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Math Gr4 Ch15

M
madterrell

This document provides a summary of Chapter 15 from a mathematics textbook. The chapter covers adding and subtracting decimals through 6 lessons: 1) rounding decimals, 2) estimating decimal sums and differences, 3) using a problem-solving strategy of working backward, 4) adding decimals, 5) choosing a problem-solving strategy, and 6) subtracting decimals. Each lesson includes examples and practice problems to illustrate the concepts and build skills in adding and subtracting decimals.

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Chapter 15 Decimals: Addition and Subtraction Click the mouse or press the space bar to continue.
Decimals: Addition and Subtraction 15 Lesson 15-1 Round Decimals Lesson 15-2 Estimate Decimal Sums and Differences Lesson 15-3 Problem-Solving Strategy: Work Backward Lesson 15-4 Add Decimals Lesson 15-5 Problem-Solving Investigation: Choose a Strategy Lesson 15-6 Subtract Decimals
15-1 Round Decimals Five-Minute Check (over Chapter 14) Main Idea California Standards Example 1 Example 2 Example 3
15-1 Round Decimals • I will round decimals.
15-1 Round Decimals Standard 4NS2.2 Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer.
15-1 Round Decimals About 2.93 million people live in San Diego County, California. How many people live in San Diego County when rounded to the nearest whole number?
15-1 Round Decimals One Way: Use a Number Line 2.93 is between 2 and 3. It is closer to 3. So, round 2.93 to 3.
15-1 Round Decimals Another Way: Use Rounding Rules Use the same process that you use with rounding whole numbers. 2.93 Answer: To the nearest whole number, 2.93 rounds to 3.
15-1 Round Decimals Round 4.65 to the nearest whole number. A. 3 B. 4 C. 5 D. 6
15-1 Round Decimals Round 46.45 to the nearest whole number. Use the rounding rules. 46.45 Answer: To the nearest whole number, 46.45 rounds to 46.
15-1 Round Decimals Round 87.38 to the nearest whole number. A. 89 B. 88 C. 87 D. 86
15-1 Round Decimals A golfer had an average score of 72.84 in one season. Round this score to the nearest tenth. Use rounding rules. 72.84 Answer: To the nearest tenth, 72.84 rounds to 72.8.
15-1 Round Decimals Round 92.37 to the nearest tenth. A. 92.2 B. 92.3 C. 92.4 D. 92.5
Math Gr4 Ch15
15-2 Estimate Decimal Sums and Differences Five-Minute Check (over Lesson 15-1) Main Idea California Standards Key Concept: Estimate Decimal Sums Key Concept: Estimate Decimal Differences Example 1 Example 2
15-2 Estimate Decimal Sums and Differences • I will use rounding to estimate sums and differences.
15-2 Estimate Decimal Sums and Differences Standard 4NS2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places.
15-2 Estimate Decimal Sums and Differences Martina is going white water rafting with her family. During their first day, they will travel 6.5 miles before lunch and 8.75 miles after lunch. About how far will they travel on their first day? To estimate the sum of decimals, you can round each decimal to the nearest whole number and then add.
15-2 Estimate Decimal Sums and Differences
15-2 Estimate Decimal Sums and Differences
15-2 Estimate Decimal Sums and Differences Belkis rides her bike 4.6 miles on Saturday and 6.25 miles on Sunday. About how many miles does she ride her bike altogether on both days? You need to estimate 4.6 + 6.25. Round each addend to the nearest whole number. Then add. 4.6 5 Round 4.6 to 5 + 6.25 +6 Round 6.25 to 6 11 Answer: So, Belkis rode her bike about 11 miles.
15-2 Estimate Decimal Sums and Differences Adriano ran 2.3 miles on Friday and 3.45 miles on Saturday. About how many miles did he run altogether on both days? A. 3 B. 4 C. 5 D. 6
15-2 Estimate Decimal Sums and Differences Jairo has $38.55. If he buys a CD that costs $16.99, about how much money will he have left? You need to estimate $38.55 – $16.99. Round each decimal to the nearest whole number. Then subtract.
15-2 Estimate Decimal Sums and Differences $38.55 $39 Round $38.55 to $39. – $16.99 – $17 Round $16.99 to $17. $39 – $17 $22 Answer: So, Jairo will have about $22 left.
