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**Chapter 15 Decimals: Addition and Subtraction**

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**Lesson 15-1 Round Decimals **

Decimals: Addition and Subtraction 15 Lesson Round Decimals Lesson Estimate Decimal Sums and Differences Lesson Problem-Solving Strategy: Work Backward Lesson Add Decimals Lesson Problem-Solving Investigation: Choose a Strategy Lesson Subtract Decimals Chapter Menu

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**Five-Minute Check (over Chapter 14) Main Idea and Vocabulary **

15-1 Round Decimals Five-Minute Check (over Chapter 14) Main Idea and Vocabulary California Standards Example 1: Round Decimals Example 2: Round Decimals Example 3: Round Decimals Lesson 1 Menu

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**I will round decimals. decimal decimal point 15-1 Round Decimals**

Lesson 1 MI/Vocab

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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. Lesson 1 Standard 1

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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? Lesson 1 Ex1

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**One Way: Use a Number Line**

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. Lesson 1 Ex1

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**Another Way: Use Rounding Rules**

15-1 Round Decimals Another Way: Use Rounding Rules Use the same process that you use with rounding whole numbers. 2.93 Lesson 1 Ex1

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15-1 Round Decimals Answer: To the nearest whole number, rounds to 3. About 3 million people live in San Diego County, California. Lesson 1 Ex1

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**Round 4.65 to the nearest whole number.**

15-1 Round Decimals Round 4.65 to the nearest whole number. 3 4 5 6 Lesson 1 CYP1

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**Round 46.45 to the nearest whole number.**

15-1 Round Decimals Round to the nearest whole number. Use the rounding rules. 46.45 Answer: To the nearest whole number, rounds to 46. Lesson 1 Ex2

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**Round 87.38 to the nearest whole number.**

15-1 Round Decimals Round to the nearest whole number. 89 88 87 86 Lesson 1 CYP2

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**Answer: To the nearest tenth, 72.84 rounds to 72.8.**

15-1 Round Decimals A golfer had an average score of in one season. Round this score to the nearest tenth. Use the rounding rules. 72.84 Answer: To the nearest tenth, rounds to 72.8. Lesson 1 Ex3

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**Round 92.37 to the nearest tenth.**

15-1 Round Decimals Round to the nearest tenth. 92.2 92.3 92.4 92.5 Lesson 1 CYP3

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End of Lesson 1

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**Five-Minute Check (over Lesson 15-1) Main Idea and Vocabulary **

15-2 Estimate Decimal Sums and Differences Five-Minute Check (over Lesson 15-1) Main Idea and Vocabulary California Standards Key Concept: Estimate Decimal Sums Key Concept: Estimate Decimal Differences Example 1: Estimate Sums Example 2: Estimate Differences Lesson 2 Menu

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**I will use rounding to estimate sums and differences.**

15-2 Estimate Decimal Sums and Differences I will use rounding to estimate sums and differences. estimate Lesson 2 MI/Vocab

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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. Lesson 2 Standard 1

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15-2 Estimate Decimal Sums and Differences Lesson 2 Key Concept 1

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15-2 Estimate Decimal Sums and Differences Lesson 2 Key Concept 2

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**Answer: So, Belkis rode her bike about 11 miles.**

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 Round each addend to the nearest whole number. Then add. Round 4.6 to 5. Round 6.25 to 6. 6.25 + 4.6 5 + 6 11 Answer: So, Belkis rode her bike about 11 miles. Lesson 2 Ex1

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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? 3 4 5 6 Lesson 2 CYP1

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15-2 Estimate Decimal Sums and Differences Jairo has $ If he buys a CD that costs $16.99, about how much money will he have left? You need to estimate $38.55 – $ Round each decimal to the nearest whole number. Then subtract. Lesson 2 Ex2

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**Answer: So, Jairo will have about $22 left.**

15-2 Estimate Decimal Sums and Differences Round $38.55 to $39. Round $16.99 to $17. $38.55 $16.99 – $39 $17 – $39 $17 – $22 Answer: So, Jairo will have about $22 left. Lesson 2 Ex2

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15-2 Estimate Decimal Sums and Differences Sonia has $ If she buys a pair of shoes for $24.99, about how much money will she have left? $18 $19 $20 $21 Lesson 2 CYP2

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End of Lesson 2

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**Five-Minute Check (over Lesson 15-2) Main Idea California Standards **

