## enVision Math Common Core 2nd Grade Answers Key Topic 9 Fluently Add and Subtract within 1,000

**Essential Question:** What are procedures for adding and subtracting whole numbers?

**enVision STEM Project: Changing Environments**

**Do Research** Forest fires destroy, but they also make room for new growth. Use the Internet or other sources to find information about forest fires. Describe the effect of forest fires on plant and animal populations.

**Journal: Write a Report** Include data with numbers for the population you researched. Also in your report:

- Choose a kind of animal or plant. Tell how a change in the environment can affect the number of animals or plants.
- Write and solve an addition and a subtraction problem using your data.

**Review What You Know**

**Vocabulary**

Choose the best term from the box. Write it on the blank.

• Associative Property of Addition

• Commutative Property of Addition

• compatible numbers

• inverse operations

Question 1.

___ are easy to add or subtract mentally.

Answer:

Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.

Thus, Compatible numbers are easy to add or subtract mentally.

Question 2.

According to the _______, the grouping of addends can be changed, and the sum will remain the same.

Answer:

The commutative property of addition says that changing the order of addends does not change the sum.

So, According to the commutative property of addition, the grouping of addends can be changed, and the sum will remain the same.

Question 3.

Addition and subtraction are ___

Answer:

Inverse operations are pairs of mathematical manipulations in which one operation undoes the action of the other.

Thus Addition and subtraction are inverse operations.

**Rounding**

Round each number to the nearest ten.

Question 4.

57

Answer:

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Here 7 is greater than 5.

So, 57 round to the nearest ten is 60.

Question 5.

241

Answer:

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

So, 241 round to the nearest ten is 240.

Question 6.

495

Answer:

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Thus 495 round to the nearest ten is 500.

Round each number to the nearest hundred.

Question 7.

732

Answer:

When rounding to the nearest hundred, look at the tens place of the number.

If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

Thus the number 732 to the nearest hundred is 700.

Question 8.

81

Answer:

When rounding to the nearest hundred, look at the tens place of the number.

If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

Thus the number 81 to the nearest hundred is 100.

Question 9.

553

Answer:

When rounding to the nearest hundred, look at the tens place of the number.

If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

Thus the number 553 to the nearest hundred is 600.

**Estimating Sums**

Use compatible numbers to estimate each sum.

Question 10.

27 + 12

Answer:

Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.

Write 27 and 12 to the nearest ten.

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

27 to the nearest ten is 30.

12 to the nearest ten is 10.

30 + 10 = 40

Thus the estimated sum is 40.

Question 11.

133 + 102

Answer:

Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.

If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

133 to the nearest ten is 130.

102 to the nearest ten is 100.

130 + 100 = 230

Thus the estimated sum is 230.

Question 12.

504 + 345

Answer:

Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.

When rounding to the nearest hundred, look at the tens place of the number.

If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

Thus the number 504 to the nearest hundred is 500.

Thus the number 345 to the nearest hundred is 300.

500 + 300 = 800

Thus the estimated sum is 800.

Question 13.

52 + 870

Answer:

Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.

When rounding to the nearest hundred, look at the tens place of the number.

If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Thus the number 52 to the nearest ten is 50.

Thus the number 870 to the nearest hundred is 900.

900 + 50 = 950

Thus the estimated sum is 950.

Question 14.

293 + 278

Answer:

Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.

When rounding to the nearest hundred, look at the tens place of the number.

If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Thus the number 293 to the nearest hundred is 300.

Thus the number 278 to the nearest hundred is 300.

300 + 300 = 600

Thus the estimated sum is 600.

Question 15.

119 + 426

Answer:

Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.

When rounding to the nearest hundred, look at the tens place of the number.

If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.

Thus the number 119 to the nearest hundred is 100.

Thus the number 426 to the nearest hundred is 400.

100 + 400 = 500

Thus the estimated sum is 500.

**Estimating Differences**

Question 16.

Tony and Kim play a video game. Tony scores 512 points. Kim scores 768 points. About how many more points does Kim score than Tony? Which estimation method did you use?

Answer:

Given,

Tony and Kim play a video game. Tony scores 512 points. Kim scores 768 points.

768 – 512

Write the nearest hundred values for both the numbers to estimate the sum.

When rounding to the nearest hundred, look at the tens place of the number.

If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

Thus the number 512 to the nearest hundred is 500.

Thus the number 768 to the nearest hundred is 800.

800 – 500 = 300

Thus Kim scores nearly .00 points than Tony.

Question 17.

Which number sentence shows the most reasonable estimate for

A. 425 – 250 = 175

B. 500 – 200 = 300

C. 400 – 300 = 100

D. 470 – 230 = 240

Answer: 500 – 200 = 300

**Pick a Project**

**PROJECT 9A**

How do you know which is the tallest building?

Project: Research the Heights of Tall Buildings

**PROJECT 9B**

How can you record what you bought over time? Project: Create an Addition Skit

**PROJECT 9C**

How long before the space shuttle launches?

Project: Write a Report About Your Vacation

**3-ACT MATH PREVIEW**

**Math Modeling**

**Fun Raiser**

Before watching the video, think: When a school needs extra money for a field trip or a student club, it might hold a fundraiser to collect that money.

This check is SO BIG, we must have collected a ton of money!

### Lesson 9.1 Use Partial Sums to Add

**Activity**

**Solve & Share**

There are 2 bins of oranges. One bin has 378 oranges. The other bin has 243 oranges. Find the sum of 378 + 243. Think about place value.

You can use structure. You can break apart the problem to show each of the addends in expanded form.

**Look Back!** Adam has 9 bags of oranges with 8 oranges in each. He also has a bin with 325 oranges. How many oranges does Adam have in all? Think about how you can use place value or other tools to help solve the problem. Explain your solution, what tool you used, and why.

**Essential Question** How Can You Break Apart Addition Problems to Solve?

**Visual Learning Bridge**

**A.**

Margot counted 243 manatees one year and 179 manatees the next. How many manatees did Margot count all together?

**B.**

You can estimate and then use place value to add the numbers.

The sum is about 400 manatees.

**C.**

**One Way**

Add each place value. Start with hundreds.

300, 110, and 12 are partial sums.

243 + 179 = 422 manatees

**D.**

**Another Way**

Add each place value. Start with ones.

When you add by place value, you add the hundreds, the tens, and the ones.

243 + 179 = 422 manatees

422 is close to the estimate of 400.

So, 422 is a reasonable sum.

**Convince Me!**

**Critique Reasoning** Lexi used partial sums to complete the problem. Critique Lexi’s reasoning. Is her work correct? Explain.

**Guided Practices**

**Do You Understand?**

Question 1.

Suppose you were adding 527 + 405. What numbers would you combine when adding the tens? Why?

Answer:

When rounding to the nearest hundred, look at the tens place of the number.

If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

Add 3 to 527 = 530

530

410

940

Thus, It would be 3 because when you add it, it gets to be 932 and the tens place is 3.

Question 2.

Find the error. Show how to find the correct answer.