15-2 Estimate Decimal Sums and Differences Sonia has $42.67. If she buys a pair of shoes for $24.99, about how much money will she have left? A. $18 B. $19 C. $20 D. $21
Math Gr4 Ch15
15-3 Problem-Solving Strategy: Work Backward Five-Minute Check (over Lesson 15-2) Main Idea California Standards Example 1: Problem-Solving Strategy
15-3 Problem-Solving Strategy: Work Backward • I will solve problems by working backward.
15-3 Problem-Solving Strategy: Work Backward Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
15-3 Problem-Solving Strategy: Work Backward Standard 4NS3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.
15-3 Problem-Solving Strategy: Work Backward Rey has lacrosse practice in the evenings. He gets home from school and eats a snack for 15 minutes. Then he spends 1 hour doing his homework. It takes him 15 minutes to get to practice. Practice is at 5 P.M. What time does Rey get home from school?
15-3 Problem-Solving Strategy: Work Backward Understand What facts do you know? • Rey eats a snack for 15 minutes. • He works on homework for 1 hour. • It takes 15 minutes to get to practice at 5 P.M. What do you need to find? • What time Rey gets home from school.
15-3 Problem-Solving Strategy: Work Backward Plan Work backward to solve the problem.
15-3 Problem-Solving Strategy: Work Backward Solve Start with the end result. Then work backward one step at a time. 5 P.M. – 15 minutes = 4:45 P.M. practice time to get starts to practice 4:45 P.M. – 1 hour = 3:45 P.M. time spent on homework
15-3 Problem-Solving Strategy: Work Backward Solve 3:45 P.M. – 15 minutes = 3:30 P.M. time spent eating Answer: So, Rey got home from school at 3:30 P.M.
15-3 Problem-Solving Strategy: Work Backward Check Look back at the problem. 15 + 1 hour + 15 minutes = 1 hour and 30 minutes. If he gets home at 3:30 P.M., one hour and 30 minutes later would be 5 P.M. The answer is correct.
Math Gr4 Ch15
15-4 Add Decimals Five-Minute Check (over Lesson 15-3) Main Idea California Standards Example 1 Example 2 Addition of Decimals
15-4 Add Decimals • I will add decimals.
15-4 Add Decimals Standard 4NS2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places. Standard 4MR2.1 Use estimation to verify the reasonableness of calculated results.
15-4 Add Decimals Odina slept 8.3 hours on Monday night and 7.66 hours on Tuesday night. How many hours did she sleep on the two nights combined? Estimate 8.3 + 7.66 8 + 8 = 16 Step 1 Line up the decimal points. 8.30 Write a 0 in the + 7.66 hundredths place as a placeholder.
15-4 Add Decimals Step 2 Add. Add the digits in each 8.30 place value. Then bring + 7.66 the decimal point straight 15.96 down in the sum. Answer: So, Odina slept a total of 15.96 hours.
15-4 Add Decimals Check for Reasonableness. Since 15.96 is close to the estimate of 16, the answer is reasonable.
15-4 Add Decimals Meredith studied for 2.4 hours on Tuesday night and 1.83 hours on Wednesday night. How many hours did she spend studying on the two nights combined? A. 3.23 B. 4.23 C. 4.33 D. 5.23
15-4 Add Decimals Kate spent $1.25 for a juice box and $1.79 for yogurt. How much did she spend in all? You need to find $1.25 + $1.79. Estimate $1 + $2 = $3 Step 1 Line up the decimal points. $1.25 + $1.79
15-4 Add Decimals Step 2 Add. 1 1 $1.25 Add the digits in each place value. + $1.79 Regroup if necessary. $3.04 Answer: So, Kate spent $3.04.
15-4 Add Decimals Check for Reasonableness. The sum of $3.04 is close to the estimate of 3, so the answer is reasonable.
15-4 Add Decimals Jerome spent $2.55 on a sandwich and $1.75 on a bottle of juice. How much did he spend in all? A. $3.20 B. $4.20 C. $4.30 D. $4.75
Math Gr4 Ch15
15-5 Problem-Solving Investigation: Choose a Strategy Five-Minute Check (over Lesson 15-4) Main Idea California Standards Example 1: Problem-Solving Investigation
15-5 Problem-Solving Investigation: Choose a Strategy • I will choose the best strategy to solve a problem.
15-5 Problem-Solving Investigation: Choose a Strategy Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
15-5 Problem-Solving Investigation: Choose a Strategy Standard 4SDAP1.1 Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts.