15-3 Problem-Solving Strategy: Work Backward Five-Minute Check (over Lesson 15-2) Main Idea California Standards Example 1: Problem-Solving Strategy Lesson 3 Menu

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**I will solve problems by working backward.**

15-3 Problem-Solving Strategy: Work Backward I will solve problems by working backward. Lesson 3 MI/Vocab

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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. Lesson 3 Standard 1

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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. Lesson 3 Standard 2

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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? Lesson 3 Ex1

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**Understand What facts do you know? Rey eats a snack for 15 minutes.**

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. Lesson 3 Ex1

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**Plan Work backward to solve the problem. 15-3**

Problem-Solving Strategy: Work Backward Plan Work backward to solve the problem. Lesson 3 Ex1

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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 starts time to get to practice 4:45 P.M. – 1 hour = 3:45 P.M. time spent on homework Lesson 3 Ex1

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**Solve 3:45 P.M. – 15 minutes = 3:30 P.M.**

15-3 Problem-Solving Strategy: Work Backward Solve 3:45 P.M. – 15 minutes = 3:30 P.M. time spent eating Answer: So, Rey gets home from school at 3:30 P.M. Lesson 3 Ex1

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**Check Look back at the problem.**

15-3 Problem-Solving Strategy: Work Backward Check Look back at the problem. 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. Lesson 3 Ex1

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End of Lesson 3

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**Five-Minute Check (over Lesson 15-3) Main Idea California Standards **

15-4 Add Decimals Five-Minute Check (over Lesson 15-3) Main Idea California Standards Example 1: Add Decimals Example 2: Add Decimals Addition of Decimals Lesson 4 Menu

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15-4 Add Decimals I will add decimals. Lesson 4 MI/Vocab

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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. Lesson 4 Standard 1

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**Step 1 Line up the decimal points.**

15-4 Add Decimals Odina slept 8.3 hours on Monday night and hours on Tuesday night. How many hours did she sleep on the two nights combined? Estimate = 16 Step 1 Line up the decimal points. Write a 0 in the hundredths place as a placeholder. 8.30 + 7.66 Lesson 4 Ex1

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**Answer: So, Odina slept a total of 15.96 hours.**

15-4 Add Decimals Step 2 Add. Add the digits in each place value. Then bring down the decimal point. 8.30 7.66 + 15.96 Answer: So, Odina slept a total of hours. Lesson 4 Ex1

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**Check for Reasonableness**

15-4 Add Decimals Check for Reasonableness Since is close to the estimate of 16, the answer is reasonable. Lesson 4 Ex1

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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? 3.23 hours 4.23 hours 4.33 hours 5.23 hours Lesson 4 CYP1

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**Step 1 Line up the decimal points.**

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 $ $1.79. Estimate $1 + $2 = $3 Step 1 Line up the decimal points. $1.25 + $1.79 Lesson 4 Ex2

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**Step 2 Add. $1.25 $1.79 + $3. 4 Answer: So, Kate spent $3.04. 15-4**

Add Decimals Step 2 Add. 1 1 $1.25 $1.79 + Add the digits in each place value. Regroup if necessary. $3. 4 Answer: So, Kate spent $3.04. Lesson 4 Ex2

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**Check for Reasonableness**

15-4 Add Decimals Check for Reasonableness The sum of $3.04 is close to the estimate of 3, so the answer is reasonable. Lesson 4 Ex2

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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? $3.20 $4.20 $4.30 $4.75 Lesson 4 CYP2

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End of Lesson 4

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**Five-Minute Check (over Lesson 15-4) Main Idea California Standards **

15-5 Problem-Solving Investigation: Choose a Strategy Five-Minute Check (over Lesson 15-4) Main Idea California Standards Example 1: Problem-Solving Investigation Lesson 5 Menu

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**I will choose the best strategy to solve a problem.**

15-5 Problem-Solving Investigation: Choose a Strategy I will choose the best strategy to solve a problem. Lesson 5 MI/Vocab

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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. Lesson 5 Standard 1

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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. Lesson 5 Standard 2

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**YOUR MISSION: Find with person owns each pet.**

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. YOUR MISSION: Find with person owns each pet. Lesson 5 Ex1

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**Understand What facts do you know?**

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. Lesson 5 Ex1

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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. Lesson 5 Ex1

