## Envision Math Common Core 4th Grade Answers Key Topic 2 Fluently Add and Subtract Multi-Digit Whole Numbers

Essential Questions:
How can sums and differences of whole numbers be estimated? What are standard procedures for adding and subtracting whole numbers?

enVision STEM Project: The World’s Fastest Vehicles
Do Research Since 1970, the speed record has been broken many times. Use the Internet or other sources to find five vehicles that can go faster than 1,000 kilometers per hour.
Journal: Write a Report Include what you found. Also in your report:

• Make a table that includes the type of vehicle, whether the vehicle moves on land, water, or in space, and the speed of the vehicle.
• Use place value to find the fastest and the slowest vehicle in your table.
• Calculate the difference between the speeds of two of the vehicles in your table.

Review What You Know

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

• equation
• estimate
• period
• rounding

Question 1.
An __________ is an approximate number or answer.
An estimate is an apporoximate number or answer.

Question 2.
A process that determines which multiple of 10, 100, 1,000, and so on a number is closest to is called _________.
A process that determines which multiple of 10, 100, 1000, and So on a number is closest to is called rounding.

Question 3.
A number sentence that uses the equal sign (=) to show two expressions have the same value is an __________.
A number sentence that uses the equal sign(=) to show two expressions have the same value is an equation.

Find each sum.
Question 4.
4 + 6
4 + 6 = 10

Question 5.
7 + 5
7 + 5 = 12

Explanation:
The sum of 7 and 5 is 12.

Question 6.
29 + 8
29 + 8 = 37

Explanation:
The sum of 29 and 8 is 37.

Question 7.
14 + 5
14 + 5 = 19

Question 8.
13 + 7
13 + 7 = 20

Explanation:
The sum of 13 and 7 is 20.

Question 9.
37 + 7
37 + 7 = 42

Question 10.
289 + 126
289 + 126 = 415

Explanation:
The sum of 289 and 126 is 415.

Question 11.
468 + 329
468 + 329 =797

Explanation:
The sum of 468 and 329 is 797.

Question 12.
157 + 211
157 + 211 = 368

Explanation:
The sum of 15 and 211 is 368.

Subtraction Facts and Mental Math

Find each difference.
Question 13.
27 – 3
27 – 3 = 24

Question 14.
6 – 4
6 – 4 = 2

Question 15.
15 – 8
15 – 8 = 7

Question 16.
11 – 8
11 – 8 = 3

Explanation:
The difference between 11 and 8 is 3.

Question 17.
66 – 2
66 – 2 = 64

Question 18.
17 – 8
17 – 8 = 9

Explanation:
The difference between 17 and 8 is 9.

Question 19.
416 – 404
416 – 404 = 12

Explanation:
The difference between 416 and 404 is 12.

Question 20.
220 – 205
220 – 205 = 15

Explanation:
The difference between 220 and 205 is 15.

Question 21.
148 – 106
148 – 106 = 132

Explanation:
The difference between 148 and 106 is 42.

Rounding

Question 22.
Construct Arguments Why does 843,000 round to 840,000 rather than 850,000 when rounded to the nearest ten thousand?

The rule for rounding to the nearest ten thousand is to look at the last four digits.If the last four digits are  5000 or greater, then we round our ten thousands digit up, and if it is less than 5000, then we keep our ten thousands digit the same.
So, 843,000 rounds downs to 840000.

Pick a Project

PROJECT 2A
What are the largest cities in your home state?
Project: Map the Population of Your State’s Largest Cities

PROJECT 2B
How did the United States become a nation?
Project: Write a Report on U.S. Expansion

PROJECT 2C
How do the sizes of the planets compare to the size of Earth?
Project: Make a Model of the Solar System

PROJECT 2D
How high is high?
Project: Compare Mountain Elevations

### Lesson 2.1 Finding Sums and Differences with Mental Math

Solve & Share
Luke collected 1,034 baseball cards, 1,289 football cards, and 1,566 hockey cards. Use mental math to find the number of cards in Luke’s collection. Solve this problem any way you choose.
I can … use properties and strategies to change a problem to add and subtract with mental math.

Look Back! Construct Arguments How could you use mental math to solve 1,289 + 1,566? 1,034 + 1,566? How is the thinking different?

Essential Question
How Can You Use Mental on Math to Solve Problems?

Visual Learning Bridge
Katy’s dad washes windows at one of the tallest buildings in Miami, the Four Seasons Hotel. He worked Saturdays in October and earned more money than in September. How much did he earn in the two months combined?
Find $1,985 +$2,595 with mental math.

Washing Windows Earned $1,985 in Sept. Earned$2,595 in Oct.
+5+10 +80 +500 +2,000
Make Ten

Break apart 1,985 to get a number that makes a ten, hundred, or thousand when added to 2,595. Then, use the Associative Property of Addition to change the grouping.
1,985 + 2,595
= (1,580 + 405) + 2,595
= 1,580 + (405 + 2,595)
= 1,580 + 3,000
= 4,580
Katy’s dad earned $4,580. Add On Break one addend apart and add on. You can start with either addend because of the Commutative Property of Addition. Katy’s dad earned$4,580.

Use Compensation
Add 15 to 1,985. Then subtract 15 from 2,595 to compensate. Adding 15 and subtracting 15 is the same as adding zero. Adding zero doesn’t change the sum because of the Identity Property of Addition.
1,985 + 2,595
= (1,985 + 15) + (2,595 – 15)
= 2,000 + 2,580
= 4,580

Convince Me! Use Structure How could you make ten by breaking apart 2,595?

Another Example!
Subtract 2,595 – 1,985 with mental math.

Count Up
Count from 1,985 up to 2,595.

Find how much you counted up.
5 + 10 + 595 = 610

Count Down
Count down 1,985 from 2,595.

Use Compensation
Adding the same amount to both numbers in a subtraction problem doesn’t change the difference.
1,990
2,510
(2,595 + 15) – (1,985 + 15)
= 2,610 – 2,000
= 610

Guided Practice

Do You Understand?
Question 1.
Explain how to find 2,987 + 4,278 with mental math. What property does your strategy use?
7265

Explanation:
Use Compensation
Add 13 to 2,987. Then subtract 13 from 4278 to compensate. Adding 13 and subtracting 13 is the same as adding zero. Adding zero doesn’t change the sum because of the Identity Property of Addition.
2987 + 4278
= (2987 + 13) + (4278 – 13)
= 3000 + 4265
= 7265
Therefore, the sum of 2987 and 4278 is 7265.