15-5 Problem-Solving Investigation: Choose a Strategy Jennifer: My friends and I have pets. We all have different kinds of pets. Among the three of us, we have a lizard, a cat, a gerbil, and a snake. I do not have a cat. Rondell’s pet is not a gerbil or a snake. Lorena’s two pets are not lizards. My pet does not begin with the letters s or g.
15-5 Problem-Solving Investigation: Choose a Strategy YOUR MISSION: Find with person owns each pet.
15-5 Problem-Solving Investigation: Choose a Strategy Understand What facts do you know? • You know the clues for each person’s pet. What do you need to find? • You need to find which person owns each pet.
15-5 Problem-Solving Investigation: Choose a Strategy Plan Make a table to show what you know. Then use logical reasoning to find which person owns each pet.
15-5 Problem-Solving Investigation: Choose a Strategy Solve Make a table. Write a yes or no for each fact that you are given. Once you write yes in the table, you can write no in the rest of the boxes in that row and column.
15-5 Problem-Solving Investigation: Choose a Strategy Solve Answer: So, Jennifer owns a lizard. Lorena owns a gerbil and a snake. Rondell owns a cat.
15-5 Problem-Solving Investigation: Choose a Strategy Check Look back at the problem. The solution matches the facts given in the problem. So, the answer is correct.
Math Gr4 Ch15
15-6 Subtract Decimals Five-Minute Check (over Lesson 15-5) Main Idea California Standards Example 1 Example 2 Subtraction of Decimals
15-6 Subtract Decimals • I will subtract decimals.
15-6 Subtract Decimals Standard 4NS2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places. Standard 4MR2.1 Use estimation to verify reasonableness of calculated results.
15-6 Subtract Decimals A fruit stand sells a bag of grapes for $1.70 and a bunch of bananas for $1.19. What is the difference in price? Estimate $1.70 – $1.19 $1.7 – $1.2 = $0.50 Step 1 Line up the decimal points. $1.70 – $1.19
15-6 Subtract Decimals Step 2 Subtract. Regroup if needed. 6 10 $1.70 – $1.19 Bring the decimal point $0.51 straight down in the sum. Answer: So, the difference in price is $0.51.
15-6 Subtract Decimals Check for Reasonableness. Since the answer of $0.51 is close to the estimate of $0.50, the answer is reasonable.
15-6 Subtract Decimals Find the difference between 2.25 and 1.4. A. 1.85 B. 0.85 C. 0.05 D. 0.80
15-6 Subtract Decimals Arati is 52.5 inches tall and her sister is 48.8 inches tall. How much taller is Arati than her sister? Estimate 52.5 – 48.8 53 – 49 = 4 Step 1 Line up the decimal points. 52.5 – 48.8
15-6 Subtract Decimals Step 2 Subtract. 11 4 1 15 52.5 Subtract the digits in each – 48.8 place value. Regroup if 3.7 necessary. Answer: So, Arati is 3.7 inches taller than her sister.
15-6 Subtract Decimals Check for Reasonableness. The answer 3.7 is close to the estimate of 4. So, the answer is reasonable. You can also add to check. 48.8 + 3.7 52.5 So, the answer is correct.