Answer:

First round the numbers to the nearest hundred.

237 to the nearest hundred is 200

285 to the nearest hundred is 300

200 + 300 = 500

So, the estimated answer is 500.

**Do You Know How?**

In 3, estimate the sum. Use place-value blocks or drawings and partial sums to add.

Question 3.

Answer:

When rounding to the nearest hundred, look at the tens place of the number.

If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

365 to the nearest hundred is 400

422 to the nearest hundred is 400

400 + 400 = 800

So, the estimated answer is 800.

**Independent Practice**

**Leveled Practice** In 4-11, estimate each sum. Use place-value blocks or drawings and partial sums to add.

Question 4.

Answer:

When rounding to the nearest hundred, look at the tens place of the number.

If the tens digit is 0, 1, 2, 3, or 4, you will round down to the previous hundred.

If that digit is 5, 6, 7, 8, or 9, you will round up to the next hundred.

356 to the nearest hundred is 400

123 to the nearest hundred is 100

400 + 100 = 500

So, the estimated answer is 500.

Question 5.

Answer:

550 + 423 = 973

973 is close to 1000.

So, the estimated sum is 1000.

Question 6.

185 + 613

Answer:

185 + 613 = 798

798 is close to 800.

So, the estimated sum is 800.

Question 7.

730 + 168

Answer:

730 + 168 = 898

898 is close to 900.

So, the estimated sum is 900.

Question 8.

546 + 143

Answer:

546 + 143 = 689

689 is close to 700.

So, the estimated sum is 700.

Question 9.

362 + 524

Answer:

362 + 524 = 886

886 is close to 900.

So, the estimated sum is 900.

Question 10.

644 + 101

Answer:

644 + 101 = 745

745 is close to 700.

So, the estimated sum is 700.

Question 11.

463 + 315

Answer:

463 + 315 = 778

778 is close to 800.

So, the estimated sum is 800.

**Problem Solving**

Question 12.

**Model with Math** John read a book with 377 pages. Jess read a book with 210 pages. How many pages did John and Jess read? Use place-value blocks and partial sums to solve. Draw a model to represent the problem.

Answer:

Given,

John read a book with 377 pages. Jess read a book with 210 pages.

377 + 210 = 587

587 is close to 600.

So, the estimated sum is 600.

Question 13.

Explain how the solids shown in Group A and Group B could have been sorted.

Answer:

Question 14.

Henry believes the sum of 275 + 313 is 598. Is Henry correct? Use place-value blocks or drawings and partial sums in your explanation.

Answer:

Given,

Henry believes the sum of 275 + 313 is 598.

The sum of 275 and 313 os 588.

Henry is not correct.

Question 15.

**Higher Order Thinking** A school cafeteria sold 255 lunches on Monday, 140 lunches on Tuesday, and 226 lunches on Wednesday. Did the cafeteria sell more lunches on Monday and Tuesday or on Tuesday and Wednesday? Use place value blocks or drawings to solve.

Answer:

Given,

A school cafeteria sold 255 lunches on Monday, 140 lunches on Tuesday, and 226 lunches on Wednesday.

225 + 140 = 365

140 + 226 = 366

Thus cafeteria sells more lunches on Tuesday and Wednesday.

**Assessment Practice**

Question 16.

Which shows breaking 622 + 247 apart by place value to find the sum?

A. 600 + 200; 22 + 40; 2 + 7

B. 600 + 300; 20 + 40; 2 + 7

C. 600 + 200; 20 + 40; 2 + 7

D. 600 + 200; 20 + 47; 2 + 7

Answer: A. 600 + 200; 22 + 40; 2 + 7

Question 17.

Break 331 + 516 apart by place value. Find the sum.

A. 848

B. 847

C. 748

D. 488

Answer:

331 + 516 = 847

Thus the correct answer is option B.

### Lesson 9.2 Use Regrouping to Add

**Activity**

**Solve & Share**

Suppose a bus travels 276 miles on Monday and 248 miles on Tuesday. How many miles does the bus travel?

You can use appropriate tools, such as place-value blocks, to add larger numbers. What other strategies can you use to solve

this problem?

**Look Back!** On Wednesday, the bus gets stuck in traffic. It travels 8 miles each hour for 8 hours. The bus needs to travel 600 miles total from Monday to Wednesday to make it to its destination. Does the bus make it to its destination? Why would it be a good idea to estimate first before you solve this problem?

**Visual Learning Bridge**

**Essential Question**

How Can You Use Regrouping to Solve Addition Problems?

You know one way to record partial sums.

A.

Jason’s family drove from Ocala, Florida to Miami. They drove 139 miles in the morning and 187 miles in the afternoon. How far did Jason’s family drive? Find 139 + 187. ?

Estimate: 139 + 187 is about 100 + 200, or 300 miles.

Jason’s family drove 326 miles. 300 is close to 326, so the sum is reasonable.

**B.**

Here is another way. Write the partial sums.

Regroup the ones. 16 ones = 1 ten + 6 ones

Regroup the tens. 12 tens = 1 hundred + 2 tens

When you regroup, you name a whole number in a different way.

139 + 187 = 326

Jason’s family drove 326 miles.

**Convince Me!**

**Model with Math** Show how to use place-value blocks to find 128 +235 using regrouping.

**Another Example!**

Find 154 + 163.

You can find partial sums. Then you can regroup place values to find the final sum.

Regroup the tens.

1 hundred + 1 ten = 11 tens

154 + 163 = 317

**Guided Practice**

**Do You Understand?**

Question 1.

When you add 3-digit numbers, how do you know if you need to regroup?

Answer: When you add 3-digit numbers if the sum of the place value is greater than 9 then we can know we have to regroup the addend.

Question 2.

To add 546 + 327, would you need to regroup? Explain.

Answer:

546 + 327

7 + 6 = 13, yes we need to regroup

546 + 327 = 873

**Do You Know How?**

In 3 and 4, estimate by rounding. Then find each sum. Use place-value blocks or drawings to help.

Question 3.

Answer:

Question 4.

Answer:

**Independent Practice**

In 5-12, estimate and then find each sum.

Question 5.

Answer:

The estimated number of 136 is 100.

The estimated number of 252 is 300.

The sum of 100 and 300 is 400.

Question 6.

Answer:

The estimated number of 678 is 700.

The estimated number of 129 is 100.

The sum of 700 and 100 is 800.

Question 7.

Answer:

The estimated number of 564 is 600.

The estimated number of 283 is 300.

The sum of 600 and 300 is 900.

Question 8.

Answer:

The estimated number of 118 is 100.

The estimated number of 335 is 300.

The sum of 100 and 300 is 400.

Question 9.

172 + 534

Answer:

The estimated number of 172 is 200.

The estimated number of 534 is 500.

The sum of 200 and 500 is 700.

Question 10.

324 + 508

Answer:

The estimated number of 324 is 300.

The estimated number of 508 is 500.

The sum of 300 and 500 is 800.

Question 11.

582 + 230

Answer:

The estimated number of 582 is 600.