Do You Know How?
For 2-4, use mental math strategies to solve.
Question 2.
6,794 – 999

Explanation:
1+794+5000=5795
The difference between 6794 and 999 is 5795.

Question 3.
4,505 + 3,515
7620

Explanation:
Make Ten

Break apart 4505 to get a number that makes a ten, hundred, or thousand when added to 3515. Then, use the Associative Property of Addition to change the grouping.
4505 + 3115
= (4000+505) + 3115
= 4000 + (505 + 3115)
= 4000 + 3620
= 7620
Therefore, the sum of 4505 and 3115 is 7620.

Question 4.
9,100 + 2,130 + 900
7620

Explanation:
Make Ten

Break apart 9100 to get a number that makes a ten, hundred, or thousand when added to 2130 and 900. Then, use the Associative Property of Addition to change the grouping.
9100 + 2130 + 900
=(9000+100) + 2130 + 900
=9000 + (100+900) + 2130
=9000 + 1000 + 2130
=10000 + 2130
=12130
Therefore, the sum of 9100, 2130 and 900 is 12130.

Independent Practice

For 5-10, use mental math to solve.
Question 5.
7,000 – 827

Explanation:
3+170+6000=6173
The difference between 7000 and 827 is 6173.

Question 6.
1,225 + 975
2200

Explanation:
Use Compensation
Add 75 to 1,225. Then subtract 75 from 975 to compensate. Adding 15 and subtracting 15 is the same as adding zero. Adding zero doesn’t change the sum because of the Identity Property of Addition.
1,225 + 975
= (1225 + 75) + (975 – 75)
= 1300 + 900
= 2200
The sum of 1225 and 975 is 2200.

Question 7.
5,491 – 2,860

Explanation:
40+60+2491=2591
The difference between 5491 and 2860 is 2591.

Question 8.
6,686 – 1,443

Explanation:
7+50+500+4686=5243
The difference between 16686 and 1443 is 5243

Question 9.
8,375 + 31,145
39520

Explanation:
Make Ten

Break apart 8375 to get a number that makes a ten, hundred, or thousand when added to 31145. Then, use the Associative Property of Addition to change the grouping.
8375 + 31145
= (8000+375) + 31145
= 000 + (375 + 31145)
= 8000 + 31520
= 39520
Therefore, the sum of 8375 and 31145 is 39520.

Question 10.
23,100 + 74,900
98000

Explanation:
Make Ten

Break apart 23100 to get a number that makes a ten, hundred, or thousand when added to 74900. Then, use the Associative Property of Addition to change the grouping.
23100 + 74900
= (23000+100) + 74900
= 23000 + (100 + 74900)
= 23000 + 75000
= 98000
Therefore, the sum of 23100 and 74900 is 98000.

Problem Solving

For 11-12, use the table at the right.

Question 11.
Precision How much greater is the area of California than Montana? Explain how to use mental math to solve.

Question 12.
Round the land area of the state with the least number of square miles to the nearest ten thousand.

Question 13.
The town of Worman Grove has collected 28,481 pens for a school supplies drive. Their goal is 30,000 pens. Show how to use counting on to find how many more pens they need to reach their goal.

Question 14.
Conservationists weigh two Northern elephant seals. An adult seal weighs 6,600 pounds, and its pup weighs 3,847 pounds. What is their combined weight? Explain how to use mental math to solve.

Question 15.
Higher Order Thinking Is Kelly’s answer correct? What mistake did she make?
Kelly’s Work
5,356 + 2,398
= (5,356 + 2) +(2,398 + 2)
5,358 + 2,400 = 7,758
Kelly’s work is wrong.her mistake is she has to add and subtract the number if the question is to find the sum.

Explanation:
(5356-2) + (2398+2)
5354 + 2400
7754
Therefore 5356 + 2398 = 7754.

Assessment Practice

Question 16.
Use mental math to find 1,218 + 1,598.
A. 2,716
B. 2,720
C. 2,816
D. 2,820
C.2816

Explanation:
1218+1598
Break apart 1218 as 1000 and 218 and and the second part with 1598.
=(1000+218)+1598
=1000+(218+1598)
=1000+1816
=2816
1218+1598=2816

Question 17.
Use mental math to find 5,280 – 1,997.
A. 3,177
B. 3,180
C. 3,277
D. 3,283
D.3283

Explanation:
5280-1997
Adding the same amount to both numbers in a subtraction problem doesn’t change the difference
=(5280+3) – (1997+3)
=5283 – 2000
=3823
5280-1997=3823

### Lesson 2.2 Estimate Sums and Differences

Solve & Share
A manufacturer in Detroit produces three new cars that weigh 6,127 pounds, 4,652 pounds, and 3,393 pounds. If these are are loaded on a truck, has the truck reached its 15,000-pound maximum? Use an estimate to decide. Solve this problem any way you choose.
I can … use rounding and place value to estimate sums and differences.

Explanation:
When these three cars are loaded in the truck, the truck doesn’t reach the maximum limit of 15000pounds as the estimated total weight of the three cars is 14200.

Look Back! Why can you solve the problem using only an estimate rather than finding the exact weight of the three cars?

Essential Question
How Can You Estimate Sums and Differences of Whole Numbers?
We can estimate the sums and difference of whole numbers by rounding of them to the nearest hundreds and thousands.

Visual Learning Bridge
Books, magazines, and movies were checked out of the public library. About how many more books were checked out than magazines and movies combined?

Estimate: Round to the nearest thousand.
Find the number of magazines and movies.

Subtract the number of magazines and movies from the rounded number of books.
13,000 – 6,000 = 7,000
About 7,000 more books were checked out.

Estimate: Round to the nearest hundred.
Find the number of magazines and movies.

Subtract the number of magazines and movies from the rounded number of books.
12,600 – 6,400 = 6,200
About 6,200 more books were checked out.

Convince Me! Construct Arguments The head librarian at the public library says she will establish a separate checkout desk for magazines and movies if the difference between the number of books and the number of these other materials is greater than 6,500. Which of the estimates above should you use to help her make her decision? Explain.

Another Example!
Decide if each computation is reasonable.
You can use an estimate to decide whether or not an exact answer is reasonable.
39,482 + 26,357 = 65,839
39,482 + 26,357 is about 40,000 + 26,000 = 66,000
The sum, 65,839, is reasonable because it is close to the estimate of 66,000.