15-6 Subtract Decimals Find the difference between 78.2 and 55.1. A. 231 B. 2.31 C. 23.1 D. 0.231
Math Gr4 Ch15
Decimals: Addition and Subtraction 15 Five-Minute Checks Addition of Decimals Subtraction of Decimals
Decimals: Addition and Subtraction 15 Lesson 15-1 (over Chapter 14) Lesson 15-2 (over Lesson 15-1) Lesson 15-3 (over Lesson 15-2) Lesson 15-4 (over Lesson 15-3) Lesson 15-5 (over Lesson 15-4) Lesson 15-6 (over Lesson 15-5)
Decimals: Addition and Subtraction 15 (over Chapter 14) Compare. Write <, >, or =. 6 73 10 A. < B. > C. =
Decimals: Addition and Subtraction 15 (over Chapter 14) Compare. Write <, >, or =. 5.6 5 A. < B. > C. =
Decimals: Addition and Subtraction 15 (over Chapter 14) Compare. Write <, >, or =. 1 2 2.1 10 A. < B. > C. =
Decimals: Addition and Subtraction 15 (over Chapter 14) Compare. Write <, >, or =. 4.7 4.07 A. < B. > C. =
Decimals: Addition and Subtraction 15 (over Chapter 14) Use a number line to order from greatest to least. 11 1 , 11.9, 11 38 , 11.25 2 100 1 38 A. 11.9, 11.25, 11 , 11 2 100 38 1 B. 11 , 11.9, 11.25, 11 100 2 1 38 C. 11.9, 11 , 11 , 11.25 2 100 38 1 D. 11 , 11.9, 11 , 11.25 100 2
Decimals: Addition and Subtraction 15 (over Chapter 14) Use a number line to order from greatest to least. 4 3 , 4.62, 3.2, 4 5 5 10 4 5 A. 3.2, 3 , 4 , 4.62 5 10 5 4 B. 4 , 4.62, 3 , 3.2 10 5 5 4 C. 4.62, 4 , 3.2, 3 10 5 5 4 D. 4.62, 4 , 3 , 3.2 10 5
Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 1.43 to the nearest whole number. A. 1.5 B. 1 C. 2 D. 0
Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 26.72 to the nearest whole number. A. 26 B. 20 C. 27 D. 30
Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 53.54 to the nearest whole number. A. 53 B. 50 C. 53.5 D. 54
Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 67.15 to the nearest whole number. A. 67 B. 70 C. 60 D. 68
Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 3.16 to the nearest tenth. A. 3.1 B. 3 C. 0 D. 3.2
Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 9.35 to the nearest tenth. A. 9.3 B. 9 C. 9.4 D. 10
Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 48.51 to the nearest tenth. A. 49 B. 48.5 C. 48 D. 48.1
Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 92.64 to the nearest tenth. A. 92.7 B. 93 C. 92.1 D. 92.6
Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 1.5 + 3.4 A. 4 B. 4.5 C. 5 D. 4.9
Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 37.61 + 12.84 A. 49 B. 50.5 C. 50 D. 51
Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 28.90 – 8.27 A. 21 B. 38 C. 22 D. 20.8
Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 66.3 – 19.51 A. 47.7 B. 45 C. 46 D. 46.8
Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 2.18 + 17.4 A. 19 B. 19.6 C. 20 D. 15.2
Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 22.78 + 29.82 A. 52 B. 53 C. 52.6 D. 51
Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. $52.25 – $44.77 A. $8.00 B. $7.50 C. $12.52 D. $7.00
Decimals: Addition and Subtraction 15 (over Lesson 15-3) Solve. Use the Work Backward strategy. A number is added to 2. Next, the sum is divided by 3. Then, 1 is subtracted from the quotient. The result is 3. What is the number? A. 2 B. 7 C. 10 D. 12
Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 0.8 + 0.4 A. 0.12 B. 12 C. 1.2 D. 1.4
Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 8.20 + 1.46 A. 9.6 B. 10.66 C. 9.12 D. 9.66
Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 4.35 + 9.47 A. 12.72 B. 13.82 C. 11.82 D. 13.72
Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. $6.07 + $6.89 A. $13.96 B. $12.86 C. $12.96 D. $12.97
Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 24.38 + 33.92 A. 58.30 B. 68.30 C. 58.29 D. 57.20
Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 45.23 + 39.68 A. 85.90 B. 74.81 C. 75.91 D. 84.91
Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. $62.50 + $19.52 A. $71.02 B. $82.02 C. $82.12 D. $81.02
Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 5.3 + 2.47 + 1.15 A. 8.82 B. 3.05 C. 8.92 D. 4.15
Decimals: Addition and Subtraction 15 (over Lesson 15-5) Use any problem-solving strategy to solve. Finn, Malik, and Kwag are all wearing different colored shirts. Their shirts are red, blue, or green. Malik’s shirt is not blue. Finn’s shirt color doesn’t start with an “r” or a “g”. Kwag’s shirt is green. What color shirt is each boy wearing? A. Finn: red; Malik: blue; Kwag: green B. Finn: blue; Malik: green; Kwag: red C. Finn: yellow; Malik: red; Kwag: green D. Finn: blue; Malik: red; Kwag: green
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Math Gr4 Ch15

  • 1. Chapter 15 Decimals: Addition and Subtraction Click the mouse or press the space bar to continue.
  • 2. Decimals: Addition and Subtraction 15 Lesson 15-1 Round Decimals Lesson 15-2 Estimate Decimal Sums and Differences Lesson 15-3 Problem-Solving Strategy: Work Backward Lesson 15-4 Add Decimals Lesson 15-5 Problem-Solving Investigation: Choose a Strategy Lesson 15-6 Subtract Decimals
  • 3. 15-1 Round Decimals Five-Minute Check (over Chapter 14) Main Idea California Standards Example 1 Example 2 Example 3
  • 4. 15-1 Round Decimals • I will round decimals.