The estimated number of 230 is 200.

The sum of 600 and 200 is 800.

Question 12.

207 + 238

Answer:

The estimated number of 207 is 200.

The estimated number of 238 is 200.

The sum of 200 and 200 is 400.

**Problem Solving**

In 13 and 14, use the table at the right.

Question 13.

How many soup can labels did Grades 1 and 2 collect? Estimate by rounding to the nearest hundred. Then solve. Write an equation that represents the problem.

Answer:

Estimate: 400 + 300 = 700

385 + 294 = 679, grade 1 and 2 collected 679 labels.

Question 14.

**Make Sense and Persevere** Is your answer to Exercise 13 reasonable? Explain.

Answer: Yes, 679 is close to my estimate of 700, so 679 is a reasonable answer.

Question 15.

**Number Sense** The roller coaster Kingda Ka is 192 feet taller than the first Ferris wheel. Use the symbols < and > to compare the heights of the two rides in two different ways.

Answer: 264 feet < 456 feet; 456 feet > 264 feet

Question 16.

**Higher Order Thinking** Pete can run 178 yards in one minute. Sharon can run 119 more yards than Pete in one minute. How many yards can they both run in one minute?

Answer:

Given,

Pete can run 178 yards in one minute.

Sharon can run 119 more yards than Pete in one minute.

178 + 119 = 297 yards

178 + 297 = 475 yards

Question 17.

Abi practiced her flute for 215 minutes last week and 178 minutes this week. How many minutes has Abi practiced?

Answer:

Given,

Abi practiced her flute for 215 minutes last week and 178 minutes this week.

215 + 178 = 393

Thus Abi practiced 393 minutes.

**Assessment Practice**

Question 18.

What is 126 + 229?

A. 355

B. 345

C. 255

D. 245

Answer: 355

The sum of 126 and 229 is 355.

Thus the correct answer is option A.

Question 19.

What is the value of the unknown in 248 + = 521?

A. 248

B. 263

C. 273

D. 283

Answer: 273

Let the missing number be x.

248 + x = 521

x = 521 – 248

x = 273

Thus the correct answer is option C.

### Lesson 9.3 Add 3 or More Numbers

**Activity**

**Solve & Share**

A pet store has 162 goldfish, 124 angelfish, and 6 bowls with 9 pufferfish in each. How many fish are there in all?

You can generalize. Use what you know about adding two numbers to add three numbers.

**Look Back!** How can you decide if your answer is reasonable?

**Visual Learning Bridge**

**Essential Question
**How Can You Add More Than Two Numbers?

**A.**

Different kinds of birds are for sale at a pet store. How many birds are for sale?

Find 137 + 155 + 18.

Round to the nearest ten to estimate: 140 + 160 + 20 = 320.

**B.**

**One Way**

Use partial sums.

In all, 310 birds are for sale.

**C.**

**Another Way**

Use column addition.

The answer is reasonable because 310 is close to the estimate of 320.

In all, 310 birds are for sale.

**Convince Me!**

**Model with Math** For the partial sums above, Billy said, “20 plus 90 is 110. 110 plus 200 equals 310.” Is Billy correct? Use models, properties, or equations to represent and explain your thinking.

**Guided Practice**

**Do You Understand?**

In 1 and 2, look at the example on the previous page.

Question 1.

If you add the numbers in this order, do you get the same sum? Explain why or why not.

Answer:

Question 2.

Why is the 20 crossed out in the column addition problem?

Answer: 5 + 7 + 8 = 20

**Do You Know How?**

In 3 and 4, estimate and then find each sum.

Question 3.

Answer:

The number 123 round to the nearest ten is 120.

The number 168 round to the nearest ten is 170.

The number 36 round to the nearest ten is 40.

Thus the estimated sum is 330.

Question 4.

Answer:

The number 247 round to the nearest ten is 250.

The number 362 round to the nearest ten is 360.

The number 149 round to the nearest ten is 150.

Thus the estimated sum is 760.

You can use partial sums or column addition to add.

**Independent Practice**

**Leveled Practice** In 5-15, estimate and then find each sum.

Question 5.

Answer:

The number 64 round to the nearest ten is 60.

The number 42 round to the nearest ten is 40.

The number 88 round to the nearest ten is 90.

60 + 40 + 90 = 190

Thus the estimated sum is 190.

Question 6.

Answer:

The number 354 round to the nearest ten is 350.

The number 85 round to the nearest ten is 90.

The number 72 round to the nearest ten is 70.

350 + 90 + 70 = 510

Thus the estimated sum is 510.

Question 7.

Answer:

The number 307 round to the nearest ten is 310.

The number 37 round to the nearest ten is 40.

The number 234 round to the nearest ten is 230.

310 + 40 + 230 = 580

Thus the estimated sum is 580.

Question 8.

Answer:

The number 714 round to the nearest ten is 710.

The number 163 round to the nearest ten is 160.

The number 99 round to the nearest ten is 100.

710 + 160 + 100 = 970

Thus the estimated sum of the above numbers is 970

Question 9.

Answer:

The number 602 round to the nearest ten is 600.

The number 125 round to the nearest ten is 130.

The number 231 round to the nearest ten is 230.

600 + 130 + 230 = 960

Thus the estimated sum of the above numbers is 960.

Question 10.

Answer:

The number 64 round to the nearest ten is 60.

The number 42 round to the nearest ten is 40.

The number 88 round to the nearest ten is 90.

Question 11.

Answer:

The number 64 round to the nearest ten is 60.

The number 42 round to the nearest ten is 40.

The number 88 round to the nearest ten is 90.

Question 12.

Answer:

The number 125 round to the nearest ten is 130.

The number 35 round to the nearest ten is 40.

The number 124 round to the nearest ten is 120.

The number 239 round to the nearest ten is 240.

130 + 40 + 120 + 240 = 530

So, the sum of 125, 35, 124, 239 is 523.

Question 13.

32 + 9 + 56 +8

Answer:

When we add 32 + 9 + 56 +8 we get 105.

The number 105 round to the nearest hundred is 100.

Thus the estimated sum is 100.

Question 14.

481 + 78 + 42

Answer:

When we add 481 + 78 + 42 we get 601.

The number 601 round to the nearest hundred is 600.

Thus the estimated sum is 600.

Question 15.

398 + 219 + 23 + 251

Answer:

When we add 398 + 219 + 23 + 251 we get 891.

The number 891 round to the nearest hundred is 900.

Thus the estimated sum is 900.

**Problem Solving**

Question 16.

Use the picture at the right to find the height of President Washington’s head carved in Mt. Rushmore. Write an equation to solve the problem.

Answer:

Add all the numbers to find the height of President Washington’s head carved in Mt. Rushmore.

228 + 252 + 240 = 720 inches

Question 17.

**Algebra** Jada spends $74 on a hat, shoes, and shorts. If the hat costs $22 and the shoes cost $33, how much were the shorts? Write and solve an equation. Use an unknown to represent the cost of the shorts.