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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. Lesson 5 Ex1

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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. Lesson 5 Ex1

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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. Lesson 5 Ex1

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End of Lesson 5

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**Subtraction of Decimals**

15-6 Subtract Decimals Five-Minute Check (over Lesson 15-5) Main Idea California Standards Example 1: Subtract Decimals Example 2: Subtract Decimals Subtraction of Decimals Lesson 6 Menu

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**I will subtract decimals.**

15-6 Subtract Decimals I will subtract decimals. Lesson 6 MI/Vocab

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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. Lesson 6 Standard 1

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**Step 1 Line up the decimal points.**

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 – $ $1.7 – $1.2 = $0.50 Step 1 Line up the decimal points. $1.70 – $1.19 Lesson 6 Ex1

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**Step 2 Subtract. Regroup if needed.**

15-6 Subtract Decimals Step 2 Subtract. Regroup if needed. 6 10 $1.70 $1.19 – Place the decimal point. $0. 5 1 Answer: So, the difference in price is $0.51. Lesson 6 Ex1

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**Check for Reasonableness**

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. Lesson 6 Ex1

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**Find the difference between 2.25 and 1.4.**

15-6 Subtract Decimals Find the difference between 2.25 and 1.4. 1.85 0.85 0.05 0.80 Lesson 6 CYP1

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**Step 1 Line up the decimal points.**

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 – – 49 = 4 Step 1 Line up the decimal points. 52.5 – 48.8 Lesson 6 Ex2

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**Answer: So, Arati is 3.7 inches taller than her sister.**

15-6 Subtract Decimals Step 2 Subtract. 11 4 1 15 Subtract the digits in each place value. Regroup if necessary. 52.5 48.8 – 3. 7 Answer: So, Arati is 3.7 inches taller than her sister. Lesson 6 Ex2

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**Check for Reasonableness**

15-6 Subtract Decimals Check for Reasonableness The answer 3.7 is close to the estimate of 4. So, the answer is reasonable. Lesson 6 Ex2

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**Find the difference between 78.2 and 55.1.**

15-6 Subtract Decimals Find the difference between 78.2 and 55.1. 231 2.31 23.1 0.231 Lesson 6 CYP2

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End of Lesson 6

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**15 Five-Minute Checks Math Tool Chest Image Bank Addition of Decimals**

Decimals: Addition and Subtraction 15 Five-Minute Checks Math Tool Chest Image Bank Addition of Decimals Subtraction of Decimals CR Menu

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**1. Exit this presentation. **

To use the images that are on the following four slides in your own presentation: 1. Exit this presentation. 2. Open a chapter presentation using a full installation of Microsoft® PowerPoint® in editing mode and scroll to the Image Bank slides. 3. Select an image, copy it, and paste it into your presentation. IB Instructions

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IB 1

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IB 3

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IB 4

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**Lesson 15-1 (over Chapter 14) Lesson 15-2 (over Lesson 15-1) **

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) 5Min Menu

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**Compare. Write <, >, or =.**

(over Chapter 14) Compare. Write <, >, or =. 3 10 < > = 5Min 1-1

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**Compare. Write <, >, or =.**

(over Chapter 14) Compare. Write <, >, or =. < > = 5Min 1-2

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**Compare. Write <, >, or =.**

(over Chapter 14) Compare. Write <, >, or =. 1 10 < > = 5Min 1-3

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**Compare. Write <, >, or =.**

(over Chapter 14) Compare. Write <, >, or =. < > = 5Min 1-4

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**Use a number line to order from greatest to least.**

(over Chapter 14) Use a number line to order from greatest to least. 11 , 11.9, , 11.25 38 100 1 2 A , 11.25, , 11 38 100 1 2 B , 11.9, 11.25, 11 38 100 1 2 C , , , 11.25 38 100 1 2 D , 11.9, , 11.25 38 100 1 2 5Min 1-5

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**Use a number line to order from greatest to least.**

(over Chapter 14) Use a number line to order from greatest to least. 3 , 4.62, 3.2, 4 4 5 10 A , 3 , , 4.62 4 5 10 B , 4.62, 3 , 3.2 4 5 10 C , , 3.2, 3 4 5 10 D , , 3 , 3.2 4 5 10 5Min 1-6

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**Round 1.43 to the nearest whole number.**