  • 5. 15-1 Round Decimals Standard 4NS2.2 Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer.
  • 6. 15-1 Round Decimals About 2.93 million people live in San Diego County, California. How many people live in San Diego County when rounded to the nearest whole number?
  • 7. 15-1 Round Decimals One Way: Use a Number Line 2.93 is between 2 and 3. It is closer to 3. So, round 2.93 to 3.
  • 8. 15-1 Round Decimals Another Way: Use Rounding Rules Use the same process that you use with rounding whole numbers. 2.93 Answer: To the nearest whole number, 2.93 rounds to 3.
  • 9. 15-1 Round Decimals Round 4.65 to the nearest whole number. A. 3 B. 4 C. 5 D. 6
  • 10. 15-1 Round Decimals Round 46.45 to the nearest whole number. Use the rounding rules. 46.45 Answer: To the nearest whole number, 46.45 rounds to 46.
  • 11. 15-1 Round Decimals Round 87.38 to the nearest whole number. A. 89 B. 88 C. 87 D. 86
  • 12. 15-1 Round Decimals A golfer had an average score of 72.84 in one season. Round this score to the nearest tenth. Use rounding rules. 72.84 Answer: To the nearest tenth, 72.84 rounds to 72.8.
  • 13. 15-1 Round Decimals Round 92.37 to the nearest tenth. A. 92.2 B. 92.3 C. 92.4 D. 92.5
  • 15. 15-2 Estimate Decimal Sums and Differences Five-Minute Check (over Lesson 15-1) Main Idea California Standards Key Concept: Estimate Decimal Sums Key Concept: Estimate Decimal Differences Example 1 Example 2
  • 16. 15-2 Estimate Decimal Sums and Differences • I will use rounding to estimate sums and differences.
  • 17. 15-2 Estimate Decimal Sums and Differences Standard 4NS2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places.
  • 18. 15-2 Estimate Decimal Sums and Differences Martina is going white water rafting with her family. During their first day, they will travel 6.5 miles before lunch and 8.75 miles after lunch. About how far will they travel on their first day? To estimate the sum of decimals, you can round each decimal to the nearest whole number and then add.
  • 19. 15-2 Estimate Decimal Sums and Differences
  • 20. 15-2 Estimate Decimal Sums and Differences
  • 21. 15-2 Estimate Decimal Sums and Differences Belkis rides her bike 4.6 miles on Saturday and 6.25 miles on Sunday. About how many miles does she ride her bike altogether on both days? You need to estimate 4.6 + 6.25. Round each addend to the nearest whole number. Then add. 4.6 5 Round 4.6 to 5 + 6.25 +6 Round 6.25 to 6 11 Answer: So, Belkis rode her bike about 11 miles.
  • 22. 15-2 Estimate Decimal Sums and Differences Adriano ran 2.3 miles on Friday and 3.45 miles on Saturday. About how many miles did he run altogether on both days? A. 3 B. 4 C. 5 D. 6
  • 23. 15-2 Estimate Decimal Sums and Differences Jairo has $38.55. If he buys a CD that costs $16.99, about how much money will he have left? You need to estimate $38.55 – $16.99. Round each decimal to the nearest whole number. Then subtract.
  • 24. 15-2 Estimate Decimal Sums and Differences $38.55 $39 Round $38.55 to $39. – $16.99 – $17 Round $16.99 to $17. $39 – $17 $22 Answer: So, Jairo will have about $22 left.
  • 25. 15-2 Estimate Decimal Sums and Differences Sonia has $42.67. If she buys a pair of shoes for $24.99, about how much money will she have left? A. $18 B. $19 C. $20 D. $21
  • 27. 15-3 Problem-Solving Strategy: Work Backward Five-Minute Check (over Lesson 15-2) Main Idea California Standards Example 1: Problem-Solving Strategy
  • 28. 15-3 Problem-Solving Strategy: Work Backward • I will solve problems by working backward.
  • 29. 15-3 Problem-Solving Strategy: Work Backward Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
  • 30. 15-3 Problem-Solving Strategy: Work Backward Standard 4NS3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.
  • 31. 15-3 Problem-Solving Strategy: Work Backward Rey has lacrosse practice in the evenings. He gets home from school and eats a snack for 15 minutes. Then he spends 1 hour doing his homework. It takes him 15 minutes to get to practice. Practice is at 5 P.M. What time does Rey get home from school?
