? A 11.22 centimeters B 12.12 centimeters C 11.12 centimeters D 12.22 centimeters 18. The distance from Sabinian’s house to his uncle’s house is 12.58 miles. If Sabinian travels another 9.49 miles, he will reach his grandmother’s house. What is the distance from Sabinian’s house to his grandmother’s house? A 22.07 miles B 21.97 miles C 21.07 miles D 22.08 miles Spiral Review 19. Rolando worked for 2_ 4 hour before practice and 5_ 4 hour after practice. How many hours did Rolando work in all? 20. Write __5 16 as a sum of unit fractions. 7_ 4 or 1 3_ 4 hours __1 16 ∙ __116 ∙ __116 ∙ __116 ∙ __116 gg CorrectionKey=NL-A 5_mnlese694762_c05p03.indd 178 5/26/2022 1:28:24 PM

179A Go Math! Grade 5 LESSON 5.4 Lesson at a Glance Subtract Decimals 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 ● Model with mathematics. ● Attend to precision. ● Construct arguments and critique reasoning of others. ● Look for and make use of structure. I Can Objective I can solve real-world decimal problems using subtraction. Learning Goal Solve real-world decimal problems using subtraction. Language Objective Students write a subtraction problem and then explain to a partner in their own words how to use that problem to solve a real-world problem. MATERIALS • MathBoard • index cards • markers ACROSS THE GRADES Before Grade 4 After Compose and decompose four-digit numbers in multiple ways using thousands, hundreds, tens and ones. Demonstrate each composition or decomposition using objects, drawings and expressions or equations. Explore the addition and subtraction of multi-digit numbers with decimals to the hundredths. Add and subtract multi-digit numbers with decimals to the thousandths, including using a standard algorithm with procedural fluency. ABOUT THE MATH Teaching for Depth Frequently throughout this lesson and chapter, remind students that when you subtract decimal numbers, you regroup the same way you regroup whole numbers. For example, if there are not enough tens to subtract, you regroup 1 hundred as 10 tens. In the same way, if there are not enough hundredths to subtract, you regroup 1 tenth as 10 hundredths. In other words, for both decimal and whole numbers, you regroup 1 of the greater unit as 10 of the lesser unit. Throughout our base-ten number system, 1 of a larger unit is equivalent to 10 of the next smaller unit, and this equivalent relationship forms the foundation of regrouping. For more professional learning, go online to Teacher’s Corner.

39. 166 Vocabulary • Interactive Student Edition • Multilingual Glossary Fluency Builder Skills Practice Have students perform the following subtractions. 49 – 28 21 37 – 15 22 81 – 54 27 43 – 27 16 65 – 39 26 582 – 321 261 973 – 601 372 815 – 478 337 631 – 28 603 315 – 79 236 FOCUSING ON THE WHOLE STUDENT Access Prior Knowledge Choose one or more of the following activities. • Have students discuss why the number on a speed limit sign is taller than the letters. Ask them why letters or words are important to include on a traffic sign. • Have students work in pairs and write the decimals 8.5 and 4.25 in place-value charts and in expanded form. Ask them to identify the value of each digit in the two numbers and the relationship between the values of the digits in adjacent places in the chart, moving from left to right, and from right to left. Supporting All Learners Discuss with the students the fact that other countries use kilometers as a measurement of distance. Ask them how they would read the speed limit sign if they were in one of those countries. 35 kilometers per hour 1 Engage with the Interactive Student Edition I Can Objective I can solve real-world decimal problems using subtraction. Making Connections Invite students to tell you what they know about speed limits. • What is a speed limit? the maximum allowable speed of vehicles driving on a road • What does the abbreviation mph stand for? miles per hour Learning Activity Draw on the board a simple speed limit sign. Label the size of the words “Speed Limit” as 4.25 cm and the size of the number “35” as 8.5 cm. Write the question below it: “How much larger are the numbers than the letters on the sign?” Ask students what the number 35 on the traffic sign represents. the greatest speed can be 35 miles per hour Ask students why the number on a speed limit sign is larger than the words. because drivers need to see the number right away • What do you need to find? how much taller the number on the sign is than the letters • What does the number 8.5 in the problem represent? the height of the number on the speed limit sign • What does the number 4.25 in the problem represent? the height of the letters on the speed limit sign