8,215 – 5,852 = 3,643
8,215 – 5,852 is about 8,000 – 6,000 = 2,000
The difference, 3,643, is not reasonable because it is not close to the estimate of 2,000.

Guided Practice

Do You Understand?
Question 1.
Is 2,793 a reasonable difference for 6,904 – 4,111? Explain.

Explanation:
Yes, 2793 is a reasonable difference for 6,904 – 4,111 as estimated difference is 2800 and 2793 is very close to 2800.

Do You Know How?
For 2-4, estimate each sum or difference.
Question 2.

Explanation:
When rounded to the nearest hundreds,
The estimated sum is 9400.

Question 3.

Explanation:
When rounded to the nearest hundreds,
The estimated sum is 88500.

Question 4.

Explanation:
When rounded to the nearest hundreds,
The estimated difference is 13200.

Independent Practice

Leveled Practice For 5-13, estimate each sum or difference.
Question 5.

Explanation:
When rounded to the nearest thousands,
The estimated sum is 8000.

Question 6.

Explanation:
When rounded to the nearest hundreds,
The estimated difference is 515400.

Question 7.

Explanation:
When rounded to the nearest ten thousands,
The estimated sum is 110000.

Question 8.

Explanation:
When rounded to the nearest hundreds,
The estimated sum is 4300.

Question 9.

Explanation:
When rounded to the thousands
The estimated sum is 766200.

Question 10.

Explanation:
When rounded to the nearest hundreds,
The estimated difference is 14260.

Question 11.
485,635 – 231,957

Explanation:
When rounded to the nearest hundreds,
The estimated difference is 253600.

Question 12.
9,668 – 2,489

Explanation:
When rounded to the nearest hundreds,
The estimated difference is 7200.

Question 13.
368,545 + 114,254

Explanation:
When rounded to the nearest hundreds,
The estimated sum is 482800.

Problem Solving

Question 14.
The table shows the number of students at each school in the district. Is 2,981 reasonable for the total number of students at Wilson Elementary and Kwame Charter School? Explain.

Explanation:
When rounded to the nearest hundreds,
The estimated sum is 3000.
Therefore, as 2,981 is close to 3000, it is reasonable for the total number of students at Wilson Elementary and Kwame Charter School

Question 15.
enVision® STEM A satellite moves at a speed of 27,950 kilometers per hour. A satellite at a higher orbit travels at a speed of 11,190 kilometers per hour. About how much faster is one satellite than the other? Explain how to estimate.

Explanation:
When rounded to nearest thousands,
The estimated difference is 17000.

Question 16.
Critique Reasoning Elle says, “When rounding to the nearest thousand, 928,674 rounds to 930,000.” Do you agree? Explain.
No, I don’t agree with Elle as she rounded of to the nearest then thousands rather tha nearest thousand.
The nearest thousand for 928674 is 929000.
When we round of o the nearest thousand we have to look at the last three digits and if it lessthan 500 we hav eto round of to the same digit in the thousands place, if it is more than 500 then we have to roundof to the net thousand than the digit in thousands place.

Question 17.
Higher Order Thinking A football team needs to sell at least 20,000 tickets to two games to cover expenses. They sell 10,184 tickets to one game and 9,723 to the other. Estimate by rounding to the nearest thousand and by rounding to the nearest hundred. Did the team sell enough tickets? Explain your answer.

Explanation:
The estimated sum of tickets sold when rounded to hundreds is 20900
The estimated sum of tickets sold when rounded to thousands is 20000
As both sums are same or close to 20000.
Therefore, the team could sell enough ticketsto cover their expenses.

Assessment Practice

Question 18.
Last week, Mallory flew two round trips. They were 3,720 miles and 5,985 miles. Which is the best estimate of the total distance Mallory flew?
A. 11,000 miles
B. 9,700 miles
C. 8,700 miles
D. 8,000 miles
B.9700

Explanation:
The sum of miles Mallory flew when rounded to hundreds is 9700,
The sum of miles Mallory flew when rounded to thousands is 10000,
As the option B.9700 is close to the estimates So, rounded to hundreds is the best estimate.

Question 19.
Use estimation to decide which is a reasonable difference.
38,041 – 19,558
A. 21,374
B. 20,973
C. 18,473
D. 16,483
C.18473

Explanation:
As the estimated difference whrn roundrev to the nearest hundreds is 18400 and as 18473 is close to 18400, 18473 is reasonable.

### Lesson 2.3 Add Whole Numbers

Solve & Share
Students collect empty plastic water bottles to recycle. How many bottles were collected in the first two months? How many bottles were collected in all three months? Solve this problem using any strategy you choose.
I can … connect place-value concepts to using addition algorithms.

Look Back! When adding, how do you know when there are enough tens to make one hundred?

Essential Question
How Do You Add Whole Numbers Efficiently?

Visual Learning Bridge
The Florida Legislature set a statewide recycling goal. To help meet this goal, Kennedy Elementary school students collected newspaper. How many pounds of newspaper did they collect in all?
Estimate.
350 + 250 = 600

Convince Me! Use Structure in the problem above, when you add partial sums you can add the ones first or the hundreds. Can you do the same when you add using the standard algorithm?

Guided Practice

Do You Understand?
Question 1.
When you place a 1 above the tens values, what does it mean?
If i place 1 above the tens values it means that i regrouped ones.

Question 2.
When you place a 1 above the hundreds values, what does it mean?
If i place 1 above the hundreds values it means that i regouped tens.

Do You Know How?
Find the sum by using partial sums and by using the standard algorithm.
Question 3.

Explanation:
The sum of 378 and 557 is 935.

Find each sum using the strategy you choose.
Question 4
a.

Explanation:
The sum of 678 and 253 is 931.

b.

Explanation:
The sum of 325 and 256 is 581.

c.

Explanation:
The sum of 185 and 253 is 438.

Independent Practice

In 5-16, find each sum.
Question 5.

Explanation:
The sum of 148 and 157 is 305.

Question 6.

Explanation:
The sum of 389 and 461 is 850.

Question 7.

Explanation:
The sum of 365 and 458 is 823.

Question 8.

Explanation:
The sum of 126 and 138 is 264.

Question 9.

Explanation:
The sum of 371 and 454 is 825.

Question 10.