  • 32. 15-3 Problem-Solving Strategy: Work Backward Understand What facts do you know? • Rey eats a snack for 15 minutes. • He works on homework for 1 hour. • It takes 15 minutes to get to practice at 5 P.M. What do you need to find? • What time Rey gets home from school.
  • 33. 15-3 Problem-Solving Strategy: Work Backward Plan Work backward to solve the problem.
  • 34. 15-3 Problem-Solving Strategy: Work Backward Solve Start with the end result. Then work backward one step at a time. 5 P.M. – 15 minutes = 4:45 P.M. practice time to get starts to practice 4:45 P.M. – 1 hour = 3:45 P.M. time spent on homework
  • 35. 15-3 Problem-Solving Strategy: Work Backward Solve 3:45 P.M. – 15 minutes = 3:30 P.M. time spent eating Answer: So, Rey got home from school at 3:30 P.M.
  • 36. 15-3 Problem-Solving Strategy: Work Backward Check Look back at the problem. 15 + 1 hour + 15 minutes = 1 hour and 30 minutes. If he gets home at 3:30 P.M., one hour and 30 minutes later would be 5 P.M. The answer is correct.
  • 38. 15-4 Add Decimals Five-Minute Check (over Lesson 15-3) Main Idea California Standards Example 1 Example 2 Addition of Decimals
  • 39. 15-4 Add Decimals • I will add decimals.
  • 40. 15-4 Add Decimals Standard 4NS2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places. Standard 4MR2.1 Use estimation to verify the reasonableness of calculated results.
  • 41. 15-4 Add Decimals Odina slept 8.3 hours on Monday night and 7.66 hours on Tuesday night. How many hours did she sleep on the two nights combined? Estimate 8.3 + 7.66 8 + 8 = 16 Step 1 Line up the decimal points. 8.30 Write a 0 in the + 7.66 hundredths place as a placeholder.
  • 42. 15-4 Add Decimals Step 2 Add. Add the digits in each 8.30 place value. Then bring + 7.66 the decimal point straight 15.96 down in the sum. Answer: So, Odina slept a total of 15.96 hours.
  • 43. 15-4 Add Decimals Check for Reasonableness. Since 15.96 is close to the estimate of 16, the answer is reasonable.
  • 44. 15-4 Add Decimals Meredith studied for 2.4 hours on Tuesday night and 1.83 hours on Wednesday night. How many hours did she spend studying on the two nights combined? A. 3.23 B. 4.23 C. 4.33 D. 5.23
  • 45. 15-4 Add Decimals Kate spent $1.25 for a juice box and $1.79 for yogurt. How much did she spend in all? You need to find $1.25 + $1.79. Estimate $1 + $2 = $3 Step 1 Line up the decimal points. $1.25 + $1.79
  • 46. 15-4 Add Decimals Step 2 Add. 1 1 $1.25 Add the digits in each place value. + $1.79 Regroup if necessary. $3.04 Answer: So, Kate spent $3.04.
  • 47. 15-4 Add Decimals Check for Reasonableness. The sum of $3.04 is close to the estimate of 3, so the answer is reasonable.
  • 48. 15-4 Add Decimals Jerome spent $2.55 on a sandwich and $1.75 on a bottle of juice. How much did he spend in all? A. $3.20 B. $4.20 C. $4.30 D. $4.75
  • 50. 15-5 Problem-Solving Investigation: Choose a Strategy Five-Minute Check (over Lesson 15-4) Main Idea California Standards Example 1: Problem-Solving Investigation
  • 51. 15-5 Problem-Solving Investigation: Choose a Strategy • I will choose the best strategy to solve a problem.
  • 52. 15-5 Problem-Solving Investigation: Choose a Strategy Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
  • 53. 15-5 Problem-Solving Investigation: Choose a Strategy Standard 4SDAP1.1 Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts.
  • 54. 15-5 Problem-Solving Investigation: Choose a Strategy Jennifer: My friends and I have pets. We all have different kinds of pets. Among the three of us, we have a lizard, a cat, a gerbil, and a snake. I do not have a cat. Rondell’s pet is not a gerbil or a snake. Lorena’s two pets are not lizards. My pet does not begin with the letters s or g.
  • 55. 15-5 Problem-Solving Investigation: Choose a Strategy YOUR MISSION: Find with person owns each pet.