179 Go Math! Grade 5 LESSON 5.4 2 Explore Unlock the Problem In the activity, have students note the alignment of the decimal points in the vertical subtraction. Discuss the quick pictures that students draw. • To complete this subtraction, why do you begin in the hundredths place? Subtraction begins in the least (or rightmost) place value of the numbers. • Do you have to regroup to subtract hundredths? Explain how you know. yes; Possible explanation: There aren’t enough hundredths to subtract 8 hundredths from 6 hundredths. • Describe the regrouping using place-value names. Three tenths 6 hundredths are regrouped as 2 tenths 16 hundredths Construct arguments and critique reasoning of others. Math Talk Use Math Talk to focus on students’ understanding of place value and regrouping. Extend the explanation by asking students to compare and contrast regrouping used during decimal subtraction to regrouping used during decimal addition. World Real MP STRATEGY: Creative Grouping Materials: index cards, markers • Group beginning and intermediate English Language Learners with advanced English Language Learners to help with language practice. • Have students write decimal numbers on index cards. • Have students choose two cards, write the numbers, and explain the steps to subtract the decimals. • Make sure students explain how 0.3 is equivalent to 0.30. 5.6 0.41 3.02 14.1 9.09 0.3 10.5 1.01 Multilingual Support © Houghton Mifflin Harcourt Publishing Company • Image Credits: ©HMH Chapter 5 • Lesson 4 179 CHAPTER 5 Name Lesson 4 Subtract Decimals I Can solve real-world decimal problems using subtraction. UNLOCK the Problem World Real Hannah has 3.36 kilograms of apples and 2.28 kilograms of oranges. Hannah estimates she has about 1 more kilogram of apples than oranges. How many more kilograms of apples than oranges does Hannah have? How can you use this estimate to decide if your answer is reasonable? Subtract. 3.36 − 2.28 • Subtract the hundredths first. If there are not enough hundredths, regroup 1 tenth as 10 hundredths. _ hundredths − 8 hundredths = 8 hundredths • Then subtract the tenths and ones. Regroup as needed. _tenths − 2 tenths = 0 tenths _ ones − 2 ones = 1 one • Record the difference for each place value. 3.36 __ − 2.28 • What operation will you use to solve the problem? • Circle Hannah’s estimate and check that your answer is reasonable. Draw a quick picture to check your work. So, Hannah has __ more kilograms of apples than oranges. Since __ is close to 1, the answer is reasonable. Math Talk Construct arguments and critique reasoning of others. MP Explain how you know when to regroup in a decimal subtraction problem. 216 1.08 subtraction 16 2 3 1.08 1.08 Math Talk: Possible explanation: I know that I need to regroup when I don’t have enough hundredths or tenths to subtract from. CorrectionKey=NL-A 5_mnlese694762_c05l04.indd 179 5/26/2022 1:30:33 PM

ighty-one hundredths 8. one and six hundredths subtracted from eight and thirty-two hundredths Write the unknown number for n. 9. 5.28 − 3.4 = n n = __ 10. n − 6.47 = 4.32 n = __ 11. 11.57 − n = 7.51 n = __ Find the difference. 12. 8.42 − 5.14 13. 16.46 − 13.87 14. 34.27 − 17.51 15. 15.83 − 11.45 16. 12.74 − 10.54 17. 48.21 − 13.65 Possible estimates are given. 4 2 2 3.65 2.59 1.78 0.27 5.16 6.13 2.09 7.26 1.88 10.79 4.06 3.28 2.59 16.76 4.38 2.2 or 2.20 34.56 CorrectionKey=NL-A CorrectionKey=NL-A 5_mnlese694762_c05l04.indd 180 5/26/2022 1:30:34 PM

8.1 24.1 1 13 CorrectionKey=NL-A 5_mnlese694762_c05l04.indd 181 5/26/2022 1:30:34 PM Name In the Box Decimals For 1–6, find the unknown numbers that make the subtraction equation true. 1 1 4 7 . 0 − 5 . 0 9 1 0 . 9 8 2 8 3 . 4 1 −1 1 9 . 7 4 3 . 6 4 3 9 4 2 . 9 9 − 5 3 . 6 5 8 8 . 4 4 6 4 . 1 0 −5 2 9 . 1 1 4 . 9 8 5 $ 1, 2 4 . 1 − $ 4 4 5 . 3 $ 5 7 . 2 2 6 $ 8 4 . 9 2 −$ 5 6 . 0 $ 7 8 . 8 5 7 Explain how to subtract decimals. 8 Stretch Your Thinking Tell how you can check your answer for Exercise 1. LESSON 5.4 Enrich Possible answer: line up the decimal points and place values. Then subtract. Regroup the numbers as needed. Place the decimal point. Possible answer: I can add 45.09 to the answer and check that the sum is 147.07. 101.98 1 45.09 5 147.07 5 7 6 9 2 6 3 7 7 8 9 0 5 9 3 1 7 4 24 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c05e04.indd 24 13/05/22 10:37 AM Name Subtract Decimals Subtract. 6.56 − 4.33 Step 1 Estimate the difference. 6.56 − 4.33 Estimate: 7 − 4 = 3 Step 2 Line up the place values for each number in a place-value chart. Then subtract. Step 3 Use your estimate to determine if your answer is reasonable. Think: 2.23 is close to the estimate, 3. The answer is reasonable. So, 6.56 − 4.33 = 2.23 . Estimate. Then find the difference. 1 Estimate: 1.97 − 0.79 2 Estimate: 4.42 − 1.26 3 Estimate: 10.25 − 8.25 Find the difference. Check your answer. 4 5.75 − 1.11 5 25.21 − 19.05 6 42.14 − 25.07 difference Ones Tenths Hundredths 6 5 6 4 3 3 2 2 3 − LESSON 5.4 Reteach Possible estimates are given. 6.16 17.07 1 3 2 4.64 1.18 3.16 2.00 or 2 24 © Houghton Mifflin Harcourt Publishing Company DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-A 5_mnlean1836904_c05r04.indd 24 13/05/22 10:41 AM MTSS RtI1