Explanation:
The sum of 357 and 498 is 855.

Question 11.
142 + 178

Explanation:
The sum of 142 and 178 is 320.

Question 12.
565 + 694

Explanation:
The sum of 565 and 694 is 1259.

Question 13.
375 + 548

Explanation:
The sum of 375 and 548 is 923.

Question 14.
718 + 865

Explanation:
The sum of 718 and 865 is 1583.

Question 15.
909 + 624

Explanation:
The sum of 909 and 624 is 1533.

Question 16.
129 + 587

Explanation:
The sum of 129 and 587 is 716.

Problem Solving

Question 17.
Construct Arguments Harmony solved this problem using the standard algorithm, but she made an error. What was her error, and how can she fix it?

Explanation:
The sum of 437 and 175 is 612.
Harmony didnot regroup tens.she should regroup tens and place 1 above the hundreds place to solve the problem.

Question 18.
Higher Order Thinking For which problems would you use a mental strategy or the standard algorithm to solve? Explain.
499 + 121
827 +385
175 + 325
I use mental strategy to solve 499+121 and 175+325 as the number in hundreds place is small and it is easy to slove mentally, I use standard algorithm to solve 827+385 as the number in hundreds place is big.

Question 19.
A Little League team played a doubleheader (two back-to-back baseball games). The first game lasted 155 minutes. The second game lasted 175 minutes. There was a 30-minute break between games. What was the total time of the doubleheader?

Explanation:
A Little League team played a doubleheader, The first game lasted 155 minutes. The second game lasted 175 minutes. There was a 30-minute break between games.
To find the total time of the doubleheader we need to add 155, 165 and 30.
The the total time of the doubleheader is 360.

Assessment Practice

Question 20.
Select all the correct sums.
☐ 742 + 353 = 1,095
☐ 428 + 247 = 665
☐ 604 + 684 = 1,288
☐ 735 + 298 = 1,033
☐ 912 + 198 = 1,010

Explanation:
The marked sums are correct.

Question 21.
What is the missing digit in the addition problem?

Explanation:
To find the missing number first subtract 1004 and 659, we get 345 as the answer.The missing tens is 4.

### Lesson 2.4 Add Greater Numbers

Solve & Share
Erica’s class collected 4,219 bottles for the recycling center. Ana’s class collected 3,742 bottles. Leon’s class collected 4,436 bottles. How many bottles did the three classes collect? Solve this problem any way you choose.
I can … use the standard algorithm and place value to add multi-digit numbers.

Look Back! Generalize Which properties allow you to change the order and grouping of numbers to add? How did you use these properties?

Essential Question
baby How Do You Add Greater Numbers?

Visual Learning Bridge
20,000 + 4,595 = 24,595

Step 1
Use the standard algorithm for addition
To add 24,595 + 19,255, add the ones, then the tens, and then the hundreds. Regroup if necessary

Step 2
Add the thousands and the ten thousands. Regroup if necessary.

The remodeled stadium will have 43,850 seats.
You can add two or more numbers when you line up the numbers by place value. Add one place at a time.

Step 3

43,850 is close to the estimate of 44,000, so the answer is reasonable.

Convince Me! Construct Arguments When using the standard algorithm to add 24,595 + 19,255, how do you regroup 1 ten + 9 tens + 5 tens?

Another Example!
Find 30,283 + 63,423 + 6,538.
Estimate:
30,000 + 63,000 + 7,000 = 100,000

The sum is reasonable because it is close to the estimate of 100,000.

Guided Practices

Do You Understand?
Question 1.
When adding 36,424 and 24,482, why is there no regrouping in the final step?

Explanation:
When 36424 and 24482 are added there is no regrouping in the final step because the sum of the final numbers donot exceed 9.

Question 2.
Science-volunteer teams catalog 7,836 species of insects and 4,922 species of spiders. How many species did the volunteers catalog?

Explanation:
12758 species the volunteers cataloged.

Do You Know How?
Question 3.

Explanation:
The sum of 14926 and 3382 is 18308.Answer is reasonable as the estimate 18000 is close to the answer.

Question 4.

Explanation:
The sum of 423156 and 571607 is 994763.Answer is reasonable as the estimate 99500 is close to the answer.

Question 5.

Explanation:
The sum of 3258 and 1761 is 5019.Answer is reasonable as the estimate 5100 is close to the answer.

Question 6.

Explanation:
The sum of 82385 and 49817 is 132202.Answer is reasonable as the estimate 132000 is close to the answer.

Independent Practice

Question 7.

Explanation:
The sum of 14312 and 9617 is 23929.Answer is reasonable as the estimate 24000 is close to the answer.

Question 8.

Explanation:
The sum of 275558 and 605131 is 880689.Answer is reasonable as the estimate 881000 is close to the answer.

Question 9.

Explanation:
The sum of 38911 and 45681 is 84592.Answer is reasonable as the estimate 85000 is close to the answer.

Question 10.

Explanation:
The sum of 5801 and 4189 is 9990.Answer is reasonable as the estimate 10000 is close to the answer.

Question 11.

Explanation:
The sum of 8818 and 1182 is 10000.Answer is reasonable as the estimate 10000 is close to the answer.

Question 12.

Explanation:
The sum of 5555 and 7412 is 12967.Answer is reasonable as the estimate 13000 is close to the answer.

Question 13.

Explanation:
The sum of 21009 and 5529 is 26538.Answer is reasonable as the estimate 26600 is close to the answer.

Question 14.

Explanation:
The sum of 30080 and 19187 is 49267.Answer is reasonable as the estimate 49000 is close to the answer.

Question 15.
29,634 + 12,958 + 6,835

Explanation:
The sum of 29634, 12958 and 6835 is 49427.

Question 16.
64,673 + 48,262 + 8,918

Explanation:
The sum of 64673, 48262 and 8918 is 121853.

Problem Solving

Question 17.
Aubrey writes a blog. 29,604 people read her first post. The next week, 47,684 people read her second post. Aubrey’s third post had 41,582 readers. What is the total number of readers?

Explanation:
The sum of 29604, 47684 and 4152 is 81440.
Therefore the total number of readers are 81440.

Question 18.
Write the number name for 21,604.
Number name of 21604 is Twenty one thousand six hundred four.

Question 19.
Higher Order Thinking Explain the mistake made when finding the sum at the right. What is the correct sum?

The correct sum is 872879.