Answer:

Given,

Jada spends $74 on a hat, shoes, and shorts.

The hat costs $22 and the shoes cost $33

22 + 33 + x = 74

55 + x = 74

x = 74 – 55

x = 19

Thus the cost of shorts is $19.

Question 18.

**Higher Order Thinking** Meg says 95 + 76 + 86 is greater than 300, but less than 400. Is Meg correct? Why or why not?

Answer:

No Meg is not correct.

95 + 76 + 86 = 257

So, 257 is smaller than 300.

By this we can say that Meg is wrong.

Question 19.

**Reasoning** Karin had cereal, a glass of milk, and a banana for breakfast. How many calories were in her meal? Round to the nearest ten to estimate and then solve. Write an equation that includes your solution.

Answer:

Given,

Karin had cereal, a glass of milk, and a banana for breakfast.

105 round to the nearest ten is 100.

110 round to the nearest ten is 110.

150 round to the nearest ten is 150.

Now add the numbers 100 + 110 + 150 = 360

Thus the equation is 100 + 110 + 150 = 360

**Assessment Practice**

Question 20.

Use place value, partial sums, or properties of operations to find each sum.

Answer:

Question 21.

Use place value, column addition, or of operations to find each sum.

Answer:

### Lesson 9.4 Use Partial Differences to Subtract

**Activity**

**Solve & Share**

Find the difference of 534 – 108. Think about how place value can help you subtract.

You can use structure. How could you use place value to help solve the problem?

**Look Back!** Jim had 388 marbles. He gave 8 marbles to each of 7 friends. How many marbles does Jim have left? How can place value help you to subtract 3-digit numbers?

**Visual Learning Bridge**

**Essential Question**

How Can You Use Partial Differences to Subtract?

**A.**

At the end of the fourth round of a game of Digit Derby, Marco’s score was 462 points. During the fifth round of the game, Marco loses points. What is Marco’s score at the end of the fifth round? Find 462 – 181.

Estimate first.

462 – 181 = ?

500 – 200 = 300

Place value can help you break a subtraction problem into smaller problems.

**B.**

**What You Think**

Use place value to subtract.

Count back by hundreds, tens, and ones.

181 = 100 + 80 + 1

Start at 462. Count back 100 to 362.

Count back 80 to 282

Break apart 80 into 60 and 20.

Count back 1 to 281.

**C.**

**What You Write**

At the end of the fifth round, Marco’s score is 281 points.

The score is close to the estimate.

The difference is reasonable.

**Convince Me!**

**Be Precise** Why was 80 broken into 60 and 20 in the computation above?

**Guided Practice**

**Do You Understand?**

Question 1.

Why do you need to record the numbers you subtract at each step?

Answer:

To keep track of where you are in an equation, and to allow you to retrace your steps if you happen to do something wrong.

Question 2.

Ana is trying to find 634 – 210. She decides to start by subtracting 10 from 634. Do you agree with Ana? Explain.

Answer:

**Do You Know How?**

In 3 and 4, estimate and then use partial differences to subtract. Use open number lines to help.

Question 3.

Find 374 – 236.

Answer:

Question 4.

Find 369 – 175.

Answer:

**Independent Practice**

In 5-10, estimate and then use partial differences to subtract. Use open number lines to help.

Question 5.

738 – 523

Answer: 215

Question 6.

755 – 315

Answer: 440

Question 7.

336 – 217

Answer: 119

Question 8.

455 – 182

Answer: 273

Question 9.

865 – 506

Answer: 359

Question 10.

794 – 355

Answer: 439

**Problem Solving**

Question 11.

Don’s book has 316 pages. He read 50 pages last week. He read another 71 pages this week. How many more pages does Don have left to read?

Answer:

total number of pages in Don’s book = 316

Don’s read pages in last week = 50

Don’s read pages in this week = 71

Don have to left to read pages = 316 – 50 + 71 = 195

Question 12.

**Vocabulary** Explain why it is necessary to regroup when adding 172 + 264.

Answer:

264

172

436

Regrouping is used when the addition of two numbers is greater than 9.

Here 7 + 6 = 13

13 > 10

So, regrouping is necessary here.

Therefore regrouping is necessary when adding 172 + 264

Question 13.

**Use Structure** Beth had a necklace with 128 beads. The string broke, and she lost 49 beads. How many beads does Beth have left? Explain how you can break the problem into smaller problems to solve.

Answer:

Beth had a necklace with beads = 128

The string broke and she lost beads =49

Beads left with Beth = 128 – 49 = 79

Question 14.

Write the time shown on the clock in two different ways.

Answer:

9: 15

21 : 15

Question 15.

**Higher Order Thinking** Which weighs more, two Basset Hounds or one Great Dane? Show the difference in pounds between two Basset Hounds and a Great Dane. Draw bar diagrams to represent and help solve the problem.

Answer:

The weight of two basset hounds = 66 + 66 = 132pounds

The weight of one great dane = 145 pounds

The weight of one grate dane is greater than two basset hounds.

**Assessment Practice**

Question 16.

Which have a difference of 181? Use place value and partial differences to solve. Select all that apply.

428 – 247 = ?

562 – 381 = ?

498 – 307 = ?

875 – 696 = ?

946 – 765 = ?

Answer:

428 – 247 = 181

562 – 381 = 181

498 – 307 = 191

875 – 696 = 179

946 – 765 = 181

Question 17.

Which have a difference of 237? Select all that apply.

877 – 640 = ?

412 – 176 = ?

652 – 415 = ?

700 – 459 = ?

802 – 565 = ?

Answer:

877 – 640 = 237

412 – 176 = 236

652 – 415 = 237

700 – 459 = 241

802 – 565 = 237

### Lesson 9.5 Use Regrouping to Subtract

**Activity**

**Solve & Share**

Last year, there were 347 houses for sale in Mill County and 289 houses for sale in Hunter County. Of the houses for sale in both counties, 162 were sold. How many houses were not sold? Solve this problem two different ways.

You can generalize when you subtract 3-digit numbers. Think about all the strategies you can use.

**Look Back!** How are your solution strategies alike and how are they different?

**Visual Learning Bridge**

**Essential Question**

How Can You Use Regrouping to Solve Subtraction Problems?

**Glossary**

**A.**

Mike and Linda play a game. Linda has 528 points. Mike has 349 points. How many more points does Linda have than Mike? Find 528 – 349.

Estimate:

528 – 349 = ?

530 – 350 = 180

**B.**

Draw place-value blocks to show 528.

**C.** Subtract 9 ones.

Regroup 1 ten as 10 ones.

You can use place value to regroup when subtracting.

Subtract 4 tens. 528

Regroup 1 hundred as 10 tens.

Subtract 3 hundreds.

179 is close to the estimate.

**Convince Me!**

Use Appropriate Tools How could you use a tool to find 326 – 143?

**Guided Practice**

**Do You Understand?**

Question 1.

In the example on the previous page, explain how to decide if regrouping is necessary

Answer:

Question 2.

What strategies could you use to find 507 – 348?