(over Lesson 15-1) Round 1.43 to the nearest whole number. 1.5 1 2 5Min 2-1

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**Round 26.72 to the nearest whole number.**

(over Lesson 15-1) Round to the nearest whole number. 26 20 27 30 5Min 2-2

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**Round 53.54 to the nearest whole number.**

(over Lesson 15-1) Round to the nearest whole number. 53 50 53.5 54 5Min 2-3

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**Round 67.15 to the nearest whole number.**

(over Lesson 15-1) Round to the nearest whole number. 67 70 60 68 5Min 2-4

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**Round 3.16 to the nearest tenth.**

(over Lesson 15-1) Round 3.16 to the nearest tenth. 3.1 3 3.2 5Min 2-5

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**Round 9.35 to the nearest tenth.**

(over Lesson 15-1) Round 9.35 to the nearest tenth. 9.3 9 9.4 10 5Min 2-6

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**Round 48.51 to the nearest tenth.**

(over Lesson 15-1) Round to the nearest tenth. 49 48.5 48 48.1 5Min 2-7

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**Round 92.64 to the nearest tenth.**

(over Lesson 15-1) Round to the nearest tenth. 92.7 93 92.1 92.6 5Min 2-8

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**Estimate. Round to the nearest whole number.**

(over Lesson 15-2) Estimate. Round to the nearest whole number. 4 4.5 5 4.9 5Min 3-1

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**Estimate. Round to the nearest whole number.**

(over Lesson 15-2) Estimate. Round to the nearest whole number. 49 50.5 50 51 5Min 3-2

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**Estimate. Round to the nearest whole number.**

(over Lesson 15-2) Estimate. Round to the nearest whole number. – 8.27 21 38 22 20.8 5Min 3-3

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**Estimate. Round to the nearest whole number.**

(over Lesson 15-2) Estimate. Round to the nearest whole number. 66.3 – 19.51 47.7 45 46 46.8 5Min 3-4

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**Estimate. Round to the nearest whole number.**

(over Lesson 15-2) Estimate. Round to the nearest whole number. 19 19.6 20 15.2 5Min 3-5

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**Estimate. Round to the nearest whole number.**

(over Lesson 15-2) Estimate. Round to the nearest whole number. 52 53 52.6 51 5Min 3-6

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**Estimate. Round to the nearest whole number.**

(over Lesson 15-2) Estimate. Round to the nearest whole number. $52.25 – $44.77 $8.00 $7.50 $12.52 $7.00 5Min 3-7

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(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? 2 7 10 12 5Min 4-1

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**Add. Use estimation to check for reasonableness.**

(over Lesson 15-4) Add. Use estimation to check for reasonableness. 0.12 12 1.2 1.4 5Min 5-1

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**Add. Use estimation to check for reasonableness.**

(over Lesson 15-4) Add. Use estimation to check for reasonableness. 9.6 10.66 9.12 9.66 5Min 5-2

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**Add. Use estimation to check for reasonableness.**

(over Lesson 15-4) Add. Use estimation to check for reasonableness. 12.72 13.82 11.82 13.72 5Min 5-3

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**Add. Use estimation to check for reasonableness.**

(over Lesson 15-4) Add. Use estimation to check for reasonableness. $ $6.89 $13.96 $12.86 $12.96 $12.97 5Min 5-4

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**Add. Use estimation to check for reasonableness.**

(over Lesson 15-4) Add. Use estimation to check for reasonableness. 58.30 68.30 58.29 57.20 5Min 5-5

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**Add. Use estimation to check for reasonableness.**

(over Lesson 15-4) Add. Use estimation to check for reasonableness. 85.90 74.81 75.91 84.91 5Min 5-6

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**Add. Use estimation to check for reasonableness.**

(over Lesson 15-4) Add. Use estimation to check for reasonableness. $ $19.52 $71.02 $82.02 $82.12 $81.02 5Min 5-7

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**Add. Use estimation to check for reasonableness.**

(over Lesson 15-4) Add. Use estimation to check for reasonableness. 8.82 3.05 8.92 4.15 5Min 5-8

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**Finn: red; Malik: blue; Kwag: green **

(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? Finn: red; Malik: blue; Kwag: green Finn: blue; Malik: green; Kwag: red Finn: yellow; Malik: red; Kwag: green Finn: blue; Malik: red; Kwag: green 5Min 6-1

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