Explanation:
The sum of 638528 and 234351 is 872879.
The mistake is regrouping 8 and 4 thousands as 1 tensthousand is not done in the given sum.

Question 20.
Number Sense Maria added 45,273 and 35,687 and got a sum of 70,960. Is Maria’s answer reasonable? Explain.

Explanation:
Estimate:
45273-45000, 35687-36000
45000+36000=81000
The sum of 45273 and 35687 is 80960.Maria’s answer is not reasonable as the estimate is not close to the answer.

Question 21.
Make Sense and Persevere There were 130,453 pairs of skates rented at an ice rink in one year. The next year, 108,626 pairs were rented. The following year 178,119 pairs were rented. How many pairs were rented during the busiest two years? How many pairs were rented during all three years?

Explanation:
308572 pairs were rented during the busiest two years.
417198 pairs were rented during all three years

Assessment Practice

Question 22.
Select all the correct sums.
☐ 5,742 + 8,353 = 14,095
☐ 9,428 + 18,247 = 27,665
☐ 29,604 + 47,684 = 77,288
☐ 66,288 + 145,280 = 211,568
☐ 235,912 + 19,847 = 434,382

Question 23.
Select all the addition expressions that have a sum of 89,405.
☐ 78,487 + 7,998
☐ 79,562 + 9,843
☐ 2,222 + 77,183
☐ 52,514 + 36,891
☐ 6,573 + 82,832

### Lesson 2.5 Subtract Whole Numbers

Solve & Share
Carly’s parents own a motel in Orlando with 224 rooms. Last night, 176 rooms were rented. How many rooms were not rented? Solve this problem using any strategy you choose.
I can … connect place-value concepts to using the standard algorithm for subtraction

Look Back! How can you use properties to find the number of rooms not rented?

Essential Question
How Can You Subtract Whole Numbers Efficiently?

Visual Learning Bridge
The movie theater already sold 172 seats. How many seats are still available?
Subtract 358 – 172.
Estimate: 400 – 200 = 200

What You Show

What You Write

Convince Me! Use Structure How many times do you need to regroup to subtract 483 – 295? Explain.

Guided Practice

Do You Understand?
Question 1.
To subtract 859 – 583, how do you regroup 8 hundreds 5 tens?

Explanation:
The difference of 859 and 583 is 276.
I regrouped 8hundreds 5tens as 7hundreds 15tens.

Question 2.
What do you need to regroup to subtract 753 – 489 using the standard algorithm?

Explanation:
The difference of 753 and 489 is 264.
I need to regroup 5tens 3ones and 7hundreds 4tens.

Do You Know How?
In 3-6, subtract. Use an estimate to check that your answer is reasonable.
Question 3.

Estimate: 154 — 150, 89 — 90
150-90 = 60

Explanation:
The difference of 154 and 89 is 65.
The difference 65 is reasonable as it is close to the estimated difference 60.

Question 4.

Estimate: 592 — 590, 357 — 360
590-360=230

Explanation:
The difference of 592 and 357 is 235.
The difference 235 is reasonable as it is close to the estimated difference 230.

Question 5.

Estimate: 915 — 920, 288 — 290
920-290=630

Explanation:
The difference of 915 and 288 is 627.
The difference 627 is reasonable as it is close to the estimated difference 630.

Question 6.

Estimate: 743 — 740, 694 — 690
740-690=50

Explanation:
The difference of 743 and 694 is 49.
The difference 49 is reasonable as it is close to the estimated difference 50.

Independent Practice

In 7-18, subtract. Use an estimate to check that your answer is reasonable.
Question 7.

Estimate: 289 — 290, 145 — 150
290-150=140

Explanation:
The difference of 289 and 145 is 144.
The difference 144 is reasonable as it is close to the estimated difference 140.

Question 8.

Estimate: 326 — 330, 184 — 180
330-180=150

Explanation:
The difference of 326 and 184 is 142.
The difference 142 is reasonable as it is close to the estimated difference 150.

Question 9.

Estimate: 736 — 740, 218 — 220
740-220=520

Explanation:
The difference of 736 and 218 is 518.
The difference 518 is reasonable as it is close to the estimated difference 520.

Question 10.

Estimate: 525 — 530, 267 — 270
530-270=260

Explanation:
The difference of 525 and 267 is 258.
The difference 258 is reasonable as it is close to the estimated difference 250.

Question 11.

Estimate: 683 — 680, 295 — 300
680-300=380

Explanation:
The difference of 683 and 295 is 388.
The difference 388 is reasonable as it is close to the estimated difference 380.

Question 12.

Estimate: 847 — 850, 387 — 390
850-390=460

Explanation:
The difference of 847 and 837 is 460.
The difference 460 is reasonable as it is close to the estimated difference 460.

Question 13.

Estimate: 475 — 480, 98 — 100
480-100=380

Explanation:
The difference of 475 and 98 is 377.
The difference 377 is reasonable as it is close to the estimated difference 380.

Question 14.

Estimate: 826 — 830, 184 — 180
830-180=650

Explanation:
The difference of 826 and 184 is 642.
The difference 642 is reasonable as it is close to the estimated difference 650.

Question 15.

Estimate: 936 — 940, 218 — 220
940-220=720

Explanation:
The difference of 936 and 218 is 718.
The difference 718 is reasonable as it is close to the estimated difference 720.

Question 16.
167 – 79

Explanation:
The difference of 167 and 79 is 88.

Question 17.
284 – 167

Explanation:
The difference of 284 and 167 is 117.

Question 18.
817 – 548

Explanation:
The difference of 817 and 548 is 269.

Problem Solving

Question 19.
How much greater is the area of Hernando County than Union County?

Explanation:
The difference of 473 and 244 is 229.
Therefore, the area of Hernando County is 229squaremiles than Union County.

Question 20.
Make Sense and Persevere How much greater is the area of Monroe County than the area of Union County and Hernando County combined? Explain.
The area of union country and hernando country combines is 719sqmiles

Explanation:
The difference of 983 and 719 is 264.
Therefore, the area of Monroe County is 264sqmiles greater than the area of Union County and Hernando County combined.

Question 21.
Population density is measured in people per square mile. It indicates how crowded an area is. How many more people per square mile does Brevard County have than neighboring Volusia County?

Explanation:
The difference of 535 and 449 is 86.
Therefore, Brevard County have 86more people per square mile than neighboring Volusia County .