Answer:

using the mental math

500 + 7 – 300 + 40 + 8

500 + 7 – 300 + 48

200 +7 -48 = 159

**Do You Know How?**

In 3 and 4, estimate each difference and then use partial differences to subtract.

Question 3.

Answer:

estimated difference

370

– 180

190

Question 4.

Answer:

estimated difference

860

– 220

640

**Independent Practice**

In 5-12, estimate each difference and then use partial differences to subtract.

Question 5.

Answer:

estimated difference

430

-140

290

Question 6.

Answer:

estimated difference

280

– 100

180

Question 7.

Answer:

estimated difference

520

– 400

120

Question 8.

Answer:

estimated difference

530

– 240

290

Question 9.

574 – 86

Answer:

estimated difference

570 – 90 = 480

Question 10.

629 – 453

Answer:

estimated difference

630 – 450 = 180

Question 11.

979 – 569

Answer:

estimated difference

980 – 570 = 410

Question 12.

764 – 237

Answer:

estimated difference

760 – 240 = 520

**Problem Solving**

Question 13.

At the end of their game, Lora had 426 points and Theo had 158 points. How many more points did Lora have than Theo?

Answer: 268

Given

Lora had 426 points and Theo had 158 points

to find How many more points did Lora have than Theo

hence 426 subtract with 158 we get 268

Question 14.

**Model with Math** Zac and Malcolm each wrote short stories. Zac’s story is 272 lines long. Malcolm’s story is 145 lines longer than Zac’s. How long is Malcolm’s story? Explain how you can model with math to solve this problem.

Answer:

Given,

Zac and Malcolm each wrote short stories. Zac’s story is 272 lines long.

Malcolm’s story is 145 lines longer than Zac’s.

272 + 145 = 417

Therefore, Malcolm wrote 417 lines long.

Question 15.

The world’s largest basket is 186 feet tall from the base to the top of the handles. What is the height of the handles?

Answer: 83 feet

given

The world’s largest basket is 186 feet tall from the base to the top of the handles.

base to basket 103 feets

to find the height of the handles

hence 186 feet subtract with 103 feet we get 83 feet

Question 16.

**Higher Order Thinking** How many more swimmers signed up for the 1st session at Oak Pool than the 1st and 2nd sessions at Park Pool combined? Write an equation that represents the problem and includes the solution.

Answer:

given data

we have to find How many more swimmers signed up for the 1st session at Oak Pool than the 1st and 2nd sessions at Park Pool combined

hence oak pool 1st session 763 subtract with 2nd session 586 we get 177

oak pool 1st session 314 subtract with 2nd session 179 we get 135

oak pool 1st session 256 subtract with 2nd session 163 we get 93

**Assessment Practice**

Question 17.

Which shows the estimate of 627 – 441 by rounding to the nearest ten, and then the correct difference?

A. 200; 186

B. 200; 176

C. 190; 186

D. 190; 176

Answer: C

estimate of 627 – 441 we get 186

estimated 630 – 440 we get 190

Question 18.

Which shows the estimate of 901 – 512 by rounding to the nearest ten, and then the correct difference?

A. 390; 389

B. 390; 379

C. 400; 389

D. 400; 379

Answer: A

estimate of 901 – 512 we get 389

estimated 900 – 510 we get 390

### Lesson 9.6 Use Strategies to Add and Subtract

**Activity**

**Solve & Share**

Rick is allowed to receive 1,000 text messages each month. How many more text messages can Rick receive this month? Solve any way you choose. Explain how you found the answer.

Use reasoning. First think about the operations you should use.

**Look Back!** Is your answer reasonable? How can you check?

**Visual Learning Bridge**

**Essential Question** How Can You Use Strategies to Add and Subtract?

**A.**

There are 136 fewer cell phone towers in Jurloe County than in Fraser County. How many cell phone towers are there in Jurloe County? Choose a strategy, and then solve.

402 is about 400.

136 is about 100.

The difference is about 300.

You can use addition or subtraction to solve.

402 = ? + 136

402 – 136 = ?

Addition and subtraction are inverse operations.

**B.**

**One Way** Use the adding on strategy.

Find 402 = ? + 136.

There are 266 cell phone towers in Jurloe County.

**C.**

**Another Way**

The answer is reasonable because it is close to the estimate of 300.

Use partial differences to subtract.

The answer is reasonable because it differences to is close to the estimate of 300.

Find 402 – 136 = ?

There are 266 cell phone towers in Jurloe County.

**Convince Me!** Use Appropriate Tools Show how to use a tool (such as a number line or place-value blocks) to solve the problem above.

**Another Example!**

The Yellowstone River is 692 miles long. It is 51 miles shorter than the Kansas River. How long is the Kansas River? Choose a strategy, and then solve. Find 692 + 51 = ?

The Kansas River is 743 miles long.

**Guided Practice**

**Do You Understand?**

Question 1.

To subtract 507 – 348, how can you regroup the tens if there are 0 tens?

Answer:

Subtract the ones.

7 ones > 8 ones

Since there are no tens in 507, regroup the hundreds.

5 hundreds and 0 tens = 4 hundreds 10 tens

Regroup the tens

10 tens and 7 ones = 9 tens and 17 ones

Subtract the ones, tens and then the hundreds.

So, 507 – 348 = 159

Question 2.

How is using partial sums to add like using place-value blocks and regrouping?

Answer: Thinking of the place value of digits in the numbers, Finding partial sums by adding parts of numbers according to their place value, and • Adding partial sums together to get a total.

**Do You Know How?**

In 3-6, estimate and then find each sum or difference.

Question 3.

Answer:

816 subtract with 335 we get 481

estimated 820 subtract with 340 we get 480

Question 4.

Answer:

163 add with 50 we get 213

estimated 160 add with 50 we get 210

Question 5.

Answer:

900 subtract with 375 we get 535

estimated 900 subtract with 370 we get 530

Question 6.

Answer:

508 subtract with 247we get 261

estimated 510 subtract with 250 we get 260

**Independent Practice**

In 7-14, find each sum or difference. Then use estimation to check your answer.

Question 7.

Answer:

549 subtract with 167 we get 382

estimated 550 subtract with 170 we get 380

Question 8.

Answer:

411 subtract with 238 we get 173

estimated 410 subtract with 240 we get 170

Question 9.

Answer:

560 add with 144 we get 704

estimated 560 add with 140 we get 700

Question 10.

Answer:

783 add with 68 we get 851

estimated 780 add with 70 we get 850

Question 11.

400 – 219

Answer:

400 subtract with 219 we get 619

estimated 400 subtract with 220 we get 620

Question 12.

904 – 703

Answer:

904 subtract with 703 we get 201

estimated 900 subtract with 700 we get 200

Question 13.

700 + 64

Answer:

700 add with 64 we get 764

estimated 700 add with 60 we get 760

Question 14.

807 + 38

Answer:

807 add with 38 we get 845

estimated 800 add with 40 we get 840

**Problem Solving**

Question 15.