  • 56. 15-5 Problem-Solving Investigation: Choose a Strategy Understand What facts do you know? • You know the clues for each person’s pet. What do you need to find? • You need to find which person owns each pet.
  • 57. 15-5 Problem-Solving Investigation: Choose a Strategy Plan Make a table to show what you know. Then use logical reasoning to find which person owns each pet.
  • 58. 15-5 Problem-Solving Investigation: Choose a Strategy Solve Make a table. Write a yes or no for each fact that you are given. Once you write yes in the table, you can write no in the rest of the boxes in that row and column.
  • 59. 15-5 Problem-Solving Investigation: Choose a Strategy Solve Answer: So, Jennifer owns a lizard. Lorena owns a gerbil and a snake. Rondell owns a cat.
  • 60. 15-5 Problem-Solving Investigation: Choose a Strategy Check Look back at the problem. The solution matches the facts given in the problem. So, the answer is correct.
  • 62. 15-6 Subtract Decimals Five-Minute Check (over Lesson 15-5) Main Idea California Standards Example 1 Example 2 Subtraction of Decimals
  • 63. 15-6 Subtract Decimals • I will subtract decimals.
  • 64. 15-6 Subtract Decimals Standard 4NS2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places. Standard 4MR2.1 Use estimation to verify reasonableness of calculated results.
  • 65. 15-6 Subtract Decimals A fruit stand sells a bag of grapes for $1.70 and a bunch of bananas for $1.19. What is the difference in price? Estimate $1.70 – $1.19 $1.7 – $1.2 = $0.50 Step 1 Line up the decimal points. $1.70 – $1.19
  • 66. 15-6 Subtract Decimals Step 2 Subtract. Regroup if needed. 6 10 $1.70 – $1.19 Bring the decimal point $0.51 straight down in the sum. Answer: So, the difference in price is $0.51.
  • 67. 15-6 Subtract Decimals Check for Reasonableness. Since the answer of $0.51 is close to the estimate of $0.50, the answer is reasonable.
  • 68. 15-6 Subtract Decimals Find the difference between 2.25 and 1.4. A. 1.85 B. 0.85 C. 0.05 D. 0.80
  • 69. 15-6 Subtract Decimals Arati is 52.5 inches tall and her sister is 48.8 inches tall. How much taller is Arati than her sister? Estimate 52.5 – 48.8 53 – 49 = 4 Step 1 Line up the decimal points. 52.5 – 48.8
  • 70. 15-6 Subtract Decimals Step 2 Subtract. 11 4 1 15 52.5 Subtract the digits in each – 48.8 place value. Regroup if 3.7 necessary. Answer: So, Arati is 3.7 inches taller than her sister.
  • 71. 15-6 Subtract Decimals Check for Reasonableness. The answer 3.7 is close to the estimate of 4. So, the answer is reasonable. You can also add to check. 48.8 + 3.7 52.5 So, the answer is correct.
  • 72. 15-6 Subtract Decimals Find the difference between 78.2 and 55.1. A. 231 B. 2.31 C. 23.1 D. 0.231
  • 74. Decimals: Addition and Subtraction 15 Five-Minute Checks Addition of Decimals Subtraction of Decimals
  • 75. Decimals: Addition and Subtraction 15 Lesson 15-1 (over Chapter 14) Lesson 15-2 (over Lesson 15-1) Lesson 15-3 (over Lesson 15-2) Lesson 15-4 (over Lesson 15-3) Lesson 15-5 (over Lesson 15-4) Lesson 15-6 (over Lesson 15-5)
  • 76. Decimals: Addition and Subtraction 15 (over Chapter 14) Compare. Write <, >, or =. 6 73 10 A. < B. > C. =
  • 77. Decimals: Addition and Subtraction 15 (over Chapter 14) Compare. Write <, >, or =. 5.6 5 A. < B. > C. =
  • 78. Decimals: Addition and Subtraction 15 (over Chapter 14) Compare. Write <, >, or =. 1 2 2.1 10 A. < B. > C. =
  • 79. Decimals: Addition and Subtraction 15 (over Chapter 14) Compare. Write <, >, or =. 4.7 4.07 A. < B. > C. =
  • 80. Decimals: Addition and Subtraction 15 (over Chapter 14) Use a number line to order from greatest to least. 11 1 , 11.9, 11 38 , 11.25 2 100 1 38 A. 11.9, 11.25, 11 , 11 2 100 38 1 B. 11 , 11.9, 11.25, 11 100 2 1 38 C. 11.9, 11 , 11 , 11.25 2 100 38 1 D. 11 , 11.9, 11 , 11.25 100 2