TM and Version 2.0 Differentiated Centers Kit Grab Chapter 5 • Lesson 4 182 4 Elaborate Problem Solving Applications Attend to precision. Problem 21 Work with a partner to write a subtraction problem for this real-world problem. MP 5 Evaluate Formative Assessment I Can Have students write a subtraction problem and then explain to a partner in their own words how to demonstrate the skill for the I Can statement. I can solve real-world decimal problems using subtraction by . . . aligning the place values. That helps me subtract hundredths from hundredths, tenths from tenths, ones from ones, and so on. Exit Ticket Explain how to write a subtraction problem for a real-world problem. 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 © Houghton Mifflin Harcourt Publishing Company • Image Credits: ©HMH 182 Go Math! Grade 5 Problem Solving · Applications Fill in the bubble completely to show your answer. 21. Adrian made a poster for his math project. The capital letters on his poster are 4.29 centimeters high. The lowercase letters are 1.97 centimeters high. How much taller are the capital letters than the lowercase letters? A 6.26 centimeters B 3.72 centimeters C 5.16 centimeters D 2.32 centimeters 22. Mace’s tomato plant was 9.6 centimeters tall when he planted it. It is 21.7 centimeters tall now. How much did the tomato plant grow? A 18.3 centimeters B 28.1 centimeters C 12.1 centimeters D 31.3 centimeters 23. Janus bought 2.07 pounds of potato salad. She ate 0.25 pound. Her brother ate 0.38 pound. How much potato salad was left? A 0.63 pound C 1.82 pounds B 2.70 pounds D 1.44 pounds 24. Allie is 158.7 centimeters tall. Her older brother is 3.55 centimeters taller than she is. Her younger brother is 9.53 centimeters shorter than her older brother. How tall is Allie’s younger brother? A 162.25 centimeters C 171.78 centimeters B 147.7 centimeters D 152.72 centimeters CorrectionKey=NL-A 5_mnlese694762_c05l04.indd 182 5/26/2022 1:30:36 PM

Practice and Homework Subtract Decimals 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. 183 Go Math! Grade 5 Chapter 5 • Lesson 4 183 © Houghton Mifflin Harcourt Publishing Company Possible estimates are given. LESSON 5.4 Practice and Homework Name Subtract Decimals Estimate. Then find the difference. 1. Estimate: _ 4.08 __ − 1.74 2.34 2. Estimate: _ 13.54 − __ 6.7 6.84 Find the difference. Check your answer. 3. 16.05 − __ 1.5 14.55 4. 21.4 −__ 16.97 4.43 Find the unknown number for n. 5. 7.3 – n = 1.9 n = _ 6. n – 8.12 = 11.52 n = _ Find the difference. 7. 14.36 – 12.65 8. 69.32 – 32.46 9. Find one-tenth less than the number. a. 6.83? _ b. 7? _ 10. Find one-hundredth less than the number. a. 5.57? _ b. 8.9? _ Problem Solving World Real 11. Hiemo compared the labels of two brands of peanut butter. Brand X has 16.2 grams of fat. Brand Y has 12.7 grams of fat. How much more fat does Brand X contain than Brand Y? 12. Franca ran 63.6 kilometers. Philip ran 8 kilometers less than Franca. How many kilometers did Philip run? 2 5.4 1.71 6.73 5.56 3.5 grams 55.6 kilometers 7 19.64 36.86 6.9 8.89 gg CorrectionKey=NL-A 5_mnlese694762_c05p04.indd 183 5/26/2022 1:30:28 PM

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