How much more money does the Elm School Art Club need to raise? Complete the bar diagram and solve the problem.

Elm School

Answer:

By seeing the above figure we can find the amount of money to reach the goal.

$305 – $178 = $127

Therefore, the amount of money to reach goal is $127.

Question 16.

There were some ears of corn for sale at the farmers’ market. Three hundred eighty-eight ears of corn were sold. At the end, there were 212 ears left. How many ears of corn were for sale at the start?

Answer:

Given,

There were some ears of corn for sale at the farmers’ market.

Three hundred eighty-eight ears of corn were sold.

At the end, there were 212 ears left.

388 + 212 = 600

Thus there were 600 ears of corn for sale at the start.

Question 17.

Dina was adding books to the library shelves. She put 117 nonfiction books on the shelves. Then there were 204 nonfiction books. How many nonfiction books were on the shelves before?

Answer:

Given,

Dina was adding books to the library shelves.

She put 117 nonfiction books on the shelves.

Then there were 204 nonfiction books.

204 – 117 = 87

Thus there were 87 on the shelves before.

Question 18.

**Construct Arguments** The students at Cleveland School are collecting soda can tabs. The goal of each class is to collect 500 tabs. So far, the second graders have collected 315 tabs. The third graders have collected 190 more tabs than the second graders. Have the third graders reached their goal? Construct an argument to explain.

Answer:

Given,

The students at Cleveland School are collecting soda can tabs.

The goal of each class is to collect 500 tabs.

So far, the second graders have collected 315 tabs.

The third graders have collected 190 more tabs than the second graders.

315 + 190 = 505

505 > 500

Yes, the third graders reached their goal.

Question 19.

**Higher Order Thinking** Dylan had $405 in his savings account and spent $253. Brian had $380 in his savings account and spent $48 less than Dylan. Now who has more money in his savings account? How much more?

Answer:

Given,

Dylan had $405 in his savings account and spent $253.

$405 – $253 = $152

Brian had $380 in his savings account and spent $48 less than Dylan.

$253 – $48 = $205

$380 – $205 = $175

Brian has more money in his savings account.

**Assessment Practice**

Question 20.

Use a place-value strategy to find the value of the unknown in 426 + ? = 712.

A. 186

B. 216

C. 284

D. 286

Answer: D

by subtracting 712 with 426 we get 286

hence 426+286 = 712

Question 21.

Use the relationship between addition and subtraction to find the value of the unknown in ? +334 = 800.

A. 434

B. 466

C. 534

D. 566

Answer: B

by subtracting 800 with 334 we get 466

hence 466 +334 = 800

### Lesson 9.7 Construct Arguments

**Activity**

**Problem Solving**

**Solve & Share**

Use each of the digits 0, 1, 2, 3, 4, and 5 only once. Write the digits in the space below to make two 3-digit addends with the greatest sum. Write the sum of the two addends. How do you know you have made the greatest sum?

**Thinking Habits**

Be a good thinker! These questions can help you.

• How can I use numbers, objects, drawings, or actions to justify my argument?

• Am I using numbers and symbols correctly?

• Is my explanation clear and complete?

**Look Back! Construct Arguments** Make different 3-digit addends to find the least possible sum. What is the difference between the greatest possible sum and the least possible sum? Construct an argument to explain how you know that your answer is correct.

**Visual Learning Bridge**

**Essential Question**

How Can You Construct Arguments?

**A.**

Nancy has $457 in her savings account and wants to have $500 by the end of the year. Christopher has $557 in his savings account and wants to have $600 by the end of the year. Who needs to save more money by the end of the year? My conjecture: They both need to save the same amount.

A conjecture is a statement that you think is true. It needs to be proved or disproved.

How can I explain why my conjecture is correct?

I need to construct an argument to justify my conjecture.

Here’s my thinking.

**B.**

**How can I construct an argument?**

**I can**

• use numbers, objects, drawings, or actions correctly to explain my thinking.

• make sure my explanation is simple, complete, and easy to understand.

**C.**

I will use drawings and numbers to explain my thinking.

The distance from 457 to 500 on the number line is the same as the distance from 557 to 600.

The number lines show that it takes the same amount of money to get from $457 to $500 as it takes to get from $557 to $600.

So, 500 – 457 = 600 – 557. My conjecture is correct.

**Convince Me! Construct Arguments** Construct another math argument to justify the conjecture above.

**Guided Practice**

**Construct Arguments**

Mr. Lee had $375 in the bank. Then he spent $242. Ms. Davis had $675 in the bank, and then spent $542. Who has more money left? Conjecture: They both have the same amount of money left.

Question 1.

Draw a diagram to represent the math.

Diagrams can help you support an argument.

Answer:

Question 2.

Use your diagram to justify the conjecture.

Answer:

**Independent Practice**

**Construct Arguments**

A Grade 2 class has made 165 paper cranes and wants to reach a total of 250. A Grade 3 class has made 255 paper cranes and wants to reach a total of 350. Which class has fewer paper cranes left to make to reach its goal?

Conjecture: The Grade 2 class has to make fewer paper cranes to reach its goal.

Question 3.

Draw a diagram at the right to represent the math.

Answer:

Question 4.

Use your diagram to justify the conjecture.

Answer:

Question 5.

Explain another way you could justify the conjecture.

Answer:

**Problem Solving**

**Performance Task**

**Band Practice**

Some musicians set goals for the number of minutes they want to practice before a concert, which is 5 days away. They want to know who has to practice the least number of minutes to reach his or her goal.

Question 6.

**Make Sense and Persevere** How can you find the number of minutes Aria has to practice to reach her goal?

Answer:

Question 7.

**Reasoning** So far Dexter and Sawyer have both practiced the same number of minutes. Do they need the same amount of practice time to reach their goals? Explain.

Answer:

When you construct arguments, you explain why your work is right.

Question 8.

**Reasoning** Who has the least number of minutes left to practice to reach his or her goal?

Answer;

Question 9.

Construct Arguments Construct a math argument to explain why your answer to Exercise 8 is correct.

Answer:

### Topic 9 Fluency Practice

**Activity**

**Point&Tally**

Find a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue. Partner 1 and Partner 2 each point to a black number at the same time. Both partners add those numbers.

If the answer is on your color, you get a tally mark. Work until one partner has seven tally marks. While playing the game, partners can use subtraction to check their addition.

**Topic 9 Vocabulary Review**

Word List

• conjecture

• estimate

• inverse operations

• place value

• regroup

• round

**Understand Vocabulary**

Draw a line to match each term to an example.

Question 1.

place value 515 + 141 is about 660.

Answer:

515

+414

656

The actual number is 656.

Here ones place is greater than 5.

So, we have to add 1 to the next ten.

Thus the estimated number of 656 is 660.

Question 2.

estimate 305 + 299 = 604 and 604 – 299 = 305

Answer:

The estimated number of 305 is 300.