Question 22.
Higher Order Thinking What mistake did Leon make? What is the correct difference?

Explanation:
The difference of 793 and 576 is 217.
The correct difference is 217,The mistake made by leon is he unnecessarily regrouped hundreds.to find the differene of the above numbers their is no need of regrouping hundreds.

Assessment Practice

Question 23.
What is the difference?

A. 1,183
B. 335
C. 266
D. 265
D.265.

Explanation:
The difference of 724 and 459 is 265.

Question 24.
What is the missing digit in the subtraction statement?

Explanation:
The difference of 634 and 297 is 337.
Therefore, the missing number in the subtraction statement is 9.

### Lesson 2.6 Subtract Greater Numbers

Solve & Share
Nevada has a land area of 109,781 square miles. Colorado has a land area of 103,642 square miles. How much larger is Nevada than Colorado? Solve this problem any way you choose.
I can … use the standard algorithm and place value to subtract whole numbers.

Look Back! Estimate the difference in the areas of the two states. Is your answer close to this estimate?

Essential Question
How Do You Subtract Greater Numbers Efficiently?

Visual Learning Bridge
Three of the country’s most scenic national parks are in Alaska. How much larger is the area of Gates of the Arctic than the combined area of Denali and Kenai Fjords?
Find the total area of Denali and Kenai Fjords.

Step 1
Find 34,287 – 21,893.
Subtract the ones. Regroup if necessary

Step 2
Subtract the tens, hundreds, thousands, and ten thousands.
Regroup if necessary

Gates of the Arctic is 12,396 square kilometers larger.

Step 3

Convince Me! Critique Reasoning The work shown is NOT correct. What errors were made? Show how to find the correct answer.

Another Example!
Find 38,792. – 33,215.
Estimate:
39,000 – 33,000 = 6,000

Guided Practice

Do You Understand?
Question 1.
In the subtraction problem above, why was the zero in the ten thousands place not written in the answer?

Question 2.
The total land area of New Jersey is 19,047 square kilometers. Write and solve an equation to show how to find how much more land area Gates of the Arctic has than New Jersey.
34287-19407 sqkm = 14880 sqkm

Explanation:
The Gates of the Arctic has 14880sqkilometers more land area than New Jersey.

Do You Know How?
Question 3.
139,484 – 116,691
Estimate: 140000-120000=20000

Explanation:
The difference of 139484 and 116691 is 22793.
The difference 22793 is reasonable as it is close to the estimate 20000.

Question 4.
2,164 – 1,398
Estimate:2200-1400=800

Explanation:
The difference of 2164 and 1398 is 766.
The difference 766 is reasonable as it is close to the estimate 800.

Question 5.
49,735 – 25,276
Estimate: 50000-25000=25000

Explanation:
The difference of 49735 and 25276 is 24459.
The difference 24459 is reasonable as it is close to the estimate 25000.

Question 6.
281,311 – 3,427
Estimate: 281000-3000=278000

Explanation:
The difference of 281311 and 3427 is 277884.
The difference 277884 is reasonable as it is close to the estimate 280000.

Independent Practice

Question 7.

Estimate: 82000-47000=35000

Explanation:
The difference of 82376 and 47294 is 35082.
The difference 35082 is reasonable as it is close to the estimate 35000.

Question 8.

Estimate: 654000-562000=92000

Explanation:
The difference of 653642 and 562410 is 91232
The difference 91232 is reasonable as it is close to the estimate 92000.

Question 9.

Estimate: 9000-4000=5000

Explanation:
The difference of 9128 and 3753 is 5375
The difference 5375 is reasonable as it is close to the estimate 5000.

Question 10.

Estimate: 43000-8000=35000

Explanation:
The difference of 42648 and 8169 is 34479
The difference 34479 is reasonable as it is close to the estimate 35000.

Question 11.

Estimate: 426000-87000=339000

Explanation:
The difference of 425637 and 86942 is 338695
The difference 338695 is reasonable as it is close to the estimate 339000.

Question 12.

Estimate: 8500-2000=6500

Explanation:
The difference of 8457 and 1946 is 6511
The difference 6511 is reasonable as it is close to the estimate 6500.

Question 13.

Estimate: 216000-176000=40000.

Explanation:
The difference of 215714 and 176313 is 39401
The difference 39401 is reasonable as it is close to the estimate 40000.

Question 14.

Estimate: 86000-74000=12000

Explanation:
The difference of 85968 and 74084 is 11884
The difference 11884 is reasonable as it is close to the estimate 12000.

Problem Solving

Question 15.
Reasoning A crayon company makes 87,491 blue crayons, 36,262 red crayons, and 25,063 gray crayons. How many more blue crayons are made than red and gray crayons combined?
There are 61325 red and gray crayons combined

Explanation:
The difference of 87491 and 61325 is 26166.
Therefore there are 26166 blur crayons are made more than red and grey crayons.

Question 16.
Number Sense Patrick subtracted 4,832 – 2,322 and got 2,510. Is his difference reasonable? Explain.

Explanation:
Estimate: 4800-2300=2500
The difference 2510 is reasonable as it is close to estimate 2500.

Question 17.
Higher Order Thinking Nadia found 9,476 – 8,185 using the algorithm shown. Show how to find 1,784 – 1,339 with Nadia’s algorithm.
9,476 – 8,185 = 1,000 + 300 – 10 + 1
= 1,291
1784-1339 = 500-100+40+5

Explanation:
Using Nadia’s algorithm i shown the difference 1784 and 1339 by adding and subtracting numbers.

Question 18.
How many more people attended the street fair in 2019 than in 2017 and 2018 combined?

193301 people attended the street fair in 2017 and 2018 combined

Explanation:
The difference of 362839 and 169538 is 169538.
Therefore, 169538 more people attended the street fair in 2019 than in 2017 and 2018 combined.

Question 19.
On Monday, from the peak of Mount Kilimanjaro, a group of mountain climbers descended 3,499 feet. On Tuesday, they descended another 5,262 feet. How many feet did the mountain climbers descend after 2 days? How many more feet do they have to descend to reach the bottom?

8761 feet the mountain climbers descend after 2 days

Explanation:
The difference of 19341 and 8761 is 10580.
10580 feet they have to descend to reach the bottom.

Assessment Practice

Question 20.
What is the missing digit in the subtraction statement?

Explanation:
The difference of 365928 and 187669 is 178259.
So, the missing digit in the number 178259 in the above question is 8.