  • 81. Decimals: Addition and Subtraction 15 (over Chapter 14) Use a number line to order from greatest to least. 4 3 , 4.62, 3.2, 4 5 5 10 4 5 A. 3.2, 3 , 4 , 4.62 5 10 5 4 B. 4 , 4.62, 3 , 3.2 10 5 5 4 C. 4.62, 4 , 3.2, 3 10 5 5 4 D. 4.62, 4 , 3 , 3.2 10 5
  • 82. Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 1.43 to the nearest whole number. A. 1.5 B. 1 C. 2 D. 0
  • 83. Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 26.72 to the nearest whole number. A. 26 B. 20 C. 27 D. 30
  • 84. Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 53.54 to the nearest whole number. A. 53 B. 50 C. 53.5 D. 54
  • 85. Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 67.15 to the nearest whole number. A. 67 B. 70 C. 60 D. 68
  • 86. Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 3.16 to the nearest tenth. A. 3.1 B. 3 C. 0 D. 3.2
  • 87. Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 9.35 to the nearest tenth. A. 9.3 B. 9 C. 9.4 D. 10
  • 88. Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 48.51 to the nearest tenth. A. 49 B. 48.5 C. 48 D. 48.1
  • 89. Decimals: Addition and Subtraction 15 (over Lesson 15-1) Round 92.64 to the nearest tenth. A. 92.7 B. 93 C. 92.1 D. 92.6
  • 90. Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 1.5 + 3.4 A. 4 B. 4.5 C. 5 D. 4.9
  • 91. Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 37.61 + 12.84 A. 49 B. 50.5 C. 50 D. 51
  • 92. Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 28.90 – 8.27 A. 21 B. 38 C. 22 D. 20.8
  • 93. Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 66.3 – 19.51 A. 47.7 B. 45 C. 46 D. 46.8
  • 94. Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 2.18 + 17.4 A. 19 B. 19.6 C. 20 D. 15.2
  • 95. Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. 22.78 + 29.82 A. 52 B. 53 C. 52.6 D. 51
  • 96. Decimals: Addition and Subtraction 15 (over Lesson 15-2) Estimate. Round to the nearest whole number. $52.25 – $44.77 A. $8.00 B. $7.50 C. $12.52 D. $7.00
  • 97. Decimals: Addition and Subtraction 15 (over Lesson 15-3) Solve. Use the Work Backward strategy. A number is added to 2. Next, the sum is divided by 3. Then, 1 is subtracted from the quotient. The result is 3. What is the number? A. 2 B. 7 C. 10 D. 12
  • 98. Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 0.8 + 0.4 A. 0.12 B. 12 C. 1.2 D. 1.4
  • 99. Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 8.20 + 1.46 A. 9.6 B. 10.66 C. 9.12 D. 9.66
  • 100. Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 4.35 + 9.47 A. 12.72 B. 13.82 C. 11.82 D. 13.72
  • 101. Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. $6.07 + $6.89 A. $13.96 B. $12.86 C. $12.96 D. $12.97
  • 102. Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 24.38 + 33.92 A. 58.30 B. 68.30 C. 58.29 D. 57.20
  • 103. Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 45.23 + 39.68 A. 85.90 B. 74.81 C. 75.91 D. 84.91
  • 104. Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. $62.50 + $19.52 A. $71.02 B. $82.02 C. $82.12 D. $81.02
  • 105. Decimals: Addition and Subtraction 15 (over Lesson 15-4) Add. Use estimation to check for reasonableness. 5.3 + 2.47 + 1.15 A. 8.82 B. 3.05 C. 8.92 D. 4.15
  • 106. Decimals: Addition and Subtraction 15 (over Lesson 15-5) Use any problem-solving strategy to solve. Finn, Malik, and Kwag are all wearing different colored shirts. Their shirts are red, blue, or green. Malik’s shirt is not blue. Finn’s shirt color doesn’t start with an “r” or a “g”. Kwag’s shirt is green. What color shirt is each boy wearing? A. Finn: red; Malik: blue; Kwag: green B. Finn: blue; Malik: green; Kwag: red C. Finn: yellow; Malik: red; Kwag: green D. Finn: blue; Malik: red; Kwag: green
  • 107. This slide is intentionally blank.