Question 3.

regroup 232 = 2 hundreds 3 tens 2 ones

Answer:

Given,

regroup 232 = 2 hundreds 3 tens 2 ones

We can regroup 232 as

1 hundred 13 tens 2 ones

Question 4.

inverse operations 47 = 3 tens 17 ones

Answer:

47 = 3 tens 17 ones

We can regroup 47 as 4 tens 7 ones

Write always, sometimes, or never.

Question 5.

When rounding to the nearest ten, a number with a 5 in the ones digit ___ rounds to the next ten.

Answer: When rounding to the nearest ten, a number with a 5 in the ones digit always rounds to the next ten.

Question 6.

A conjecture is ___ true.

Answer: A conjecture is never true.

Question 7.

A digit with a greater place value is ____ written to the right of a digit with a lesser place value.

Answer: A digit with a greater place value is sometimes written to the right of a digit with a lesser place value.

Question 8.

A ten can ____ be regrouped as 10 hundreds.

Answer: A ten can never be regrouped as 10 hundreds.

**Use Vocabulary in Writing**

Question 9.

Explain how to find 600 – 281, and then explain how to check that the difference is correct. Use at least 2 terms from the Word List in your explanation.

Answer:

We can find the difference of 600 and 281 by using estimation.

The estimation of 281 is 300.

600 – 300 = 300

Actual difference:

600 – 281 = 319

The nearest hundred to 319 is 300.

### Topic 9 Reteaching

**Set A**

pages 337–340

Find the sum of 257 + 186.

You can break apart 257 + 186 by place value to solve.

Break apart each number by place value and find the sum of the numbers in each place. Then add the sums.

So, 257 + 186 = 443.

**Remember** that you can use place value to add numbers by breaking large addition problems into smaller addition problems.

In 1-5, use place-value blocks or drawings and partial sums to add.

Question 1.

135 + 152

Answer: 287

Question 2.

650 + 138

Answer: 788

Question 3.

535 + 423

Answer: 958

Question 4.

475 + 264

Answer: 739

Question 5.

Yvette took 137 photographs on Friday. She took 248 photographs on Saturday. How many did she take in all?

Answer:

Given,

Yvette took 137 photographs on Friday.

She took 248 photographs on Saturday.

137 + 248 = 385

Thus Yvette takes 385 photographs in all.

**Set B**

pages 341-344

Find 235 + 187.

Estimate by rounding: 240 + 190 = 430. Use place-value blocks to represent each number and find partial sums. Regroup to find the final sum.

**Remember** that an estimate can help you check whether your answer is reasonable.

In 1-6, estimate and find each sum.

Question 1.

Answer:

236 add with 217 we get 453

estimated 240 add with 220 we get 460

Question 2.

Answer:

407 add with 436 we get 843

estimated 410 add with 440 we get 850

Question 3.

235 +59

Answer:

235 add with 59 we get 294

estimated 230 add with 60 we get 290

Question 4.

584 + 326

Answer:

584 add with 326 we get 910

estimated 590 add with 230 we get 820

Question 5.

196 + 243

Answer:

196 add with 243 we get 439

estimated 200 add with 240 we get 440

Question 6.

465 + 357

Answer:

465 add with 357 we get 822

estimated 460 add with 360 we get 820

**Set C**

pages 345–348

Find 124 + 32 + 238.

Estimate by rounding:

120 + 30 + 240 = 390.

You can solve using partial sums.

You can solve using column addition.

So, 124 + 32 + 238 = 394.

Remember that adding three numbers is like adding two numbers. In 1-7, estimate and then use partial sums to add.

Question 1.

Answer:

estimated

210

50

+ 310

570

Question 2.

Answer:

estimated

410

270

+ 140

820

Question 3.

146 +86 + 53

Answer:

estimated

150+90+50 by adding we get 290

Question 4.

125 + 224 + 306

Answer:

by adding 120,220,and 310 we get 650

Question 5.

A flower shop has 124 tulips, 235 roses, and 85 carnations. How many flowers does the flower shop have?

Answer: 444

given

A flower shop has 124 tulips, 235 roses, and 85 carnations

to find How many flowers does the flower shop have

hence by adding 124 tulips, 235 roses, and 85 carnations we get 444

Question 6.

Mike’s Café sells 237 sandwiches on Friday. It sells 448 sandwiches on Saturday and 102 sandwiches on Sunday. How many sandwiches are sold on all 3 days?

Answer:

Given,

Mike’s Café sells 237 sandwiches on Friday.

It sells 448 sandwiches on Saturday and 102 sandwiches on Sunday.

237 + 448 + 102 = 787

Therefore Mike’s cafe sold 787 sandwiches on all 3 days.

Question 7.

Three planes leave an airport. Each plane has 239 seats. The first plane has 224 passengers. The second plane has 189 passengers. The third plane has 122 passengers. How many passengers are on all 3 planes?

Answer:

Given,

Three planes leave an airport.

Each plane has 239 seats. The first plane has 224 passengers. The second plane has 189 passengers. The third plane has 122 passengers.

Add all the number of passengers in 3 planes.

224 + 189 + 122 = 535

Therefore, there are 535 passengers in all 3 planes.

**Set D**

pages 349-352

So, 548 – 263 = 285.

**Remember** that place value can help you break a subtraction problem into smaller problems.

In 1-6, find each difference. Estimate and then use place value and partial differences to subtract.

Question 1.

489 – 253

Answer:

489 subtract with 253 we get 236

estimated 490 subtract with 250 we get 240

Question 2.

544 – 162

Answer:

544 subtract with 162 we get 382

estimated 540 subtract with 160 we get 380

Question 3.

856 – 328

Answer:

856 subtract with 328 we get 528

estimated 860 subtract with 330 we get 530

Question 4.

349 – 98

Answer:

349 subtract with 98 we get 251

estimated 350 subtract with 100 we get 250

Question 5.

873 – 184

Answer:

873 subtract with 184 we get 689

estimated 870 subtract with 180 we get 690

Question 6.

526 – 207

Answer:

526 subtract with 207 we get 733

estimated 530 subtract with 210 we get 740

**Set E**

pages 353-356

Find 416 – 243.

Estimate: 420 – 240 = 180.

**Remember** to regroup if necessary.

In 1-8, estimate each difference. Then find each difference.

Question 1.

Answer:

458 subtract with 176 we get 634

estimated 460 subtract with 180 we get 640

Question 2.

Answer:

236 subtract with 79 we get 315

estimated 240 subtract with 80 we get 320

Question 3.

Answer:

863 subtract with 526 we get 337

estimated 860 subtract with 530 we get 330

Question 4.

Answer:

748 subtract with 279 we get 469

estimated 750 subtract with 280 we get 470

Question 5.

400 – 227

Answer:

400 subtract with 227 we get 173

estimated 400 subtract with 230 we get 170

Question 6.

306 – 198

Answer:

306 subtract with 198 we get 108

estimated 310 subtract with 200 we get 110

Question 7.

220 – 187

Answer:

220 subtract with 187 we get 33

estimated 220 subtract with 190 we get 30

Question 8.