Question 21.
What is the difference 62,179 – 31,211?
A. 31,968
B. 30,986
C. 30,968
D. 30,000
C.30968

Explanation:
The difference of 62179 and 31211 is 30968.

### Lesson 2.7 Subtract Across Zeros

Solve & Share
London, England, is 15,710 kilometers from the South Pole. Tokyo, Japan, is 13,953 kilometers from the South Pole. How much farther is London than Tokyo from the South Pole? Solve this problem any way you choose.
I can … use the standard algorithm to subtract from numbers with zeros.

Look Back! Explain how you decided what operation to use to find how much farther London is than Tokyo from the South Pole.

Essential Question
How Do You Subtract Across Zeros?

Visual Learning Bridge
A music hall is hosting a concert. The hall sells 4,678 tickets to the show. How many tickets are still available?

Regroup.

Subtract.

Since the difference 1,322 is close to the estimate 1,300, the difference is reasonable.
There are still 1,322 tickets available for the concert.

Convince Me! Use Structure How would you regroup if the hall had 5,900 seats?

Guided Practice

Do You Understand?
Question 1.
Leesa used compensation to solve the problem on the previous page. She subtracted (6,000 – 1) – (4,678 – 1) = 5,999 – 4,677 = 1,322. How could you use Leesa’s approach to subtract 5,000 – 1,476?
3524

Explanation:
Using Leesa’s approach we can solve 5000-1476 by subrtacting 1 from both the numbers as shown below
=(5000-1)-(1476-1)
=4999-1475
=3524
Therefore, the difference of 5000 and 1476 is 3524.

Question 2.
One passenger flew 11,033 kilometers from Oslo to Lima. Another passenger flew 8,593 kilometers from Oslo to Los Angeles. How many more kilometers was the flight to Lima?

Do You Know How?
For 3-8, subtract.
Question 3.

Question 4.

Question 5.

Question 6.

Question 7.
101,001 – 8,915

Question 8.
9,050 – 3,461

Independent Practice

For 9-23, subtract.
Question 9.

Question 10.

Question 11.

Question 12.

Question 13.

Question 14.

Question 15.

Question 16.

Question 17.

Question 18.

Question 19.

Question 20.

Question 21.
6,090 – 5,130

Question 22.
11,246 – 9,489

Question 23.
790,008 – 643,829

Problem Solving

Question 24.
Construct Arguments Will the difference between 44,041 and 43,876 be greater or less than 1,000? Explain.

Question 25.
Vocabulary Define variable and give an example of how a variable is used in an equation.

For 26-27, use the table at the right.

Question 26.

Question 27.

Assessment Practice

Question 28.
Select all the correct differences.
☐ 5,000 – 1,856 = 3,244
☐ 10,700 – 8,243 = 2,457
☐ 64,002 – 43,178 = 20,934
☐ 98,000 – 59,214 = 38,786
☐ 600,482 – 428,531 = 171,951

Question 29.
Find the difference.

A. 17,355
B. 20,757
C. 21,757
D. 98,243

### Lesson 2.8 Problem Solving

Reasoning
Solve & Share
A group of students collected donations for a toy drive. They collected a total of 3,288 toys one week and 1,022 toys the next week. They donated 1,560 toys to the Coal City Charity and the rest were donated to Hartville Charity. How many toys were donated to Hartville Charity? Use reasoning about numbers to show and explain how the two quantities of toys given to charity are related.
I can … make sense of quantities and relationships in problem situations.

Thinking Habits

• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?

Look Back! Reasoning Over three weeks, the students collected a total of 8,169 toys. How many toys did they collect in the third week? Complete the bar diagram to show your reasoning. Did the students collect more toys in the third week than in weeks 1 and 2 combined? Explain.

Essential Question
How Can You Use Quantitative Reasoning to Solve Problems?

Visual Learning Bridge
Kara and Carl join their mother on a boat off the coast of the Florida Keys. Their mother is a scientist studying blue marlins. Each child gets to help weigh two marlins. How much more did Kara’s marlins weigh than Carl’s?

How can you draw a diagram to help reason how the numbers in the problem are related?
I can represent the relationship between the numbers with a bar diagram.

How can I use reasoning to solve this problem?
I can

• identify the quantities I know.
• draw diagrams and write equations to show relationships.
• connect the solution back to the real world problem.

Here’s my thinking.
K = the total weight of Kara’s marlins, and C = the total weight of Carl’s marlins.

Kara’s marlins weighed 299 pounds more than Carl’s.

Convince Me! Reasoning Write a problem that can be solved using the bar diagram below. Write an equation to solve. Use reasoning to think about the meaning of each number before starting.

Guided Practice

Reasoning
A manufacturer shipped 12,875 fidget spinners one week and 9,843 of them were sold. The next week, they shipped 19,175 and 12,752 of them were sold. How many fidget spinners had not sold yet?

Question 1.
What quantities are given in the problem, and what do the numbers mean?

Question 2.
Use the bar diagrams that show the relationships of the numbers in the problem. Write and solve equations which could be used to find f, the spinners not sold the first week; s, the spinners not sold the second week; and t, the total spinners not sold.

Independent Practice

Reasoning A wall is being built with 16,351 stones. The builders have placed 8,361 stones, and they have 7,944 stones left. Do they have enough stones? How many more stones do they need?

Use Exercises 3-5 to answer the question.
Question 3.
What quantities are given in the problem, and what do the numbers mean?

Question 4.
Complete the bar diagram to show how to find s, the number of stones the builders have in all. Then, write and solve an equation. Do they have enough? Explain.

Question 5.
Complete the bar diagram to show how to find the difference, d, of how many more stones the builders need. Then, write and solve an equation.

Problem Solving

Bird Migration Ornithology is the scientific study of birds. Every year, some birds travel great distances, or migrate, to find food and start families. The table shows the distances five species of birds flew over one year, as observed by an ornithologist. How much farther did the Arctic Tern fly than the Pectoral Short-Tailed Shearwater and the Pied Wheatear combined?

Question 6.
Reasoning What quantities are given in the problem and what do the numbers mean?

Question 7.
Make Sense and Persevere What strategy can you use to solve the problem?

Question 8.
Make Sense and Persevere What is the hidden question?
The hidden questions are the questions which must be answered before answering the main question asked in the problem.

Question 9.
Model with Math Complete the bar diagrams to show how to find the answer to the hidden question and the main question. Write and solve equations.

#### Topic 2 Fluency Practice Activity

Shade a path from START to FINISH. Follow the sums that are correct. You can only move up, down, right, or left.
I can.. add multi-digit whole numbers.

### Topic 2 Vocabulary Review

Understand Vocabulary
Word List

• algorithm
• compensation
• inverse operations
• variable

Question 1.
Circle the property of addition shown by 126 + 0 = 126.
Associative
Commutative
Identity

Question 2.
Circle the property of addition shown by 21 + 34 = 34 + 21.
Associative
Commutative
Identity

Question 3.
Circle the property of addition shown by (1 + 3) + 7 = 1 + (3 + 7).
Associative
Commutative
Identity

Question 4.
Draw a line from each term to its example.

Use Vocabulary in Writing
Question 5.
Rob found 103 + 1,875 = x using mental math. Use at least 3 terms from the Word List to describe how Rob could find the sum.

### Topic 2 Reteaching

Set A pages 37-40

Find 3,371 + 2,429. Use mental math.
Make Ten
3,371 + 2,429 = 3,371 + (29 + 2,400)
= (3,371 +29) + 2,400
= 3,400 + 2,400 = 5,800
S0, 3,371 + 2,429 = 5,800.

Remember to adjust the sum or difference when you use the compensation strategy.
Question 1.
4,153 + 2,988

Question 2.
92,425 + 31,675

Question 3.
5,342 + 1,999

Question 4.
22,283 – 14,169

Question 5.
47,676 – 16,521

Question 6.
1,089 – 961

Set B pages 41-44

Estimate the sum by rounding each number to the nearest ten thousand.

241,485 rounds to 240,000.
429,693 rounds to 430,000.

Remember that you can round numbers to any place when estimating sums and differences.

Estimate each sum or difference.
Question 1.
652,198 + 49,753

Question 2.
8,352 – 3,421

Question 3.
17,586 – 9,483

Question 4.
823,725 + 44,851

Question 5.
1,440 – 933

Question 6.
55,748 – 28,392

Question 7.
4,981 + 6,193

Question 8.
995,275 + 4,921

Set C pages 45-52

Find 72,438 + 6,854.

The answer 79,292 is close to the estimate of 79,000, so the answer is reasonable.

Remember to regroup if necessary when adding whole numbers.
Question 1.

Question 2.

Question 3.
215 + 8,823

Question 4.
142,968 + 44,456

Question 5.
2,417 + 3,573

Question 6.
572,941 + 181,662

Set D pages 53-60

Find 52,839 – 38,796.
Estimate: 53,000 – 39,000 = 14,000

Remember that you may need to regroup to subtract.

Question 1.

Question 2.

Question 3.
41,542 – 32,411

Question 4.
4,978 – 2,766

Question 5.
735,184 – 255,863

Question 6.
44,558 – 22,613

Set E pages 61-64

Find 60,904 – 54,832.
Estimate: 61,000 – 55,000 = 6,000

Remember you may need to regroup more than one place at a time to subtract across zeros.
Question 1.

Question 2.

Question 3.
70,000 – 25,228

Question 4.
560,043 – 312,562

Question 5.
8,052 – 1,205

Question 6.
20,008 – 16,074

Set F pages 65-68

Thinking Habits

• What do the numbers and symbols in the problem mean?
• How are the numbers or quantities related?
• How can I represent a word problem using pictures, numbers, or equations?

Remember that you can draw a bar diagram and use it to reason about a problem.

Raahil traveled 11,469 kilometers from home to visit his mother’s family in Qatar. He then traveled 12,332 kilometers from Qatar to visit his father’s family in Brisbane, Australia.
Question 1.
Draw a bar diagram that shows the distance Raahil traveled to Brisbane.

Question 2.
Write and solve an equation for your bar diagram.

### Topic 2 Assessment Practice

Question 1.
The table shows the number of hot dogs Frank’s hot dog stand sold this weekend.

A. Estimate the number of hot dogs sold by rounding each number in the table to the nearest thousand and finding the sum.

B. Write and solve an equation to find how many hot dogs were sold.

Question 2.
Find 8,000 – 6,280.

Question 3.
Enter the missing digit to complete the subtraction.

Question 4.
Find the difference.

A. 6,811
B. 6,351
C. 6,333
D. 6,331

Question 5.
Complete the equation to make it true. Write your answer in the box.
12,769 + 16,065 = _________ + 15,402

Question 6.

Question 7.
Which of the following statements is true? Select all that apply.
☐ 12,395 + 14,609 = 27,004
☐ 76,237 – 4,657 = 42,430
☐ 67,407 – 38,227 = 29,180
☐ 69,844 + 1,014 = 70,452
☐ 34,980 – 1,999 = 32,981

Question 8.
Find the sum.

Question 9.
Sandra used addition properties to rewrite the equation below. Select all the equations Sandra might have written.
1,450 + 1,125 + 1,050 = n
☐ (1,400 + 1,100 + 1,000) + (50 + 25 + 50) = n
☐ 1,450 + 1,050 = n 1,125 + 1,050 + 1,450 = n
☐ 1,000 + 1,000 + 1,000 + 450 + 50 + 125 = 1
☐ (1,450 + 1,050) + 1,125 = n

Question 10.
Joe and Sara recorded the number of birds they saw in the park over two summers.

A. Write and solve equations to find how many more total birds Joe and Sara saw this year than last year.

B. Estimate how many more birds were seen in the park this year than last year by rounding each number in the table and solving the problem. Use the estimate to check if your answer to Part A is reasonable.

Taking Inventory Jiao runs a wholesale art supply website. She fills bulk orders for craft and hobby stores.
Question 1.
Part A
Crafts and Stuff ordered oak and ebony beads. Explain how to use mental math and properties of addition to find how many beads Jiao sent.

Part B
Jiao sends an order of oak and bayong beads to Jill’s Crafts and an order of ash and ebony beads to Create. How much larger is the order for Create? Write and solve equations to find j, the number of beads in the order to Jill’s Crafts; c, the number of beads in the order to Create; and d, the difference.

Question 2.
Part A
Write and solve an equation to show how many glass beads, b, Create will have if they order the bubble and smoky beads.

Part B
Jiao sends the molded and stained beads to Hometown Craft Supply. Explain how to use compensation to find how many more molded beads than stained beads were sent.