657 – 122

Answer:

657 subtract with 122 we get 535

estimated 660 subtract with 120 we get 540

**Set F**

pages 357-360

Two hundred seventy-three people have finished a marathon. A total of 458 people entered the marathon. How many people are still running?

You can use a bar diagram and addition or subtraction to solve.

Remember to regroup when needed.

In 1 and 2, estimate. Then solve.

Question 1.

Damian’s conservation club wants to plant 640 seedlings. They have 172 seedlings that they still need to plant to meet their goal. How many seedlings have they planted so far?

Answer:

Given,

Damian’s conservation club wants to plant 640 seedlings.

They have 172 seedlings that they still need to plant to meet their goal.

640 – 172 = 468

Therefore they have planted 468 seedlings so far.

Question 2.

The Smith family is driving to Dallas. The trip is 450 miles. So far, they have driven 315 miles. How many miles are left in the trip?

Answer:

Given,

The Smith family is driving to Dallas.

The trip is 450 miles. So far, they have driven 315 miles.

450 – 315 = 135

Thus 135 miles are left in the trip.

**Set G**

pages 361-364

Think about these questions to help you construct arguments.

**Thinking Habits**

• How can I use numbers, objects, drawings, or actions to justify my argument?

• Am I using numbers and symbols correctly?

• Is my explanation clear and complete?

**Remember** that a conjecture needs to be proved to be true.

Emma has $191. She spends $105. She donates $52 to charity. Can Emma save $30?

**Conjecture: Emma can save $30.**

Question 1.

Draw a diagram to represent the math.

Answer:

Question 2.

Use your diagram to justify the conjecture.

Answer:

### Topic 9 Assessment Practice

Question 1.

Find the sum of 337 and 285. Use place value and find the sums of the hundreds, tens, and ones.

Answer:

Question 2.

An estimate of 431 – 249 using compatible numbers is 425 – 250 = 175. Would it be reasonable for the exact difference to be 182? Explain.

Answer:

Question 3.

Which addends are broken apart correctly? broken apart correctly. Select all that apply.

320 + 148

(300 + 100) + (20 + 40) + (20 + 8)

270 + 341

(2 + 70) + (3+ 4+1)

318 + 393

300 + (10 + 90) + (8 + 3)

532 + 360

(500 + 300) + (30 + 60) + 2

526 + 230

(500 + 200) + (20 + 30) + 6

Answer:

Question 4.

Find the sum of 176, 204, and 59.

A. 329

B. 339

C. 429

D. 439

Answer: D

the sum of 176, 204, and 59

176+204+59 we get 439

Question 5.

What is 276 + 289?

A. 509

B. 537

C. 565

D. 593

Answer: C

by adding 276 and 289 we get 565

Question 6.

Find 237 + 20. Then subtract the sum from 302.

Answer:

The sum of 237 + 20 = 257

302 – 257 = 45

Question 7.

Subtract 168 from 300.

A. 32

B. 122

C. 132

D. 142

Answer:

300 – 168 = 132

Thus the correct answer is option C.

Question 8.

A. Is 268 + 37 less than 346? Make a conjecture.

B. Construct an argument to prove your conjecture.

Answer:

305 < 346

Question 9.

What is 825 – 647?

A. 78

B. 82

C. 128

D. 178

Answer:

The subtraction of 825 and 647 is 178.

Thus the correct answer is option D.

Question 10.

Find 335 + 108 + 12. Then subtract the sum from 600.

Answer:

The sum of 335 + 108 + 12 = 455

600 – 455 = 145

Question 11.

Find 283 + 45. Then subtract 139 from the sum. What is the difference?

A. 189

B. 328

C. 377

D. 467

Answer:

283 + 45 = 328

328 – 139 = 189

Thus the correct answer is option A.

Question 12.

Describe how to use place-value blocks to regroup to solve the subtraction problem below. What is the difference?

Answer:

3 hundreds 1 tens 6 ones

-2 hundreds 2 tens 6 ones

This can be regrouped as

2 hundreds 11 tens 6 ones

– 2 hundeds 2 tens 6 ones

0 hundreds 9 tens 0 ones

The solution is 90

Question 13.

Find the difference between 254 and 125.

A. If you need to regroup to find the difference, explain how to do it. If you do not need to regroup, explain why not.

B. Find the difference.

Answer: 129

Question 14.

Put the steps in order to find 756 – 345.

Answer:

Question 15.

What is the difference between 408 + 240 and 259?

Answer:

408 + 240 = 648

648 – 259 = 389

Question 16.

Use place value to subtract 639 from 737. How many times do you have to regroup?

A. 3

B. 2

C. 1

D. 0

Answer: 2

Question 17.

Subtract.

457 – 338

A. 109

B. 119

C. 121

D. 129

Answer:

457 – 338 = 119

Thus the correct answer is option B.

Question 18.

Subtract 246 from 332.

Answer:

332 – 246 = 82

### Topic 9 Performance Task

**Video Arcade**

Nita, Arif, and Sarah have been playing games at the video arcade.

The Tickets Estimates list below shows the number of tickets the friends estimated they would win before they started playing.

The Tickets Won table shows the numbers of tickets each friend won.

**Tickets Estimates**

• Nita estimated she would win 165 tickets.

• Arif estimated he would win 150 tickets.

• Sarah estimated she would win 175 tickets.

Question 1.

How many tickets did each of the friends win in all?

Answer:

Tickets won playing sports games by Nita = 96 + 112 = 208

Tickets won playing sports games by Arif = 94 + 91 = 185

Tickets won playing sports games by Sarah= 104 + 117 = 221

208 + 185 + 221 = 614 tickets

Question 2.

Show how many more tickets each friend won than his or her estimate.

Answer:

Question 3.

Arif says if he won 24 more tickets, he would have won more tickets than Nita. Is he correct? Explain.

Answer:

Tickets won playing sports games by Nita = 96 + 112 = 208

Tickets won playing sports games by Arif = 94 + 91 = 185

208 – 185 = 23

Question 4.

The three friends put all of their tickets together. How many tickets did they win in all?

Answer:

Tickets won playing sports games by Nita = 96 + 112 = 208

Tickets won playing sports games by Arif = 94 + 91 = 185

Tickets won playing sports games by Sarah= 104 + 117 = 221

208 + 185 + 221 = 614 tickets

Tickets can be used to buy prizes. The Arcade Prizes table shows how many tickets each prize costs.

Use the Arcade Prizes table to answer Question 5.

Question 5.

Use the total number of tickets you found in Question 4. The 3 friends will use this number of tickets to get 1 prize each and 1 more prize as a gift. Stuffed Animal

There are 2 rules the friends must follow.

• They cannot use more than their total number of tickets.

• After their purchases, they do not want more than 50 tickets remaining.

**Part A**

Arif starts a prize log to record the prizes they will get. In the table below, record some prizes the friends could choose, the cost of the prize, and show how many tickets they will have left.

**Part B**

If the friends made your choices from Part A, how many of their tickets would they use to get prizes? Explain how you found the answer.

Answer: