Practice with the help of enVision Math Common Core Grade 4 Answer Key Topic 2 Fluently Add and Subtract Multi-Digit Whole Numbers regularly and improve your accuracy in solving questions.

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

Addition Facts and Mental Math

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

Question 5.
7 + 5
Answer:
7 + 5 = 12

Explanation:
The sum of 7 and 5 is 12.

Question 6.
29 + 8
Answer:
29 + 8 = 37

Explanation:
The sum of 29 and 8 is 37.

Question 7.
14 + 5
Answer:
14 + 5 = 19

Question 8.
13 + 7
Answer:
13 + 7 = 20

Explanation:
The sum of 13 and 7 is 20.

Question 9.
37 + 7
Answer:
37 + 7 = 42

Question 10.
289 + 126
Answer:
289 + 126 = 415

Explanation:
The sum of 289 and 126 is 415.

Question 11.
468 + 329
Answer:
468 + 329 =797

Explanation:
The sum of 468 and 329 is 797.

Question 12.
157 + 211
Answer:
157 + 211 = 368

Explanation:
The sum of 15 and 211 is 368.

Subtraction Facts and Mental Math

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

Question 14.
6 – 4
Answer:
6 – 4 = 2

Question 15.
15 – 8
Answer:
15 – 8 = 7

Question 16.
11 – 8
Answer:
11 – 8 = 3

Explanation:
The difference between 11 and 8 is 3.

Question 17.
66 – 2
Answer:
66 – 2 = 64

Question 18.
17 – 8
Answer:
17 – 8 = 9

Explanation:
The difference between 17 and 8 is 9.

Question 19.
416 – 404
Answer:
416 – 404 = 12

Explanation:
The difference between 416 and 404 is 12.

Question 20.
220 – 205
Answer:
220 – 205 = 15

Explanation:
The difference between 220 and 205 is 15.

Question 21.
148 – 106
Answer:
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?

Answer:
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
Katy’s dad earned $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?
Answer:
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
Answer:

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

Question 3.
4,505 + 3,515
Answer:
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
Answer:
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
Answer:

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

Question 6.
1,225 + 975
Answer:
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
Answer:

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

Question 8.
6,686 – 1,443
Answer:

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

Question 9.
8,375 + 31,145
Answer:
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
Answer:
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.
Answer:

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

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.
Answer:

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.
Answer:

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
Answer:
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:
Add and subtract same number, the answer will not differ.
(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
Answer:
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
Answer:
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.

Answer:

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?
Answer:
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.
Answer:

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.

Answer:

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

Question 3.

Answer:

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

Question 4.

Answer:

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.

Answer:

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

Question 6.

Answer:

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

Question 7.

Answer:

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

Question 8.

Answer:

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

Question 9.

Answer:

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

Question 10.

Answer:

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

Question 11.
485,635 – 231,957
Answer:

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

Question 12.
9,668 – 2,489
Answer:

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

Question 13.
368,545 + 114,254
Answer:

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.

Answer:

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.
Answer:

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.
Answer:
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.
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
Answer:
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
Answer:
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?
Add 358 + 277.
Estimate.
350 + 250 = 600

Add using partial sums.
Add using the standard algorithm.

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?
Answer:
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?
Answer:
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.

Answer:

Explanation:
The sum of 378 and 557 is 935.

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

Answer:

Explanation:
The sum of 678 and 253 is 931.

b.

Answer:

Explanation:
The sum of 325 and 256 is 581.

c.

Answer:

Explanation:
The sum of 185 and 253 is 438.

Independent Practice

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

Answer:

Explanation:
The sum of 148 and 157 is 305.

Question 6.

Answer:

Explanation:
The sum of 389 and 461 is 850.

Question 7.

Answer:

Explanation:
The sum of 365 and 458 is 823.

Question 8.

Answer:

Explanation:
The sum of 126 and 138 is 264.

Question 9.

Answer:

Explanation:
The sum of 371 and 454 is 825.

Question 10.

Answer:

Explanation:
The sum of 357 and 498 is 855.

Question 11.
142 + 178
Answer:

Explanation:
The sum of 142 and 178 is 320.

Question 12.
565 + 694
Answer:

Explanation:
The sum of 565 and 694 is 1259.

Question 13.
375 + 548
Answer:

Explanation:
The sum of 375 and 548 is 923.

Question 14.
718 + 865
Answer:

Explanation:
The sum of 718 and 865 is 1583.

Question 15.
909 + 624
Answer:

Explanation:
The sum of 909 and 624 is 1533.

Question 16.
129 + 587
Answer:

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?

Answer:

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
Answer:
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?
Answer:

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
Answer:

Explanation:
The marked sums are correct.

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

Answer:

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
Plans for remodeling a sports stadium include adding an additional 19,255 seats. How many seats will be in the remodeled stadium?
Seats in the original stadium:
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
Use an estimate to check if your answer is reasonable.

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.
Explain how to check that your answer is reasonable.
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?
Answer:

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?
Answer:

Explanation:
12758 species the volunteers cataloged.

Do You Know How?
For 3-6, find each sum. Check that your answer is reasonable.
Question 3.

Answer:

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

Question 4.

Answer:

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

Question 5.

Answer:

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

Question 6.

Answer:

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

Independent Practice

For 7-16, find each sum. Check that your answer is reasonable.

Question 7.

Answer:

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

Question 8.

Answer:

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

Question 9.

Answer:

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

Question 10.

Answer:

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

Question 11.

Answer:

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

Question 12.

Answer:

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

Question 13.

Answer:

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

Question 14.

Answer:

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
Answer:

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

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

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?
Answer:

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.
Answer:
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?

Answer:
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.
Answer:

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?
Answer:

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
Answer:

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
Answer:

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?
Answer:

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?
Answer:

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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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
Answer:

Explanation:
The difference of 167 and 79 is 88.

Question 17.
284 – 167
Answer:

Explanation:
The difference of 284 and 167 is 117.

Question 18.
817 – 548
Answer:

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?

Answer:

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.
Answer:
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?
Answer:

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?

Answer:

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
Answer:
D.265.

Explanation:
The difference of 724 and 459 is 265.

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

Answer:

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
Operations that undo each other are inverse operations. Addition and subtraction have an inverse relationship. Add to check your answer.

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?
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.
Answer:
34287-19407 sqkm = 14880 sqkm

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

Do You Know How?
For 3-6, subtract. Estimate to check whether your answers are reasonable.
Question 3.
139,484 – 116,691
Answer:
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
Answer:
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
Answer:
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
Answer:
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

For 7-14, subtract. Estimate to check if your answers are reasonable.
Question 7.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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.

Answer:
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?
Answer:
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.
Answer:
Yes, Patrick’s answer is reasonable.

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
Answer:
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?

Answer:
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?

Answer:
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?

Answer:


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
Answer:
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?
Answer:
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?
Answer:

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

Answer:

Question 4.

Answer:

Question 5.

Answer:

Question 6.

Answer:

Question 7.
101,001 – 8,915
Answer:

Question 8.
9,050 – 3,461
Answer:

Independent Practice

For 9-23, subtract.
Estimate to check if your answer is reasonable.
Question 9.

Answer:

Question 10.

Answer:

Question 11.

Answer:

Question 12.

Answer:

Question 13.

Answer:

Question 14.

Answer:

Question 15.

Answer:

Question 16.

Answer:

Question 17.

Answer:

Question 18.

Answer:

Question 19.

Answer:

Question 20.

Answer:

Question 21.
6,090 – 5,130
Answer:

Question 22.
11,246 – 9,489
Answer:

Question 23.
790,008 – 643,829
Answer:

Problem Solving

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

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

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

Question 26.
How many more hip-hop than country downloads were sold?
Answer:

Question 27.
Higher Order Thinking How many more hip-hop and Latin downloads were sold than rock and country downloads? Explain.
Answer:

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
Answer:

Question 29.
Find the difference.

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

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
Be a good thinker! These questions can help you.

• 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?
Answer:

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.
Answer:

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?
Answer:

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.
Answer:

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.

Answer:

Problem Solving

Performance Task
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?
Answer:

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

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.
Answer:

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.

Answer:

Topic 2 Fluency Practice Activity

Follow the Path
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

• add on
• algorithm
• Associative Property of Addition
• Commutative Property of Addition
• compensation
• Identity Property of Addition
• inverse operations
• variable

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

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

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

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

Answer:

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.
Answer:

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
Answer:

Question 2.
92,425 + 31,675
Answer:

Question 3.
5,342 + 1,999
Answer:

Question 4.
22,283 – 14,169
Answer:

Question 5.
47,676 – 16,521
Answer:

Question 6.
1,089 – 961
Answer:

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
Answer:

Question 2.
8,352 – 3,421
Answer:

Question 3.
17,586 – 9,483
Answer:

Question 4.
823,725 + 44,851
Answer:

Question 5.
1,440 – 933
Answer:

Question 6.
55,748 – 28,392
Answer:

Question 7.
4,981 + 6,193
Answer:

Question 8.
995,275 + 4,921
Answer:

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.

Answer:

Question 2.

Answer:

Question 3.
215 + 8,823
Answer:

Question 4.
142,968 + 44,456
Answer:

Question 5.
2,417 + 3,573
Answer:

Question 6.
572,941 + 181,662
Answer:

Set D pages 53-60

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

The answer is reasonable.

Remember that you may need to regroup to subtract.

Question 1.

Answer:

Question 2.

Answer:

Question 3.
41,542 – 32,411
Answer:

Question 4.
4,978 – 2,766
Answer:

Question 5.
735,184 – 255,863
Answer:

Question 6.
44,558 – 22,613
Answer:

Set E pages 61-64

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

The answer is reasonable.

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

Answer:

Question 2.

Answer:

Question 3.
70,000 – 25,228
Answer:

Question 4.
560,043 – 312,562
Answer:

Question 5.
8,052 – 1,205
Answer:

Question 6.
20,008 – 16,074
Answer:

Set F pages 65-68

Think about these questions to help you reason abstractly and quantitatively.
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.
Answer:

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

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.
Answer:

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

Question 2.
Find 8,000 – 6,280.
Answer:

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

Answer:

Question 4.
Find the difference.

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

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

Question 6.
Find the difference. Then use addition to check your work.

Answer:

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
Answer:

Question 8.
Find the sum.

Answer:

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
Answer:

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.
Answer:

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.
Answer:

Topic 2 Performance Task

Taking Inventory Jiao runs a wholesale art supply website. She fills bulk orders for craft and hobby stores.
Question 1.
Use the Wooden Beads table to answer the questions.
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.

Answer:

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.
Answer:

Question 2.
Use the Glass Beads table to answer the questions.
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.

Answer:

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.
Answer:

Question 3.
Use the Metal Beads table to answer the questions.
Part A
Write and solve an equation to show how many more beads, b, are in an order of gold beads than in an order of platinum beads.

Answer:

Part B
Craftology orders the brass and copper beads. After they arrive, the store sells 29,735 of them. How many beads does Craftology have left from their order? Show your computations.
Answer:

Practice with the help of enVision Math Common Core Grade 3 Answer Key Topic 15 Attributes of Two-Dimensional Shapes regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 15 Attributes of Two-Dimensional Shapes

Essential Question:
How can two-dimensional shapes be described, analyzed, and classified?

enVision STEM Project: Forces and Motion
Do Research Use the Internet or other sources to find information about forces and the motion of an object. What does a balanced force mean? What happens when forces are unbalanced?

Journal: Write a Report Include what you found. Also in your report:

• Give examples of balanced and unbalanced forces on objects.
• Draw a picture that shows force acting on an object and the result.
• Describe the shapes in your drawing.

Review What You Know

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

• circle
• hexagon
• pentagon
• triangle

Question 1.
A shape with exactly 6 sides is called a _________.

Answer:
The shape with exactly 6 sides is called a hexagon.

Explanation:
In the above-given question,
given that,
the terms are circle, hexagon, pentagon, and triangle.
6 sides = hexagon.
hexagon is one of the two-dimensional shapes.
for example:

Question 2.
A shape with exactly 3 sides is called a __________.

Answer:
The shape with exactly 3 sides is called a triangle.

Explanation:
In the above-given question,
given that,
the terms are circle, hexagon, pentagon, and triangle.
3 sides = triangle.
triangle is one of the two-dimensional shapes.
for example:

Question 3.
A shape with exactly 5 sides is called a ___________.

Answer:
The shape with exactly 5 sides is called a pentagon.

Explanation:
In the above-given question,
given that,
the terms are circle, hexagon, pentagon, and triangle.
5 sides = pentagon.
The pentagon is one of the two-dimensional shapes.
for example:

Name Shapes

Write the name of each figure.
Question 4.

Answer:
The name of the figure is a square.

Explanation:
In the above-given question,
given that,
the figure has four sides.
so square has four sides.
the area of the square = s x s.
where s = side.
so the name of the figure is a square.

Question 5.

Answer:
The name of the figure is a rectangle.

Explanation:
In the above-given question,
given that,
the figure has four sides.
so rectangle has the four sides.
the area of the rectangle = l x b.
where l = length, and b = breadth.
so the name of the figure is a rectangle.

Question 6.

Answer:
The name of the figure is a triangle.

Explanation:
In the above-given question,
given that,
the figure has three sides.
so triangle has three sides.
the area of the triangle =1/2( b x h).
where b = base, and h = height.
so the name of the figure is a triangle.

Question 7.

Answer:
The name of the figure is a hexagon.

Explanation:
In the above-given question,
given that,
the figure has six sides.
so hexagon has six sides.
the area of the pentagon = p x a/2.
where p = perimeter, and a = anotherm.
so the name of the figure is a hexagon.

Shapes

In 8-11 write the number of vertices each figure has.
Question 8.

Answer:
The number of vertices = 3.

Explanation:
In the above-given question,
given that,
the figure is a triangle.
the highest or the top point is called the vertex.
the number of vertices = 3.
triangle has 3 vertices.

Question 9.

Answer:
The number of vertices = 4.

Explanation:
In the above-given question,
given that,
the figure is a quadrilateral.
the highest or the top point is called the vertex.
A polygon that has exactly 4 sides is called a quadrilateral.
the number of vertices = 4.
quadrilateral has 4 vertices.

Question 10.

Answer:
The number of vertices = 4.

Explanation:
In the above-given question,
given that,
the figure is a rhombus.
the highest or the top point is called a vertex.
A polygon that has four equal sides is called a rhombus.
the number of vertices = 4.
rhombus has vertices.

Question 11.

Answer:
The number of vertices = 6.

Explanation:
In the above-given question,
given that,
the figure is a hexagon.
the highest or the top point is called a vertex.
a polygon that has 6 straight sides and angles is called a hexagon.
the number of vertices = 6.
hexagon has 6 vertices.

Question 12.
How many faces does a cube have?
A. 3
B. 4
C. 5
D. 6

Answer:
Option D is the correct answer.

Explanation:
In the above-given question,
given that,
a cube has 6 sides.
cube also has six faces.
they are top, bottom, left, right, up, and down.
so option D is the correct answer.

Question 13.
How are squares and triangles the same? How are they different?

Answer:
The square and the triangles are the same.
the square and the triangles are different.

Explanation:
In the above-given question,
given that,
the squares and triangles are the same:
when they both have common names that do not indicate the number of sides.
they have four right angles.
the squares and triangles are different:
when they both have different side lengths and angles in a triangle.
so both the squares and rectangles are the same and also different.

Pick a Project

PROJECT 15A
Where do professional baseball players play their games?
Project: Create Quadrilateral Riddles

Answer:
The professional baseball players play their games on baseball grounds.

Explanation:
In the above-given question,
given that,
the baseball players will play their games on baseball grounds.
baseball is a bat-and-ball game played between two opposing teams who take turns batting and fielding.
the game proceeds when a player on the fielding team, called the pitcher, throws a ball which a player on the batting team tries to hit with a bat.

PROJECT 15B
How are books measured?
Project: Collect Data about the Shapes of Books

Answer:
The books are measured in many ways.

Explanation:
In the above-given question,
given that,
the shape of the books is measured in many ways.
the square and the rectangle.
the area of the square = s x s.
where s = side.
the area of the rectangle = l x b.
where l = length, and b = breadth.
so the books are measured in many ways.

PROJECT 15C
Where are quadrilaterals around us in everyday life?
Project: Build a Quadrilateral Model

Answer:
The quadrilaterals around us in everyday life are tabletop, book, picture frame, door, baseball diamond, etc.

Explanation:
In the above-given question,
given that,
we found quadrilaterals in everyday life.
they are tabletop, book, photo frame, door, etc.
so we can also see quadrilaterals in many pictures.

3-ACT MATH PREVIEW

Math Modeling
Square It Up

I can … model with math to solve a problem that involves using attributes of 2-D shapes to compare weights.

Lesson 15.1 Describe Quadrilaterals

Solve & Share
Fold a square piece of paper to make the fold lines as shown below. Find as many different quadrilaterals as you can using the fold lines and the edges of the square paper. Sketch each quadrilateral you find and describe it.
I can … identify quadrilaterals and use attributes to describe them.

Look Back! Describe how you used what you know about quadrilaterals to identify the shapes.

Essential Question
What Are Some Attributes of Quadrilaterals?

Answer:
Some attributes of quadrilaterals are triangles, rhombus, and the square.

Explanation:
In the above-given question,
given that,
Fold a square piece of paper to make the fold lines.
if we fold the paper in an above-given way,
we can find some shapes.
the shapes are quadrilaterals, triangles, and rhombus.

Visual Learning Bridge
The welcome to Florida sign is a quadrilateral. How can you describe quadrilaterals?
An angle is formed when two sides of a polygon meet.

Some quadrilaterals have special names.

Convince Me! Make Sense and Persevere Draw a quadrilateral that is an example of one of the shapes listed in Box B. Name the shape. Then draw a quadrilateral that is NOT an example of a shape listed in Box B.

Answer:
The trapezoid is one example of the quadrilateral.

Explanation:
In the above-given question,
given that,
the shapes are trapezoid, parallelogram, rectangle, rhombus, and square.
among all these shapes,
a trapezoid is one example.

Another Example!
These are convex polygons. All angles point outward.

These are concave polygons. One or more angles point inward.

Guided Practice

Do You Understand?
Question 1.
This figure is a rectangle, but it is NOT a square. Why?

Answer:
The square has four right angles and all sides the same length.

Explanation:
In the above-given question,
given that,
the figure is a rectangle, but it is not a square because
the rectangle has four right angles or square corners.
but the square has four right angles and all sides the same length.
area of the square = s x s.
area of the rectangle = l x b.

Question 2.
Draw two different quadrilaterals that are NOT rectangles, squares, or rhombuses.

Answer:
The two different quadrilaterals are trapezoid and parallelogram.

Explanation:
In the above-given question,
given that,
the two different quadrilaterals that are not rectangles, squares, or rhombuses:
they are trapezoid and parallelogram.
a trapezoid has exactly one pair of sides on lines that never cross.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.

Do You Know How?
In 3-6, write as many special names as possible for each quadrilateral.
Question 3.

Answer:
The special name for the quadrilateral is a parallelogram.

Explanation:
In the above-given question,
given that,
the given figure is quadrilateral.
parallelogram is also a quadrilateral.
opposite sides are the same length.
opposite angles are the same size.

Question 4.

Answer:
The special name is a rectangle.

Explanation:
In the above-given question,
given that,
the shape is a rectangle.
the rectangle has four right angles or square corners.
area of the rectangle = l x b.
where l = length and b = breadth.
so the quadrilateral is a rectangle.

Question 5.

Answer:
The special name is a parallelogram.

Explanation:
In the above-given question,
given that,
the quadrilateral has two equal lengths and two equal breadths.
so the name is a parallelogram.
parallelogram is also a quadrilateral.
opposite sides are the same length.
opposite angles are the same size.

Question 6.

Answer:
The special name is square.

Explanation:
In the above-given question,
given that,
the quadrilateral has two equal lengths and two equal breadths.
so the name is square.
square is also a quadrilateral.
four right angles and all sides the same length.

Independent Practice

In 7-9, write as many special names as possible for each quadrilateral.
Question 7.

Answer:
The special name is a rectangle.

Explanation:
In the above-given question,
given that,
the quadrilateral has opposite sides that are the same length.
so the name is a rectangle.
the rectangle is also a quadrilateral.
opposite sides are the same length.
opposite angles are the same size.

Question 8.

Answer:
The special name is a trapezoid.

Explanation:
In the above-given question,
given that,
the quadrilateral has exactly one pair of sides.
so the name is a trapezoid.
trapezoid is also a quadrilateral.
exactly one pair of sides on lines that never cross.

Question 9.

Answer:
The special name is a parallelogram.

Explanation:
In the above-given question,
given that,
the quadrilateral has two equal lengths and two equal breadths.
so the name is a parallelogram.
parallelogram is also a quadrilateral.
opposite sides are the same length.
opposite angles are the same size.

In 10, name all the possible quadrilaterals that fit the rule.
Question 10.
Has 2 pairs of opposite sides that are equal _______________

Answer:
The 2 pairs of opposite sides that are equal are parallelogram and rectangle.

Explanation:
In the above-given question,
given that,
the quadrilateral that has 2 pairs of opposite sides that are equal is a parallelogram and rectangle.
opposite sides are the same length.
opposite angles are the same size.
four right angles, or square corners.
so rectangle and parallelogram have 2 pairs of opposite sides that are equal.

Problem Solving

In 11 and 12, write the name that best describes the quadrilateral. Draw a picture to help.
Question 11.
Vocabulary A rectangle with all sides the same length is a _________.

Answer:
A rectangle with all sides the same length is a rhombus.

Explanation:
In the above-given question,
given that,
a rhombus has all sides the same length.
rhombus is a special parallelogram.
so a rectangle with all sides the same length is a parallelogram.

Question 12.
Vocabulary A parallelogram with four right angles is a __________

Answer:
A parallelogram with four right angles is a rectangle.

Explanation:
In the above-given question,
given that,
the rectangle has four right angles or square corners.
a rectangle is a special parallelogram.
a parallelogram with four right angles is a rectangle.

Question 13.
I am a quadrilateral with opposite sides the same length. Which quadrilaterals could I be?

Answer:
The quadrilateral with opposite sides of th+e same length is a parallelogram.

Explanation:
In the above-given question,
given that,
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the quadrilateral with opposite sides of the same length is a parallelogram.

Question 14.
Higher Order Thinking Jae says that the figure on the left is a trapezoid. Carmen says that the figure on the right is a trapezoid. Who is correct? Explain.

Answer:
Yes, both of them are correct.

Explanation:
In the above-given question,
given that,
Jae says that the figure on the left is a trapezoid.
Carmen says that the figure o the right is a trapezoid.
a trapezoid has exactly one pair of sides on lines that never cross.
trapezoid is also a quadrilateral.
so both of them are correct.

Question 15.
Model with Math Sue bought a book for $12, two maps for $7 each, and a pack of postcards for $4. Use math you know, bar diagrams, equations, or properties of operations, to find Sue’s total cost.

Answer:
The total cost of Sue was $23.

Explanation:
In the above-given question,
given that,
Sue bought a book for $12, two maps for $7 each,
and a pack for $4.
12 + 7 + 4.
12 + 4 = 16.
16 + 7 = 23.
so the total cost of Sue was $23.

Question 16.
Algebra Angela drew 9 rhombuses and 6 trapezoids. She wants to find b, the total number of angles in her quadrilaterals. Explain how Angela can find b.

Answer:
The total number of angles in her quadrilaterals is

Explanation:
In the above-given question,
given that,
Algebra Angela drew 9 rhombuses and 6 trapezoids.

Assessment Practice

Question 17.
A square and a rhombus are shown at the right. Which attributes do these shapes always have in common? Select all that apply.

☐ Number of sides
☐ Side lengths
☐ Angle measures
☐ Right angles
☐ Number of angles

Answer:
The attributes of these shapes always have in common are the number of sides, side lengths, right angles.

Explanation:
In the above-given question,
given that,
A square and a rhombus are shown at the right.
rhombus has all sides the same length.
a rhombus is a special parallelogram.
a square has four angles and all sides the same length.
a square is a special parallelogram.
so the number of sides, side length, and right angles have the same attributes.

Lesson 15.2 Classify Shapes

Solve & Share
Sort the shapes below into two groups. Use colored pencils or crayons to color each group a different color. How did you sort the shapes? How are the shapes in both of your groups alike?
I can … classify shapes in several ways based on how they are alike and how they are different.

Look Back! What fraction of the triangles above have each attribute: all sides equal in length, no sides equal in length, exactly two equal angles, or one right angle?

Answer:
Triangle G, B, and I have all sides equal in length.
Triangle E, F, AND L have no sides equal in length.
Exactly one right angle is A, D, and K.
triangle B, C, I, and J have two equal angles.

Explanation:
In the above-given question,
given that,
there are 12 triangles.
the triangles are the names A, B, C, D, E, F, G, H, I, J, K, and L.
The triangles that have all sides equal in length are G, B.
the triangles that have no sides equal in length are E, F, and L.
the triangles that have exactly one right angle are A, D, and K.
the triangles have two equal angles is B, C, I, and J.

Essential Question
How Can You Describe Different Question Groups of Shapes?

Visual Learning Bridge
Ethan made two groups of polygons. How are the groups different? How are the groups alike?

Here is one way the two groups are different
In Group 1, each polygon has sides that all are the same length.
In Group 2, each polygon has sides that are not all the same length.

Here are some ways the two groups are alike.
In Group 1 and Group 2, all of the polygons have 4 sides.
In Group 1 and Group 2, all of the polygons have 4 angles.
In Group 1 and Group 2, all of the polygons are quadrilaterals.

Convince Me! Construct Arguments Draw a quadrilateral that does not belong to either Group 1 or Group 2. Explain why it does not belong to either group.

Answer:
The quadrilateral that does not belong to either group 1 and group 2 is a rectangle.

Explanation:
In the above-given question,
given that,
in group 1 each polygon has sides that all are the same length.
In Group 2, each polygon has sides that are not all the same length.
In Group 1 and Group 2, all of the polygons have 4 sides.
In Group 1 and Group 2, all of the polygons have 4 angles.
In Group 1 and Group 2, all of the polygons are quadrilaterals.
so the quadrilateral that does not belong to either group 1 and group 2 is a rectangle.

Guided Practice

Do You Understand?
Question 1.
Nellie drew a group of rectangles and a group of trapezoids. How are the shapes in each group different?

Answer:
The groups of rectangles and groups of trapezoids are different.

Explanation:
In the above-given question,
given that,
Nellie drew a group of rectangles and a group of trapezoids.
rectangles have four right angles or square corners.
a rectangle is a special parallelogram.
trapezoids have exactly one pair of sides on lines that never cross.
the trapezoid is also a quadrilateral.
so rectangles and trapezoids are different.

Question 2.
How are rectangles and trapezoids alike?

Answer:
The rectangles and trapezoids are alike.

Explanation:
In the above-given question,
given that,
rectangles have four right angles or square corners.
a rectangle is a special parallelogram.
trapezoids have exactly one pair of sides on lines that never cross.
the trapezoid is also a quadrilateral.
so rectangles and trapezoids are alike.

Question 3.
What larger group of polygons do all of Nellie’s shapes belong to?

Answer:
The larger group of polygons do Nellie’s shapes belong to rectangles and trapezoids.

Explanation:
In the above-given question,
given that,
Nellie drew a group of rectangles and a group of trapezoids.
rectangles have four right angles or square corners.
a rectangle is a special parallelogram.
trapezoids have exactly one pair of sides on lines that never cross.
the trapezoid is also a quadrilateral.
so rectangles and trapezoids belong to quadrilaterals.
Nellie’s shape belongs to quadrilaterals.

Do You Know How?
In 4-6, use the groups on the previous page.
Question 4.
Draw a shape that belongs to Ethan’s Group 1.

Answer:
The shape is a parallelogram, and square.

Explanation:
In the above-given question,
given that,
Ethan draws a shape that belongs to two groups.
in group 1 he draws 3 shapes.
they are parallelogram and square.

Question 5.
Draw a shape that belongs to Ethan’s Group 2.

Answer:
The shape is a trapezoid.

Explanation:
In the above-given question,
given that,
Ethan draws a shape that belongs to two groups.
in group 2 he draws 3 shapes.
they are different types of trapezoids.
the quadrilateral is also a trapezoid.

Question 6.
Why is there a square in Group 1?

Answer:
In group 1 there is a square because it has four right angles and all sides the same length.

Explanation:
In the above-given question,
given that,
Ethan draws a shape that belongs to two groups.
in group 1 he draws 3 shapes.
among the three shapes, one is square.
the area of the square = s x s.
where s = side.
square has four right angles and all sides the same length.

Independent Practice

In 7-11, use the groups below.

Question 7.
How are the shapes in Group 1 different from the shapes in Group 2?

Answer:
The shapes in group 1 different from the shapes in group 2.

Explanation:
In the above-given question,
given that,
in group 1 there are three pentagons.
the pentagons are the same with the edges have the same length.
in group 2 there are 3 pentagons.
the pentagons have different side lengths.

Question 8.
How are the two groups alike?

Answer:
The two groups are alike because they all are pentagons.

Explanation:
In the above-given question,
given that,
in group 1 all the pentagons have equal side lengths.
in group 1 there are 3 pentagons.
in group 2 all the pentagons have different side lengths.
in group 2 there are also 3 pentagons.

Question 9.
What larger group do all the shapes belong to?

Answer:
The shapes belong to the pentagons.

Explanation:
In the above-given question,
given that,
the larger group do all the shapes belong to pentagons.
there are 4 pentagons.
they have the same equal side lengths.
2 pentagons have different side lengths.

Question 10.
Draw a shape that could go in Group 2 but not Group 1.

Answer:
The shape is pentagon.

Explanation:
In the above-given question,
given that,
right pentagon belongs to group 2.
the polygon that has 5 sides is called a pentagon.

Question 11.
Draw a shape that could go in Group 1 but not Group 2.

Answer:
The shape that could go in group 1 is a trapezoid.

Explanation:
In the above-given question,
given that,
in group 1 there are 3 pentagons.
the 3 pentagons that have the same length.
i group 2 there are 3 trapezoids.
that have different side lengths.

Problem Solving

In 12-14, use the picture at the right.

Question 12.
How are the yellow shapes and the blue shapes different? How are they alike?

Answer:
The blue and the yellow shapes are same because they all are triangles.

Explanation:
In the above-given question,
given that,
in the given figure
there is one hexagon.
there are 6 equilateral triangles.
there is 6 isosceles triangles.
they are different because they are equilateral and isosceles triangles.

Question 13.
Which larger group of polygons do the yellow and blue shapes belong to?

Answer:
The larger group of polygons do the yellow and blue shapes belong to triangles.

Explanation:
In the above-given question,
given that,
in the given figure
there is one hexagon.
there are 6 equilateral triangles.
there are 6 isosceles triangles.
so the larger group of polygons do the yellow and blue shapes belong to triangles.
6 + 6 = 12.

Question 14.
Does the pink shape belong to the group identified in Exercise 13? Explain.

Answer:
Yes, the pink shape belongs to the group identified in exercise 13.

Explanation:
In the above-given question,
given that,
the pink shape is a hexagon.
hexagon has 6 sides.
the six sides have the same side lengths.
so the pink shape belong to the group identified in exercise 13.

Question 15.
Draw a quadrilateral that is NOT a rectangle, a rhombus, or a square.

Answer:
The quadrilateral is a parallelogram.

Explanation:
In the above-given question,
given that,
the quadrilateral is a parallelogram.
opposite sides are the same length.
opposite angles are the same size.
so the quadrilateral is a parallelogram.

Question 16.
Todd bought a jacket for $57 and two maps for $9 each. What was the total cost?

Answer:
The total cost is $66.

Explanation:
In the above-given question,
given that,
Todd bought a jacket for $57.
two maps for $9 each.
57 + 9 = $66.
so the total cost is $66.

Question 17.
Use Appropriate Tools Victoria wants to make two same-sized rhombuses. What tool can she use? Explain.

Answer:
The tool is scale.

Explanation:
In the above-given question,
given that,
Victoria wants to make two same-sized rhombuses.
rhombus has all the sides the same length.
rhombus is a special type of special parallelogram.

Question 18.
Higher Order Thinking Jessalyn needs to find 3 × 3,4 × 6, and 7 × 2. She draws area models to solve the problem. What polygon group do her area models all belong to? Explain.

Answer:
The area models belong to square and rectangle.

Explanation:
In the above-given question,
given that,
Jessalyn needs to find 3 × 3,4 × 6, and 7 × 2.
3 x 3 = 9.
where the area of the square = s x s.
where s = side.
the area of the rectangle = l x b.
where l = length and b = breadth.
4 x 6 = 24.
7 x 2 = 14.
so the area models belong to squares and rectangles.

Assessment Practice

Question 19.
What is the name of a shape that is NOT always a rectangle, but is a quadrilateral?
A. Square
B. Triangle
C. Hexagon
D. Parallelogram

Answer:
The name of a shape that is not always a rectangle is triangle.

Explanation:
In the above-given question,
given that,
the quadrilateral is a square, hexagon, and parallelogram.
the polygon that has three sides is called triangle.
a quadrilateral that is not always a rectangle is triangle.
opposite sides are the same length.
opposite angles are the same size.
square has four right angles and all sides the same length.

Question 20.
Which shape could be sorted into a group of parallelograms or a group of rhombuses?
A. Square
B. Rectangle
C. Trapezoid
D. Hexagon

Answer:
Option B and option C is correct.

Explanation:
In the above-given question,
given that,
The shapes are square, rectangle, trapezoid, and hexagon.
four right angles and all sides the same length is a square.
rectangle has four right angles or square corners.
a rectangle is a special parallelogram.
a trapezoid has exactly one pair of sides on lines that never cross.
option B and option C is correct.

Lesson 15.3 Analyze and Compare Quadrilaterals

Solve & Share
Describe at least two attributes that are the same in all or some of these shapes. Describe two attributes that are different.
I can … analyze and compare quadrilaterals and group them by attributes.

Look Back! Draw a quadrilateral that is different from all the quadrilaterals above. Tell how it is different.

Answer:
The quadrilateral that is different from all the quadrilaterals is diagram E.

Explanation:
In the above-given question,
given that,
the shapes are parallelogram and rhombus.
parallelogram has opposite sides are the same length.
opposite angles are the same size.
so the quadrilateral that is different from all the quadrilaterals is E.

Essential Question
How Can You Analyze bessed to Question and Compare Shapes?

Visual Learning Bridge
What are different ways you can classify the quadrilaterals shown below?

Shapes B, D, E, F, and G are also parallelograms. Each has two pairs of sides that have the same length.

Shapes D, E, and G are also rectangles. Each has 4 right angles.

Shapes B and D are parallelograms that are also rhombuses. Each has 4 equal-length sides.

Convince Me! Reasoning Which of the shapes above can you cover with whole unit squares and not have any gaps or overlaps? What attributes do these shapes have in common?

Guided Practice

Do You Understand?
Question 1.
Which shape on the previous page is a rhombus but not a rectangle? Explain.

Answer:
The shape D is the rhombus but not a rectangle.

Explanation:
In the above-given question,
given that,
the shapes are rhombus, parallelogram.
shapes D, E, G are also rectangles.
each has 4 right angles.

Question 2.
Can you have a square trapezoid? Explain.

Answer:
Yes, the shape D is a square trapezoid.

Explanation:
In the above-given question,
given that,
the shapes are B, D, E, F, and G.
the shape D is a square trapezoid.
D, E, and G are rectangles.
so the shape D is a square trapezoid.

Do You Know How?
Question 3.
Which shapes on the previous page are not a parallelogram, rectangle, rhombus, or square?

Answer:
The shapes belong to the parallelogram, rectangle, rhombus, and square.

Explanation:
In the above-given question,
given that,
the shapes are parallelogram, rectangle, rhombus, square.
shape D is a square.
shape B is a parallelogram.
shape G is a rectangle.
so all the shape belongs to the parallelogram, rectangle, rhombus, and a square.

Question 4.
What attributes does a square have because it is always a rectangle?

Answer:
The square has four right angles and all sides the same length.

Explanation:
In the above-given question,
given that,
the square has four right angles and all sides the same length.
the rectangle is four right angles or square corners.
a rectangle is a special parallelogram.
square is a rectangle.

Independent Practice

In 5-9, list all the polygons shown at the right that fit each description. If there could be no such polygon, tell why.

Question 5.
Is not a parallelogram

Answer:
The shape E is not a parallelogram.

Explanation:
In the above-given question,
given that,
a quadrilateral that has opposite sides are the same length.
opposite angles are the same size.
but the shape E does not have the opposite sides same length.

Question 6.
Is a quadrilateral but not a parallelogram or trapezoid

Answer:
The shapes B, F, A, and D are rectangle, rhombus, and square.

Explanation:
In the above-given question,
given that,
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
a trapezoid has exactly one pair of sides on lines that never cross.
so the shapes B, F, A, and D are rectangle, rhombus, and square.

Question 7.
Is a square and not a parallelogram

Answer:
The shapes A and D are square.

Explanation:
In the above-given question,
given that,
the square is the shape A and the shape D.
the shapes A and D are square and rhombus.

Question 8.
Is a rhombus and not a rectangle

Answer:
The shape D is a rhombus but not a rectangle.

Explanation:
In the above-given question,
given that,
the shape D is a rhombus.
but the shape D is not a rectangle.
so the shape D is a rhombus.

Question 9.
Is a parallelogram and not a rhombus

Answer:
The shape G is a parallelogram but not a rhombus.

Explanation:
In the above-given question,
given that,
the shape G is a parallelogram.
the shape G is not a rhombus.
the parallelogram has opposite sides that are the same length.
so the shape G is a parallelogram but not a rhombus.

Problem Solving

Question 10.
Cy put blocks 1 and 2 together to make a new shape. How are the blocks he used alike? How are they different?

Answer:
The new shape formed is a trapezoid.

Explanation:
In the above-given question,
given that,
Cy put blocks 1 and 2 together to make a new shape.
shape 1 is a parallelogram.
shape 2 is a trapezoid.
by joining the two shapes we will get the other shape.
so the new shape formed is a trapezoid.

Question 11.
Reasoning Explain which of the shapes at the right you can cover with whole unit squares and not have any gaps or overlaps.

Answer:
The shape rectangle can cover with whole unit squares.

Explanation:
In the above-given question,
given that,
the shape rectangle is filled with squares.
they have given the two shapes.
they are parallelogram and rectangle.
so the shape rectangle can cover with whole unit squares.

Question 12.
Higher Order Thinking Draw a quadrilateral with no sides the same length. Tell why it is not a parallelogram.

Answer:
The quadrilateral with no sides the same length is not a parallelogram is a trapezoid.

Explanation:
In the above-given question,
given that,
quadrilaterals have special names.
a trapezoid has exactly one pair of sides on lines that never cross.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the quadrilateral with no sides the same length is not a parallelogram is a trapezoid.

Question 13.
Sam needs 25 minutes to get ready and 15 minutes to bike to swim practice. Practice starts at 4:00 P.M. What time should Sam start getting ready?

Answer:
Sam starts getting ready at 3:20 P.M.

Explanation:
In the above-given question,
given that,
Sam needs 25 minutes to get ready and 15 minutes to bike to swim practice.
practice starts at 4:00 P.M.
25 + 15 = 40.
so Sam starts getting ready at 3:20 P.M.

Assessment Practice

Question 14.
Look at these polygons.

Part A
Name one attribute that all 4 polygons have.

Answer:
The 4 polygons that have the same attribute is the right angles.

Explanation:
In the above-given question,
given that,
The given polygons are rectangle, trapezoid, parallelogram.
the shape A and B are rectangles.
the shape C is trapezoid.
the shape D is a parallelogram.
so the 4 polygons that have the same attribute are the right angles.

Part B
Name an attribute that both A and D have that B and C do not.

Answer:
The attribute that both A and D have is the opposite sides have the same length.

Explanation:
In the above-given question,
given that,
the shape A is a rectangle.
the shape D is a parallelogram.
the rectangle has four right angles or square corners.
the rectangle has a special parallelogram.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the attribute that both A and D have is the opposite sides have the same length.

Lesson 15.4 Problem Solving

Precision
Solve & Share
Draw shapes that match all of these clues. Use math words and numbers correctly to name each shape and explain how your shapes match the clues. Clue 1: 1 am a polygon with 4 sides.
Clue 2: I am a polygon with 4 right angles.
Clue 3: My area is 12 square units.
I can … be precise when solving math problems.

Answer:
The 1st shape is a rectangle.
the 2nd shape is a square.
the 3rd shape is a rectangle.

Explanation:
In the above-given question,
given that,
the shape that has 4 sides is a rectangle.
the shape that has 4 right angles is the square.
the area is 12 sq units.
area of a rectangle = l x b.
where l = length, and b = breadth.
area = 3 x 4.
area = 12 sq units.
so the shape formed is a rectangle.

Thinking Habits
Be a good thinker! These questions can help you.

• Am I using numbers, units, and symbols appropriately?
• Am I using the correct definitions?
• Am I calculating accurately?
• Is my answer clear?
  

Look Back! Be Precise How did you use math terms or numbers to make your explanation clear?

Essential Question
How Can You Be Precise When Solving Math Problems?

Visual Learning Bridge
What shapes can you draw for this riddle?
I am a polygon with 4 sides.
I have 4 right angles.
My opposite sides are equal in length.

What do I need to do to solve this problem?
I will read the given information and use it to draw shapes that match the description.

Answer:
The shape formed is a rectangle.

Explanation:
In the above-given question,
given that,
I am a polygon with 4 sides.
I have 4 right angles.
My opposite sides are equal in length.
the rectangle has 4 right angles or square corners.
so the shape formed with the given polygon is a rectangle.

How can I be precise in solving this problem?
I can

• correctly use the information given.
• use pictures or objects to identify possible answers.
• decide if my answer is clear and appropriate.

Here’s my thinking…

I know that the shape is a 4-sided polygon with 4 right angles and opposite sides that are equal in length.

I can draw shapes that match all of the clues. Then I can name each shape.

Each of the shapes has 4 sides, 4 right angles, and opposite sides that are equal in length.

Convince Me! Be Precise Draw a shape for this riddle. Explain how it matches the clues.
I am a polygon with 4 sides.
None of my angles are right angles.
None of my sides is the same length.

Answer:
The shape is a trapezoid.

Explanation:
In the above-given question,
given that,
I am a polygon with 4 sides.
None of my angles are right angles.
None of my sides is the same length.
a trapezoid has exactly one pair of sides on lines that never cross.
so the shape formed is a trapezoid.

Guided Practice

Be precise. Carefully Students in Mr. Tesla’s class drew pictures of their favorite consider and use the shapes. Jackie made a polygon with 4 sides. It has 4 right information you are given angles, but not all of the shape’s sides are the same length.

Question 1.
What math words and numbers are important in this problem?

Answer:
The shape formed is a trapezoid.

Explanation:
In the above-given question,
given that,
Jackie made a polygon with 4 sides.
It has 4 right information you are given angles, but not all of the shape’s sides are the same length.
a trapezoid has exactly one pair of sides on lines that never cross.
so the shape formed is a trapezoid.

Question 2.
Draw and name the type of polygon Jackie made.

Answer:
The shape formed is a trapezoid.

Explanation:
In the above-given question,
given that,
Jackie made a polygon with 4 sides.
It has 4 right information you are given angles, but not all of the shape’s sides are the same length.
a trapezoid has exactly one pair of sides on lines that never cross.
so the shape formed is a trapezoid.

Question 3.
How can you check to make sure your answer is clear and correct?

Answer:
By using the formulas we can make sure.

Explanation:
In the above-given question,
given that,
Jackie made a polygon with 4 sides.
It has 4 right information you are given angles, but not all of the shape’s sides are the same length.
a trapezoid has exactly one pair of sides on lines that never cross.
so the shape formed is a trapezoid.

Independent Practice

Be Precise Students in Mrs. Edison’s class designed a mural to show what they have learned about quadrilaterals. Ethan made a shape with opposite sides that are the same length.

Question 4.
What math words and numbers are important in this problem?

Answer:
The shape Ethan formed is rectangle and parallelogram.

Explanation:
In the above-given question,
given that,
Students in Mrs. Edison’s class designed a mural to show what they have learned about quadrilaterals.
Ethan made a shape with opposite sides that are the same length.
a rectangle has 4 right angles or square corners.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the shape Ethan formed is a rectangle and a parallelogram.

Question 5.
Draw a possible polygon that Ethan could have made. Is there more than one type of quadrilateral that would correctly match the description? Explain.

Answer:
Yes, there is more than one type of quadrilateral is rectangle and parallelogram.

Explanation:
In the above-given question,
given that,
Students in Mrs. Edison’s class designed a mural to show what they have learned about quadrilaterals.
Ethan made a shape with opposite sides that are the same length.
a rectangle has 4 right angles or square corners.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the shape Ethan formed is a rectangle and a parallelogram.

Question 6.
How can you check to make sure your answer is clear and correct?

Answer:
By using the formulas we can make sure.

Explanation:
In the above-given question,
given that,
Ethan made a shape with opposite sides that are the same length.
a rectangle has 4 right angles or square corners.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the shape Ethan formed is a rectangle and a parallelogram.

Problem Solving

Performance Task
Crazy Quilts Each student in Ms. Beardon’s art class is designing a panel for a crazy quilt. Students can use different colors, but each panel will be the same shape. The attributes of the panel design are as shown at the right.

• 4 equal sides
• 4 right angles

Draw and name a shape to match this description. Answer Exercises 7-10 to solve the problem.
Question 7.
Make Sense and Persevere What do you know? What are you asked to do?

Answer:
The shape formed is square.

Explanation:
In the above-given question,
given that,
the polygon has 4 equal sides.
the polygon has 4 right angles.
square has 4 right angles and all sides the same length.
so the attributes match the given attributes.
so the shape formed is square.

Question 8.
Be Precise What math terms and numbers can help you solve the problem?

Answer:
Yes, we are using the correct answers.

Explanation:
In the above-given question,
given that,
we are using the correct answers.

Question 9.
Use Appropriate Tools Choose tools to help you solve this problem. Then draw and name a possible panel design.
Answer:

Question 10.
Critique Reasoning Tabby followed Ms. Beardon’s directions and made a quilt panel with the shape shown below. Did she follow directions correctly? Explain.

Answer:
Yes, she follows the directions correctly.

Explanation:
In the above-given question,
given that,
Ms. Beardon’s directions and make a quilt panel.
Ms. Beardon said to draw the rectangle.
so the tabby followed his instructions and draw the rectangle.
so she follows the directions correctly.

Topic 15 Fluency Practice Activity

Follow the path
Shade a path from START to FINISH. Follow the products and quotients that are even numbers. You can only move up, down, right, or left.
I can … multiply and divide within 100.

Topic 15 Vocabulary Review

Word List

• square rhombus
• angle
• parallelogram
• polygon
• quadrilateral
• rectangle
• rhombus
• right angle
• square
• trapezoid

Understand Vocabulary
Circle all the terms that match each description.
Question 1.
A quadrilateral
square
rectangle
trapezoid
polygon

Answer:
A quadrilateral is a polygon.

Explanation:
In the above-given question,
given that,
the terms are square, rectangle, trapezoid, and polygon.
a polygon is a closed shape that has only straight sides.
a quadrilateral is a polygon with four sides and four angles.
so a quadrilateral is a polygon.

Question 2.
A polygon
angle
quadrilateral
rectangle
square

Answer:
A polygon is a quadrilateral.

Explanation:
In the above-given question,
given that,
the terms are polygon, angle, quadrilateral, rectangle, and square.
a polygon is a closed shape that has only straight sides.
a quadrilateral is a polygon with four sides and four angles.
so a polygon is a quadrilateral.

Question 3.
A polygon with 4 right angles
square
trapezoid
rhombus
rectangle

Answer:
A polygon with 4 right angles is a square.

Explanation:
In the above-given question,
given that,
the terms are square, trapezoid, rhombus, and rectangle.
square has 4 right angles and all sides the same length.
area of a square = s x s.
where s = side.
so a polygon with 4 right angles is a square.

Question 4.
A parallelogram
rhombus
triangle
rectangle
trapezoid

Answer:
A parallelogram is a rhombus.

Explanation:
In the above-given question,
given that,
the terms are rhombus, triangle, rectangle, and trapezoid.
rhombus has all sides the same length.
rhombus is a special parallelogram.
so parallelogram is a rhombus.

For each term, draw an example and a nonexample.

Answer:
The example of the right angle is square.
Rectangle has 4 right angles or square corners.
A trapezoid has exactly one pair of sides on lines that never cross.

Explanation:
In the above-given question,
given that,
the terms are right angle, rectangle, trapezoid.
square has 4 right angles and all sides the same length.
the rectangle has 4 right angles or square corners.
a trapezoid has exactly one pair of sides on lines that never cross.

Use Vocabulary in Writing
Question 8.
Use at least 3 terms from the Word List to explain why a square is a rectangle.

Answer:
Yes, the square is a rectangle.

Explanation:
In the above-given question,
given that,
the terms are right angles, equal side lengths.
so the square is also a rectangle.
square has four right angles and all sides the same length.
rectangles have four right angles or square corners.

Topic 15 Reteaching

Set A pages 585-588

You can draw quadrilaterals and describe them by their attributes.

Remember that a polygon with 4 sides is a quadrilateral

In 1-3, draw the shapes named or described below and describe their attributes.
Question 1.
Trapezoid

Answer:
Attributes: exactly one pair of sides on lines that never cross.

Explanation:
In the above-given question,
given that,
a trapezoid has exactly one pair of sides on lines that never cross.
trapezoid is also a quadrilateral.

Question 2.
Rhombus

Answer:
Attributes: all sides the same length.

Explanation:
In the above-given question,
given that,
rhombus has all sides the same length.
a rhombus is a special parallelogram.

Question 3.
A quadrilateral that is NOT a trapezoid, parallelogram, rectangle, rhombus, or square.

Answer:
A quadrilateral is not a trapezoid, a parallelogram, rectangle, rhombus, and square is the triangle.

Explanation:
In the above-given question,
given that,
a shape that has 3 sides is a triangle.
area of the triangle = 2(l + b).
where l = length, and b = breadth.

Set B pages 589-592

How are the shapes in Groups 1 and 2 different? How are they alike?

The shapes in the groups are different because in Group 1, all shapes are convex. In Group 2, all shapes are concave.
The shapes in both groups are alike because they all have straight lines and are closed. Therefore, they all are polygons.

Remember that all of the shapes in these groups have something in common.

In 1 and 2, use the groups below.

Question 1.
How are the shapes in Groups 1 and 2 different?

Answer:
In group 1 the figures are triangles.
in group 2 the figures are hexagons.

Explanation:
In the above-given question,
given that,
in group 1 the shapes are triangles.
in group 2 the shapes are hexagons.
so triangles and hexagons are different.

Question 2.
How are the shapes in Groups 1 and 2 alike?

Answer:
The shapes in groups 1 and 2 are alike when the shapes are divided.

Explanation:
In the above-given question,
given that,
in group 1 the shapes are triangles.
in group 2 the shapes are hexagons.
when the shapes in group 2 are divided into parts.
they form triangles.
so the shapes in group 1 and group 2 are alike.

Set C pages 593-596

All of the shapes below have 4 sides, so they are quadrilaterals. Some quadrilaterals can be classified into multiple groups.

Parallelograms have 2 pairs of sides that have the same length. Shapes A, B, C, and D are parallelograms.

Rhombuses have 4 equal-length sides. Shapes A and C are rhombuses.

Rectangles have 2 pairs of sides that have the same length and 4 right angles. Shapes A, B, and D are rectangles.

Squares have 4 equal-length sides and 4 right angles. Shape A is a square.

Trapezoids have 1 pair of sides on lines that do not cross. Shape E is a trapezoid.

Remember that quadrilaterals with different names can have some of the same attributes.

In 1-4, list all the polygons that fit the given attributes.

Question 1.
Has at least 2 right angles but is not a rectangle

Answer:
The shape F is a square.

Explanation:
In the above-given question,
given that,
they have given the 7 polygons.
the polygons are rectangle, rhombus, square, and trapezoid.
square has 4 right angles.
so the shape F has 2 right angles.

Question 2.
Has pairs of sides the same length but is not a rectangle

Answer:
The shape D has the pairs of sides the same length but is not a rectangle.

Explanation:
In the above-given question,
given that,
they have given the 7 polygons.
the polygons are rectangle, rhombus, square, and trapezoid.
Rhombus has all sides the same length.
so the shape D has the pairs of sides the same length but is not a rectangle.

Question 3.
Is a quadrilateral with no right angles

Answer:
The shapes D and B are quadrilaterals with no right angles.

Explanation:
In the above-given question,
given that,
they have given the 7 polygons.
the polygons are rectangle, rhombus, square, and trapezoid
the shape D is a parallelogram.
the shape B is a rhombus.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.

Question 4.
Has 4 sides of the same length but is not a square

Answer:
The shape B has 4 sides of the same length but it not a square.

Explanation:
In the above-given question,
given that,
they have given the 7 polygons.
the polygons are rectangle, rhombus, square, and trapezoid.
The shape B is the rhombus.
rhombus has all sides the same length.
so the shape B has 4 sides of the same length.

Set D pages 597-600

Think about these questions to help you attend to precision.
Thinking Habits

• Am I using numbers, units, and symbols appropriately?
• Am I using the correct definitions?
• Am I calculating accurately?
• Is my answer clear?
  

Remember to consider all parts of the question.

Anton drew a quadrilateral with 4 sides the same length and 4 right angles.
Question 1.
What quadrilateral did he draw?

Answer:
Anton drew a quadrilateral that is a square.

Explanation:
In the above-given question,
given that,
Anton drew a quadrilateral with 4 sides of the same length and 4 right angles.
square has four right angles and all sides the same length.
so Anton draws the shape that is a square.

Question 2.
Is there any other shape that he could have drawn? Explain.

Answer:
No, he cannot draw.

Explanation:
In the above-given question,
given that,
Anton drew a quadrilateral with 4 sides of the same length and 4 right angles.
the rectangle has four right angles or square corners.
square has the four right and all sides the same length.

Topic 15 Assessment Practice

Question 1.
What other category does a parallelogram fall under?
A. Quadrilateral; because it has 4 right angles
B. Square; because it has 4 sides
C. Quadrilateral; because it has 4 sides
D. Rhombus; because all 4 sides are the same length

Answer:
Option D is correct.

Explanation:
In the above-given question,
given that,
a rhombus has all sides the same length.
because the rhombus has all 4 sides the same length.
rhombus comes under parallelogram.
so option D is correct.

Question 2.
Use the words in the box below. Write the names for the shapes in the correct columns.

Answer:
Quadrilateral comes under trapezoid.
rhombus, square, and rectangle come under parallelogram.

Explanation:
In the above-given question,
given that,
the shapes are rectangle, rhombus, square, and trapezoid.
the rectangle has four right angles or square corners.
rhombus has all sides the same length.
square has four right angles and all sides the same length.
so quadrilateral comes under trapezoid.

Question 3.
Name and draw a picture of a concave polygon with 4 sides.

Answer:
The trapezoid comes under a concave polygon.

Explanation:
In the above-given question,
given that,
concave polygon means that the sides come inside.
that means some of the sides come inside and also outside.
trapezoid comes under a concave polygon.

Question 4.
What are the possible shapes a parallelogram with 4 right angles could be?

Answer:
The possible shapes that come under a parallelogram with 4 right angles are a rectangle and a square.

Explanation:
In the above-given question,
given that,
the possible shapes a parallelogram with 4 right angles.
the rectangle has four right angles or square corners.
square has four right angles and all sides the same length.

Question 5.
The shapes are sorted into two groups, circled and not circled. How are the shapes in the two groups different?

Answer:
The circled shapes come under a parallelogram.
the not circled shapes come under quadrilateral.

Explanation:
In the above-given question,
given that,
the shapes are sorted into two groups.
the groups are circled and not circled.
the circled groups come under parallelogram.
the not circled shapes come under quadrilateral.

Question 6.
Select all true statements.
☐ A trapezoid is a parallelogram.
☐ A parallelogram is a quadrilateral.
☐ A square is a rhombus.
☐ A triangle is a quadrilateral.
☐ A square is a rectangle.

Answer:
A parallelogram is a quadrilateral.
A square is a rhombus.

Explanation:
In the above-given question,
given that,
the true statements are:
a parallelogram is a quadrilateral.
a square is a rhombus.
a parallelogram has opposite sides are the same length.
opposite angles are the same size.
rhombus has all sides the same length.
square has 4 right angles and all sides the same length.

Question 7.
What two quadrilaterals did Kim use to make the rug design? What do the shapes have in common?

Answer:
The two quadrilaterals are parallelogram and trapezoid.
the two shapes that have in common side lengths.

Explanation:
In the above-given question,
given that,
Kim uses to make the rug design.
the two quadrilaterals are parallelogram and trapezoid.
the parallelogram has opposite sides are the same length, opposite angles are the same size.
a trapezoid has exactly one pair of sides on lines that never cross.

Question 8.
Look at each group.

A. How are the two groups alike?

Answer:
The two groups are alike when the opposite sides are equal.

Explanation:
In the above-given question,
given that,
In group 1 the shapes are rhombus and parallelogram.
the parallelogram has opposite sides that are the same length.
in group 2 the shapes are square and rectangle.
square has four right angles and all sides the same length.
a square is a special parallelogram.
so the two groups are alike.

B. How are the two groups different?

Answer:
The two groups are different because rectangle and square have right angles.

Explanation:
In the above-given question,
given that,
In group 1 the shapes are rhombus and parallelogram.
the parallelogram has opposite sides that are the same length.
in group 2 the shapes are square and rectangle.
square has four right angles and all sides the same length.
rectangle and square have 4 right angles.
so they are different.

Question 9.
Which statement must be true about a rectangle?
A. It is a parallelogram.
B. It is a square.
C. It is a trapezoid.
D. It is a rhombus.

Answer:
Option A is correct.

Explanation:
In the above-given question,
given that,
the rectangle is a parallelogram.
the rectangle has four right angles or square corners.
so option A is correct.

Question 10.
Is a square always a rhombus? Explain.

Answer:
No, a square does not form a rhombus.

Explanation:
In the above-given question,
given that,
square has all 4 sides the same length and has 4 right angles.
rhombus has all 4 sides equal in length.
rhombus does not have the right angles.
so square does not form a rhombus.

Question 11.
Name and draw a quadrilateral that is NOT a rectangle or rhombus. Is there another shape you could have drawn? Explain.

Answer:
The other shape is a square.

Explanation:
In the above-given question,
given that,
the square has all four sides equal length.
all four sides have right angles.
so the quadrilateral that is not a rectangle or rhombus is a square.

Topic 15 Performance Task

Pet Tags Amelia and Bryce work at a pet store that sells pet identification tags in many shapes. The Pet Tags diagram shows the different shapes available.

Use the Pet Tags art to answer Questions 1-4.

Question 1.
A customer asks Amelia if the store has any pet tags that are concave. How should Amelia respond?

Answer:
The shape A is concave.

Explanation:
In the above-given question,
given that,
A customer asks Amelia if the store has any pet tags that are concave.
the concave shape has all the sides and one side come inside.
so the shape A is concave.

Question 2.
Another customer asks Bryce which pet tags have 2 pairs of equal-length sides and are quadrilaterals. Which tags have these attributes? Include the common name of each shape.

Answer:
The shapes B and D have 2 pairs of equal-length sides are parallelogram.

Explanation:
In the above-given question,
given that,
Another customer asks Bryce which pet tags have 2 pairs of equal length sides are quadrilaterals.
the shape B is a parallelogram.
the parallelogram has opposite sides that are the same length.
opposite angles are the same size.
so the rectangle and parallelogram have 2 pairs of equal-length sides are parallelogram.

Question 3.
The store owner wants to mark for sale any pet tags that are not rectangles. Which tags should she mark for sale, and what shapes are they?

Answer:
The shapes are A, C, E, F, and H are not rectangles.

Explanation:
In the above-given question,
given that,
the store owner wants to mark for sale and any pet tags are not rectangles.
the shape A is a concave polygon.
the shape C is a pentagon.
the shape E is a hexagon.
the shape F is a triangle.
the shape H is a trapezoid.

Question 4.
The owner asks Bryce to group the tags to show which ones have at least 1 pair of equal-length sides. Complete the table with the pet tag labels.

Answer:
The shapes B and G have at least 1 pair of equal-length sides.

Explanation:
In the above-given question,
given that,
the shapes Rhombus, triangle, and square have equal side lengths.
the shapes trapezoid, parallelogram does not have equal side lengths.
the shape B is a parallelogram.
the shape G is a square.
so the shapes B and G have at least 1 pair of equal-length sides.

Question 5.
Use the Pet Tags diagram and the Tag Sort table to answer the questions in Part A and Part B.

Amelia sorts some of the pet tags into two different groups.

Part A
How are the groups different?

Answer:
The groups are different according to their shapes.

Explanation:
In the above-given question,
given that,
in group A the shapes are trapezoid, rectangle, rhombus, and square.
they have the sidelengths and right angles.
in group B the shapes are pentagon, hexagon, and trapezoids.
they are concave polygons.
so the groups are different according to their shapes.

Part B
How are the groups alike?

Answer:
The two groups are alike when they have the same angles.

Explanation:
In the above-given question,
given that,
in group A the shapes are trapezoid, rectangle, rhombus, and square.
they have the sidelengths and right angles.
in group B the shapes are pentagon, hexagon, and trapezoids.
they are concave polygons.
so the groups are alike when they have the same angles.

Use the Pet Tags diagram to answer Questions 6 and 7.
Question 6.
A customer says she wants to buy a pet tag that is a rhombus and a rectangle. What tag does she want? Explain.

Answer:
The tags B and D are rhombus and a rectangle.

Explanation:
In the above-given question,
given that,
A customer says she wants to buy a pet tag that is a rhombus and a rectangle.
the shape B is a rhombus.
the shape D is a rectangle.
rhombus has all sides the same length.
the rectangle has the opposite sides the same length and four right angles.
so the tags B and D are the rhombus and a rectangle.

Question 7.
Design a new pet tag that has 2 pairs of sides the same length, but that is not a rectangle or a rhombus. Explain the shape you drew.

Answer:
I draw the shape that is a square.

Explanation:
In the above-given question,
given that,
design a new pet tag that has 2 pairs of sides the same length, but is not a rectangle.
the shape is a square.
square has all the sides the same length and all four angles are right angles.
so the pet tag is G.

Practice with the help of enVision Math Common Core Grade 3 Answer Key Topic 12 Understand Fractions as Numbers regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 12 Understand Fractions as Numbers

Essential Question:
What are different interpretations of a fraction?
Answer:
There are five different interpretations of fractions.
Explanation:
 Fractions as parts of wholes or parts of sets.
Fractions as the result of dividing two numbers.
Fractions as the ratio of two quantities.
Fractions as operators.
Fractions as measures. 

EnVision STEM Project: Fossils and Environment
Do Research Use the Internet or other sources to find out more about what fossils tell us about past environments. Research and make a booklet of fossils found in your state. Find at least 5 fossils and use one page for each fossil. Include where each fossil was found and what type of environment each location is now.

Write a Report: Journal Include what you found. Also in your report:

• List the types of food each of the 5 creatures ate when they were alive.
• Explain whether each of the 5 creatures on your list could live in today’s environment.
• Find the lengths of different fossils to the nearest half inch. Record the lengths in a line plot.

Review What You Know

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

• halves
• thirds
• inch
• yard

Question 1.
If a shape is divided into 2 equal parts, the parts can be called _________.
Answer:
Halves

Question 2.
The width of an adult’s thumb is about 1 _________.
Answer:
Inch

Question 3.
If a shape is divided into 3 equal parts, the parts can be called _________.
Answer:
Thirds

Skip Counting on the Number Line

Skip count on the number line. Write the missing numbers.
Question 4.

Answer:
125, 130, 135, 140, 145, 150, 155
Explanation:
Add 5 to each number present on number line.
110 + 5 = 115
115 + 5 = 120
120 + 5 = 125
125 + 5 = 130
130 + 5 = 135
135 + 5 = 140
140 + 5 = 145
145 + 5 = 150
150 + 5 = 155

Question 5.

Answer:
240, 260
Explanation:
Add 20 to each number present on number line
180 + 20 = 200
200 + 20 = 220
220 + 20 = 240
240 + 20 = 260

Equal Parts

Question 6.
Circle the shapes that show halves.

Answer:

Question 7.
Circle the shapes that show fourths.
Answer:

Measurement

Question 8.
How long is the nail to the nearest inch? Explain how you know.

Answer :
2 inches
Explanation :
The nail is in between the 1.5 marks and 2 inch mark
so the nearest inch the nail is 2 inches

Pick a Project

PROJECT 12A
How long would it take to drive across the Florida Keys?
Project: Make a Map

Answer:

The Florida Keys Overseas Highway is 113 miles in length, joining the mainland of Florida (starting in Florida City, just south of Homestead) to Key West. If you drove directly from Key Largo to Key West, it would take you roughly 2.5 hours, traveling distance of 100 miles.

PROJECT 12B
Why are there so many different floors in a building?
Project: Create a flooring design

Answer:
A floor is the bottom surface of a room or vehicle. Floors vary from simple dirt in a cave to many-layered surfaces made with modern technology. Floors may be stone, wood, bamboo, metal or any other material that can support the expected load. The levels of a building are often referred to as floors, although a more proper term is storey.

PROJECT 12C
What is the most common hat size?
Project: Collect Hat Size Data and Create a Line Plot

Answer:
Head sizes and shapes differ from region to region. The most common male size is 7-5/8 and the average hat size for females 7-2/8

PROJECT 12D
What are the most popular fruits and vegetables?
Project: Draw a Garden Plot

Answer:
The most popular fruits and vegetables are,
Fruits like Mango ,Banana ,Apple, Grapes, Water melon.. so on
Vegetables like Carrot, Potato, Tomato, Brinjal … So on

Lesson 12.1 Partition Regions into Equal Parts

Solve & Share
Show two different ways to divide a 2 x 6 region into 6 equal parts. How do you know the parts are equal?
I can … read and write a unit fraction.

Look Back! How are the parts of the regions alike? How are they different?

Essential Question
How Can You Name the Equal Parts of a Whole?
Answer:
Each equal part of a whole is called one-half.
Explanation:
One half is expressed as 1/2 and read as one over two or one upon two.

Visual Learning Bridge
You can divide a whole into equal parts. What fraction can you write to represent one of these equal parts?
A fraction is a part of a whole.
Divide each green whole into four equal parts.

Divide each green whole into six equal parts.

In the green wholes:

• All parts have an equal area.
• Each part is one sixth of the area of the whole.
• One sixth can be written as the fraction \(\frac{1}{6}\).

Convince Me! Critique Reasoning Kim says that the figure at the right is divided into fourths because there are 4 equal parts. Carrie says it is not divided into fourths because the parts are not the same shape. Who is correct? Explain.

Answer:
Carrie is correct.
Explanation:
In the given figure it is not divided into fourths because the parts are not of the same shape.

Guided Practice

Do You Understand?
Question 1.
In the examples in Box A on the previous page, explain how you know the 4 parts are equal.
Answer:
All parts are equal.
Explanation:
All parts have an equal area.
Each part is one-fourth or a quarter of the whole sheet.

In 2 and 3, tell if each shape shows equal or unequal parts. If the parts are equal, label 1 of the parts using a unit fraction.
Question 2.

Answer:
Equal parts
Explanation:
The area and size of each part of the figure are equal so the figure is divided into equal parts.

Question 3.

Answer:
Unequal parts
Explanation:
The area and size of each part of the figure are not equal so the figure is divided into unequal parts.

Do You Know How?
Question 4.
Draw lines to divide the shape into 8 equal parts. Then write the fraction that represents 1 part.

Answer:

1/8 unit fraction
Explanation:
The area and size of each part of the figure must be equal .
Then the figure is divided into equal parts
The total area of the figure is 24
So we need 8 parts
24 ÷ 8 = 3

Independent Practice

In 5-7, tell if each shape shows equal or unequal parts. If the parts are equal, label 1 of the parts using a unit fraction.
Question 5.

Answer:
Unequal parts
Explanation:
The given square has unequal parts, so it is difficult to denote in fraction

Question 6.

Answer:
Equal parts
Explanation:
The area and size of each part of the figure must be equal.
Then the figure is divided into equal parts.

Question 7.

Answer:
Equal parts
Explanation:
The area and size of each part of the figure must be equal.
Then the figure is divided into equal parts.

In 8-10, draw lines to divide the shape into the given number of equal parts. Then write the fraction that represents one part.
Question 8.
6 equal parts

Answer:

Question 9.
3 equal parts

Answer:

Question 10.
4 equal parts

Answer:

Problem Solving

In 11-14, use the table of flags to answer the questions.

Question 11.
What fraction represents the white part of Nigeria’s flag?
Answer:
one third[1/3]

Question 12.
Which nation’s flag is \(\frac{1}{2}\) red?
Answer:
Poland

Question 13.
Higher Order Thinking The flag of this nation has more than 3 equal parts. Which nation is it, and what fraction represents 1 part of its flag?
Answer:
Mauritius has more than 3 equal parts.
One fourth fraction represents 1 part of its flag.

Question 14.
Which nation’s flag is NOT divided into equal parts?
Answer:
Seychelles

Question 15.
Maryann buys 24 cans of soda. The soda comes in packs of 6 cans. How many packs does she purchase? Write a multiplication equation and a division equation to show your answer.
Answer:
4 packs of can soda
Explanation:
Maryann buys 24 cans of soda
1 pack of soda cans consist of 6 cans
so :
24 ÷ 6 = 4
Maryann buys 4 packs of soda cans
6 x 4 = 24

Question 16.
Make Sense and Persevere Jim has stickers in an array of 8 rows and 4 columns. He also has a packet of 14 stickers. How many stickers does Jim have in all?
Answer:
46 stickers
Explanation:
Jim has stickers in an array of 8 rows and 4 columns.
No of stickers in array are:
8 x 4 = 32 stickers
He also has a packet of 14 stickers.
total no of stickers Jim has are:
32 + 14 = 46 stickers

Assessment Practice

Question 17.
Draw lines to show how to divide this square into 8 equal pieces. Then select the fraction that represents 1 of the pieces.

A. \(\frac{1}{2}\)
B. \(\frac{1}{3}\)
C. \(\frac{1}{4}\)
D. \(\frac{1}{8}\)
Answer:

option D
1/8 unit fracttion

Lesson 12.2 Fractions and Regions

Solve & Share
Pat made a garden in the shape of a rectangle and divided it into 4 equal parts. She planted flowers in 3 of the parts. Draw a picture of what Pat’s garden might look like.
Answer:
Pat’s garden might look like this.

I can… use a fraction to represent multiple copies of a unit fraction.

Look Back! How many parts of Pat’s garden do NOT have flowers? Explain.
Answer:
1/4 part of Pat’s garden do NOT have flowers.
Explanation:
As  she planted only 3/4 of his garden with flowers.

Essential Question
How Can You Show and Name Parts of a Region?
Answer:
Fractions name parts of a whole region.
Explanation:
When an object is divided into a number of equal parts then each part is called a faction.
There are 2 parts that make up a faction:
Numerator: Which is the number that goes on top of the fraction, tells how many parts of the whole.
Denominator: Which is the number that goes on the bottom of the fraction, tells how many equal parts in all.

Visual Learning Bridge
Mr. Peters served part of a pan of enchiladas to a friend. What does each part of the whole pan represent? What part was served? What part is left?

Answer:
Each part of the whole represent fraction.
2/6 part is served.
4/6 part is left.

Convince Me! Be Precise Below is a picture of a pie pan. Draw lines and use shading to show that five \(\frac{1}{8}\)-pieces are still in the pan, and that three \(\frac{1}{8}\)-pieces were eaten. Use a fraction to label the part of the pie that is in the pan.

Answer:
3/8 pie in the pan is eaten.
5/8 pie in the pan is left over.

Guided Practice

Do You Understand?
Question 1.
In the problem in Box A on the previous page, what fraction names all of the pieces in the pan?
Answer:
The whole pan is divided into 6 equal parts. Each part is 1/6 of the whole
Explanation:
6 copies of 1/6 is 6/6.
So the whole is 6/6.
The unit fraction is 1/6.

Question 2.
Mrs. Patel made a cake. What fraction of the whole cake does each piece represent?

Answer:
1/8 fraction of the whole cake represents each piece

Question 3.
In the picture in Exercise 2, how many \(\frac{1}{8}\)-pieces were eaten? What fraction of the whole cake was eaten?
Answer:
2 pieces were eaten.
2/8 pieces were eaten.
Explanation:
In the given picture cake is divided into 8 equal parts.
Out of which 2 pieces were eaten.

Do You Know How?
In 4-6, use the figure below.

Question 4.
How many \(\frac{1}{3}\)-parts are blue?
Answer:
Two
Explanation:
Out of 3 parts in a given picture 2 parts are blue and 1 part is yellow.

Question 5.
What fraction of the whole is blue?
Answer:
Two third
Explanation:
In the given picture 2/3 of the whole is colored with blue

Question 6.
What fraction names all of the parts in the whole?
Answer:
1/3 one thirds

Independent Practice

In 7-10, write the unit fraction that represents each part of the whole. Then write the number of blue parts and the fraction of the whole that is blue.
Question 7.

Answer:
One part is blue
The fraction of whole is 1/2
Explanation:
The given triangle is equally divided into two,
one half colored with blue and the the other with yellow.
So the fraction of whole is 1/2.

Question 8.

Answer:
3 parts are blue
The fraction of whole is 3/6
Explanation:
Given hexagon is equally divided into six equal parts,
out of six, three are colored with blue and three with yellow
So the fraction of hexagon is written as 3/6.

Question 9.

Answer:
2 parts are blue
The fraction of whole is 2/4
Explanation:
Given circle is equally divided into 4 parts,
out of which 2 are colored with blue and 2 with yellow.
So the fraction of circle is written as 2/4.

Question 10.

Answer:
6 parts are blue
The fraction of whole is 6/8
Explanation:
Given picture is equally divided into 8 parts,
Out of which 6 are colored with blue and 2 with yellow.
So the fraction of given picture is written as 6/8.

Question 11.
Draw a rectangle that shows 6 equal parts. Write the unit fraction that represents each part. Then shade \(\frac{2}{6}\) of the rectangle. Explain how you know you shaded \(\frac{2}{6}\) of the rectangle.
Answer:

The unit fraction that represents the part of the rectangle is 116

Problem Solving

Question 12.
Vocabulary Fill in the blanks.
In the fraction \(\frac{4}{7}\), 4 is the ______ and 7 is the ________.
Answer:
4 is the numerator and 7 is denominator

Question 13.
Generalize Divide the grid below into fourths. Shade 3 of the parts. Write a fraction that represents the shaded area. Write a fraction that represents the unshaded area. What can you generalize about your fractions?

Answer:

Question 14.
Christine has 6 red scarves and 3 blue scarves. Each scarf has 2 stripes. How many stripes does Christine have on her scarves? Write equations to represent and solve the problem.
Answer:
Christine has 18 stripes in total on her scarves.
Explanation:
No of red scarves = 6
No of stripes on red scarves = 6 x 2 = 12
No of blue scarves + 3
No of stripes on blue scarves = 3 x 2 = 6
Total no of stripes = 12 + 6 = 18

Question 15.
Higher Order Thinking Draw a circle that shows 6 equal parts. Shade more than \(\frac{3}{6}\) of the circle, but less than \(\frac{5}{6}\) of the circle. What fraction have you shaded?
Answer:

Explanation:
A fraction more than 3/6 is 4/6 and a fraction less than 5/6 is 4/6
so we have to shade 4/6 of the circle

Question 16.
Number Sense What is the area of the baseball card? Show your work.

Answer:
The area of baseball card is 70 cm.
Explanation:
Baseball card is in the shape of rectangle.
So the area of rectangle is length X breadth  ( l x b )
Length = 10 cm
Breadth = 7 cm
Area = length x breadth
= 10 x 7
= 70 cm.

Assessment Practice

Question 17.
Select numbers from the box to write fractions to show 3 parts of each of these vegetable trays.

Answer:

Explanation:
The first plate is divided into 4 parts out of which three parts are removed
The second plate is divided into 6 parts out of which three parts are removed
The third plate is divided into 8 parts out of which three parts are removed

Lesson 12.3 Understand the Whole

Solve & Shar
Mrs. Garcia’s third-grade class is planting a flower garden and a vegetable garden.
Draw a picture of the whole flower garden and the whole vegetable garden based on the parts shown. How did you decide what the whole of each garden looked like?
I can … identify the whole by seeing a part.

Look Back! What do the fractions and tell you about the number of equal parts in the whole?
Answer:
A basic way to interpret a fraction is by dividing a whole object into several equal parts.
The denominator tells how many equal parts the whole is subdivided into.
The numerator tells the number of those parts that are under consideration.

Essential Question
How Can You Use a Fractional Part to Find the Whole?
Answer:
For finding a fraction of a whole number, we multiply the numerator of the fraction by the given number and then divide the product by the denominator of the fraction.

Visual Learning Bridge
Anya and Novi are running in different races. The diagrams below show how much of their races each runner has completed.
Draw a picture of the whole of each track. Write a fraction to represent the whole.

You can look at the fraction to find how many parts will make up the whole.

You know Anya and Novi have each completed \(\frac{1}{6}\) of their races.
Six lengths of \(\frac{1}{6}\) make \(\frac{6}{6}\), or 1 whole.

Convince Me! Reasoning Why is Novi’s track longer than Anya’s track?
Answer:
Novi’s track is longer than Anya’s track because 1/6th of the track were of different size.

Another Example! The part of a race Rob completed is shown at the right. You can use fractional parts like this to identify the whole.
\(\frac{2}{3}\) is 2 copies of \(\frac{1}{3}\). Divide Rob’s track into 2 equal parts.

Three copies of \(\frac{1}{3}\) make \(\frac{3}{3}\), or 1 whole. Draw one more third.
1 = \(\frac{3}{3}\).

Guided Practice

Do You Understand?
Question 1.
If the distance Anya ran was of the length of the track, what fraction would you use to represent the whole track?
Answer:
The fraction of whole track = 6/6
Explanation:
Six lengths of 1/6 make 6/6 or whole.

Question 2.
What is true about the numerator and denominator of each fraction that represents one whole?
Answer:
A fraction represents a part of a whole.
Explanation:
The numerator represents how many parts of that whole are being considered,
while the denominator represents the total number of parts created from the whole.

Do You Know How?
3. Draw a picture of the whole and write a fraction to represent the whole.

Answer:

Independent Practice

In 4-7, draw a picture of the whole and write a fraction to represent the whole.
Question 4.

Answer:

1 = 3/3

Question 5.

Answer:

1 = 2/2

Question 6.

Answer:
1 = 4/4

Question 7.

Answer:

1 = 6/6

Problem Solving

Question 8.
Ronnie and Gina were shown \(\frac{1}{2}\) of a table. They each drew a picture of the whole table. Whose drawing could be correct? Explain.

Answer:
Gina’s drawing of the whole table is correct
Explanation:
Both Ronnie and Gina were correct.
but tables are generally square , rectangle or circle in shape so Gina’s table is correct

Question 9.
Higher Order Thinking If the part shown in Exercise 8 is \(\frac{1}{4}\) of a table, what could the whole table look like? Draw a picture and write a fraction to represent the whole.
Answer:

One whole

Question 10.
The Florida panther is endangered. In 1970, the population was estimated at 20 panthers. In 2017, the population was estimated at 230 panthers. About how many more panthers were there in 2017 than in 1970?

Answer:
About 210 more panthers were there in 2017 than in 1970.
Explanation:
In 1970, the population was 20 panthers.
In 2017, the population was estimated at 230 panthers.
So 230 – 20 = 210.
Question 11.
Construct Arguments Jenna and Jamal are making rugs. They have finished the parts shown. Draw pictures to show each whole rug. Whose rug will be longer when it is finished? Explain.

Answer:
Jenna: I have finished 1/3 of my rug.
Jamal: I have finished 1/3 of my rug.
Jamal: My rug is bigger than you.
Jenna: How is your rug bigger than mine. Explain?
Jamal: My 1/3 of the rug is bigger than your 1/3 of the rug
Explanation:
Jamal’s 1/3 rd of the rug is bigger than Jenna’s 1/3 of the rug

So Jamal’s rug is longer than Jenna.
Assessment Practice

Question 12.
The picture shows \(\frac{2}{3}\) of a granola bar. Which shows the whole granola bar?

Answer:
Option B

Question 13.
Each part below is \(\frac{1}{2}\) of a different whole. Which is part of the largest whole?

Answer:
Option A

Lesson 12.4 Number Line: Fractions Less Than 1

Solve & Share
At a state park, there is a 1-mile hiking path between the park entrance and the beach. Scenic lookouts are located at points and of the distance from the park entrance to the beach. Show about where the lookout points are located on the line below.
I can… represent fractions on a number line.

Look Back! If you know about where the point for \(\frac{1}{3}\) is located, how can you find about where the point for \(\frac{2}{3}\) is located?
Answer:
The line is divided into 3 parts,
We know 1/3 location on number line.
The point next to 1/3is 2/3, so we know where 2/3 point is located.

Essential Question
How Can You Record Fractions on a Number Line?
Answer:
Fractions expand our number system beyond whole numbers and integers.
Explanation:
Fractions help us to denote any decimal number with higher precision.
Representation of Fractions on the number line is important to understand how fractions represent part of a whole.

Visual Learning Bridge
Mr. Singer is picking up his daughter, Greta, from school to go to soccer practice. Greta’s school is located at \(\frac{3}{4}\) of the distance from the Singers’ house to the soccer field. How can you represent \(\frac{3}{4}\) on a number line?
Every number on a number line represents a distance from 0.

Convince Me! Critique Reasoning Jenna and Benito each marked \(\frac{1}{4}\) on a number line. The length of the part from 0 to \(\frac{1}{4}\) on Jenna’s number line is shorter than on Benito at Benito’s. Did someone make a mistake? Explain your thinking.

Jenna did a mistake by marking unit fraction on a small number line, compared with Benito number line. 
Guided Practice

Do You Understand?
Question 1.
Maliya divides a number line from 0 to 1 into 6 equal lengths. What unit fraction represents each equal length? What should Maliya label the tick mark just to the left of 1? Explain.
Answer:
5/6 unit fraction
Explanation:
0 to 1 is divided in to 6 fractions
Each 1/6 unit fraction

Question 2.
Josh divides a number line from 0 to 1 into 8 equal lengths. What should he label the first tick mark just to the right of 0? Explain.
Answer:
1/8 unit fraction.
Explanation:

Do You Know How?
In 3 and 4, divide the number line into the given number of equal lengths. Then mark and label the given fraction on the number line.
Question 3.
2 equal lengths; \(\frac{1}{2}\)

Answer:

Question 4.
4 equal lengths; \(\frac{2}{4}\)

Answer:

Explanation :
Draw a line and make 3 equal parts on number line and then mark 1/4, 2/4 and 3/4unit fraction.

Leveled Practice In 5 and 6, divide the number line into the given number of equal lengths. Then mark and label the given fraction on the number line.
Question 5.
3 equal lengths; \(\frac{2}{3}\)

Answer:
2/3 unit fraction.

Explanation : Draw a line and make 3 equal parts on number line and then mark 1/3, 2/3 and 3/3 units

Question 6.
6 equal lengths; \(\frac{2}{6}\)

Answer: 2/6

Explanation :
Draw a line and make 6 equal parts on number line and then mark 1/6, 2/6,3/6,4/6,5/6 and 6/6units

In 7 and 8, draw a number line from 0 to 1. Divide the number line into equal lengths for the given fraction. Then mark and label the given fraction on the number line.
Question 7.
\(\frac{4}{6}\)
Answer: 4/6

Explanation :
Draw a line and make 6 equal parts on number line and then mark 1/6, 2/6,3/6,4/6,5/6 and 6/6units

Question 8.
\(\frac{5}{8}\)
Answer: 5/8

Explanation :
Draw a line and make 8 equal parts on number line and then mark 1/8 , 2/8 , 3/8 , 4/8 , 5/8 , 6/8 , 7/8 and 8/8units

Problem Solving

Question 9.
Construct Arguments Terrance and Dana each drew a number line and marked \(\frac{3}{4}\). Did each person represent \(\frac{3}{4}\) in the correct place on his or her line? Explain.

Answer:
yes
Explanation:
Terrance number line is a bit smaller that Dana’s but both the number lines are divided into equal parts.

Question 10.
A gymnast starts at the left end of the balance beam and does some handsprings. When she is finished, she is at the point shown on the diagram. What fraction represents how far she went on the balance beam?

Answer:
6/8 unit fraction.
Explanation :
The balance beam is divided in to 8 equal parts of same unit lengths
the point is market at 6/8 on the balance beam.

Question 11.
Mark draws a number line and labels the points for 0 and 1. He divides the distance from 0 to 1 into 2 equal lengths and labels the fraction \(\frac{1}{2}\). If Mark divides each half into 2 equal lengths, what fractions can Mark label on his number line?
Answer:

Explanation:
Mark draws a number line and labels the points for 0 and 1 of two equal lengths and labels the fraction and label 0 , 1/2 and 1.
Mark divides each half into 2 equal lengths, each fractions is marked labels on his number line as 1/4, 2/4, 3/4 and 4/4
as shown in the above figure.

Question 12.
Higher Order Thinking Show 3 ways you can represent three eighths.
Answer:

The number ABOVE the line tells HOW MANY PARTS
we have (the colored parts).The number BELOW the line tells how many EQUAL parts
the whole is divided into. To find 3/8 of a number, we multiply the numerator 3 by the given whole number and then divide the product by the denominator 8.

Assessment Practice

Question 13.
What fraction does the red point on this number line represent?

Answer:
Option  C
Explanation:
The above line is of 6 equal parts of each label 1/6, 2/6, 3/6, 4/6, 5/6 and 6/6

Question 14.
Which number line has a red point at \(\frac{1}{3}\)?

Answer:
Option A
Explanation :
In the number line has a red point at \(\frac{1}{3}\)

Lesson 12.5 Number Line: Fractions Greater Than 1

Solve & Share
The length of one strip of paper is 1 whole unit. Fold two strips of paper in half. Open the two strips and place them end to end.
How many halves do you have? Use fractions to name each fold line. Tell how you decided. Draw a picture to show your work.
Answer:
2 halves

strip of paper is 1 whole unit. Fold two strips of paper in half,
two halves for two strips of papers , if it unfolded and kept end to end open

I can … represent fractions equal to or greater than 1 on a number line

Look Back! If you added a third strip of paper folded in half, how could you use halves to name the fold lines? Explain.
Answer:
If you add a third strip of paper folded in half, as 5/4 and 6/4.
Explanation:
One can represent fractions equal to or greater than 1 on a number line.

Essential Question
How Can You Use a Number Line to Represent Fractions Greater Than 1?
Answer:
Fractions greater than 1 have numerators larger than their denominators, those that are less than 1 have numerators smaller than their denominators; the rest are equal to 1.

Visual Learning Bridge
A marsh rabbit hopped \(\frac{7}{4}\) the length of a rabbit trail. How can you show this on a number line?
Number lines can represent fractions that are greater than 1 whole \(\frac{7}{4}\). 5 is greater than 1 whole, but less than 2 wholes. The whole is the distance between 0 and 1.

Divide each whole into 4 equal lengths.
Each length is \(\frac{1}{4}\) of the whole.
\(\frac{4}{4}\) is the same as 1 whole.

The marsh rabbit hopped 7 lengths of the unit fraction \(\frac{1}{4}\).
The point showing 7 lengths of \(\frac{1}{4}\) can be labeled as \(\frac{7}{4}\)

Answer: 7/4
Explanation:
Marsh rabbit hopped shown in the number line.

Convince Me! Be Precise One tick mark on the number line below has been named with the fraction \(\frac{2}{3}\). On the number line the lengths marked are equal. Write fractions for the other tick marks shown.

Answer:

Explanation:
Divided a number line from 0 to 1 into 3 equal lengths. Each unit fraction represents 1/3 of equal length.

Guided Practice

Do You Understand?
Question 1.
Name a fraction that is to the right of the tick mark for 2 on a number line.
Answer: 7/3
Explanation :

Question 2.
Quinn says that \(\frac{10}{8}\) comes to the right of \(\frac{9}{8}\) on a number line. Do you agree? Why or why not?
Answer: YES
Explanation:

Do You Know How?
In 3 and 4, each number line has equal lengths marked. Write the missing fractions.
Question 3.

Answer:
1/3 and 4/3 of unit fraction.
Explanation:
Marked on number line.

Question 4.

Answer:
1/4,  4/4,  5/4 and 7/4 are marked on number line.
Explanation:

Independent Practice

Leveled Practice In 5-7, each number line has equal lengths marked. Write the missing fractions.
Question 5.

Answer:
1/2 and 3/2 are missing marked on number line.
Explanation:

Question 6.

Answer:
1/4 and 4/4 or 1 are marked on number line.

Explanation:

Question 7.

Answer:
2/6,  4/6 and 5/6 are missing marked on number line.
Explanation:

In 8 and 9, divide the number lines into equal lengths. Write the missing fractions.

Question 8.

Answer:
1/3, 4/3, 5/3 7/3 and 8/3 are marked on number line.

Explanation:

Question 9.

Answer:
2/8, 3/8, 5/8 and 6/8 are missing numbers marked on number line.
Explanation:

Problem Solving

In 10 and 11, use the number line below.

Question 10.
What fraction tells how far the swimming pool is from the school? Explain how you know.
Answer:
1⅓ mile from school.
Explanation :

Question 11.
Higher Order Thinking The hospital is halfway between the grocery store and the post office. What fraction tells how far the hospital is from the school? Explain.
Answer:
4/6 unit fraction.
Explanation :
The hospital is 4/6 mile distance from the school, it is located at 4/6 on number line.

Question 12.
Tim has 78 board games. He has 10 boxes. Each box holds 9 games. If Tim puts all the games he has into the boxes, how many more games can he fit? Complete the bar diagram and solve the problem.

Answer:
12 more games.
Explanation:

Tim has 10 Boxes, each box holds 9 games.
Total boxes can hold 90 games, but the Tim has 78 games.
Required games = 90-78 = 12 games.

Question 13.
Critique Reasoning Rachel says that she can find (7 × 5) × 2 by calculating (7 × 2) + (5 × 2) = 14 + 10. Then add to get 24. Does Rachel’s reasoning make sense? Use properties of operations to explain.
Answer:
Rachel’s reasoning doesn’t make any sense.
Explanation:
Commutative Property      x + y = y+ x
Associative Property          x + (y + z) = (x + y) + z
According to the above two properties (7×5)x2=70 and
(7 × 2) + (5 × 2) = 14 + 10 =24.

Assessment Practice

Question 14.
What fraction is represented by the total length marked on the number line? Select the correct fraction from the box.

Answer:
4/3 fraction on number length.
Explanation:

Lesson 12.6 Line Plots and Length

Solve & Share
Jamie measured the lengths of 6 beetles. She measured each beetle’s length to the nearest inch and to the nearest half inch. She recorded the lengths in the two line plots below. Measure the length of each beetle below to the nearest inch and to the nearest half inch. Record your measurements in Jamie’s line plots.
I can … measure to the nearest half inch and show the data on a line plot.

Look Back! What tool did you use to measure the length of each beetle? How did you use this tool?
Answer :
I used a scale to measure the beetle.
We have to place the beetle beside the scale and then we have to mark the length of the beetle on a piece of paper.

Essential Question
How Can You Measure Lengths and Use Line Plots to Show the Data?
Answer:
Line plots, are particularly useful for showing measurement data.
Explanation:
If a class of students all measured the length of their pencils, a line plot would highlight the range and frequency of the measurements.

Visual Learning Bridge
Julio is measuring some lengths of yarn in inches. How can he use a ruler to measure to the nearest half inch?
Line up one end of the object with 0.

The fifth \(\frac{1}{2}\)-inch tick mark is closest to the end of the length of yarn.
So, to the nearest half inch, the yarn measures \(\frac{5}{2}\) inches.
This length is two whole inches and one \(\frac{1}{2}\) inch. You can write this length as 2\(\frac{1}{2}\) inches.
Answer:
Julio measured 9 other lengths of yarn in inches:

Explanation:
One can use number lines to show fractions.
A line plot is a way to organize data on a number line.

Steps to Make a Line Plot

• Draw a number line. Show a scale based on the data.
• Write a title for the line plot.
• Mark a dot for each data value.
  Answer:
  

Convince Me! Reasoning Suppose you measured a length of yarn that was about 4\(\frac{1}{2}\) inches. How would you need to change the line plot above to record this length?
Answer:
It has to extend up to 9/2.
Explanation:
The line is extended to right side and the values are increases as shown in the above line plot,
values on line is extended up to 9/2 for 4½.

Guided Practice

Do You Understand?
Question 1.
Draw a line that is 1½ inches long.
Answer:

Question 2.
If a line measures halfway between 3 and 3\(\frac{1}{2}\) inches and you need to measure to the nearest \(\frac{1}{2}\) inch, what length will you record? Why?
Answer:
3 inches is the nearest inch.

Explanation:
The line is nearer to 3 inch mark.

Do You Know How?
Question 3.
Measure the length of each of your fingers. List the measurements to the nearest half inch.
Answer:
1 Index or Point Finger of Length 3 inches
2 Middle Finger of Length 3½ inches
3 Ring Finger of Length 3 inches
4 Little Finger of Length 2½ inches
5 Thumb Finger of Length  2½ inches
Explanation:
Answers may vary from hand to hand.

Question 4.
Make a line plot to show the measurements of your fingers.
Answer:
Inches of fingers may vary from person to person.
Explanation:

Question 5.
Measure the lengths of the pieces of yarn at the right to the nearest half inch. Write the length for each piece.

Answer:
First      – 3 inches
Second – 2½ inches
Third     – 3 inches
Forth     – 2 inches
Fifth      – 2 inches
Explanation:
Length of yarn may vary.

Question 6.
Draw a line to represent another length of yarn. Measure your line to the nearest half inch.
Answer:
3½ inches length yarn.

Question 7.
Make a line plot to show the measurements of the yarn.

Answer:
3½ inches length yarn.

Problem Solving

Question 8.
Measure the lengths of 10 classroom objects to the nearest half inch. Choose objects that are between 1 and 6 inches long. Record your measurements.
Answer:

Question 9.
On grid paper, draw a line plot to show your data from Exercise 8.
Answer:

Question 10.
Make Sense and Persevere Raymond weighed his three dogs. The oldest dog weighs 74 pounds. The other two dogs each weigh 34 pounds. How many more pounds does the oldest dog weigh than the other two dogs combined?
Answer:
The oldest dog weighs 6 more ponds than the other two dogs.
Explanation:
Weight of oldest dog is 74
Weight of other two dogs (34+34) is 68
So the oldest dog weighs 6 ponds more
74 – 68 = 6

Question 11.
Draw a number line from 0 to 2. Label the wholes. Divide each whole into thirds. Label each fraction.
Answer:

In 12 and 13, use the table at the right.

Question 12.
How many more of the shortest paper chains does Rico have than the longest paper chains? Explain.
Answer:
Shortest paper chain length 6½
Rico has 3 shortest paper chains each of length 6½
Explanation :
In the table the shortest length of the paper chain is 6½
There are 3 shortest 6½

Question 13.
Higher Order Thinking Look at Rico’s measurements. Can you tell if he measured the paper chains to the nearest half inch or to the nearest inch? Explain.
Answer:
Rico’s measurements are to the nearest half inch
Explanation:
If we look at Rico’s measurements all of the measurements are in inches and nearest half inches,
there are no one fourth inches.
So Rico’s measurements are in nearest half inches.

Assessment Practice

Question 14.
Jessica used 4 of Nail A, 2 of Nail B, and 3 of Nail C to build a birdhouse. Measure each nail to the nearest half inch. Then complete the line plot.

Answer:

Lesson 12.7 More Line Plots and Length

Solve & Share
Monica and her friends measured the lengths of their shoes. Show this data by marking a dot for each length on the line plot below.
Measure the length of three classmates’ shoes. Add a dot to represent each length on the line plot. What length was the most common?
I can … measure to the nearest fourth inch and show the data on a line plot.

Look Back! Are there different ways to record the results of a data collection? Explain.
Answer:
Yes, there are different ways to record the results of a data collection.
Explanation:
We can use a scale, measuring tape, and so on to measure the data.

Essentials Question
How Can You Make and Use Line Plots?
Answer:
A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer than 25 numbers. It is a quick, simple way to organize data.

Visual Learning Bridge
Anna is measuring the length of her crayons. How can she use a ruler to measure to the nearest fourth inch?
Line up one end of the object with 0.

The tenth \(\frac{1}{4}\)-inch tick mark is closest to the end of the length of the crayon.
So, to the nearest fourth inch, the crayon measures \(\frac{10}{4}\) inches.
This length is two whole inches and two \(\frac{1}{4}\) inches. You can write this length as 2\(\frac{2}{4}\) inches.

Anna measured her other crayons.
She then recorded the data in a line plot.

Convince Me! Make Sense and Persevere Nathan also made a line plot to show the lengths of his crayons. Tell three things you know about the lengths of Nathan’s crayons.

Answer:
Nathan’s measured his crayons nearest ¼th
Most of Nathan’s crayons are 2¼ inches
The smallest crayon Nathan’s has 1 inch.

Guided Practice

Do You Understand?
Question 1.
Measure the length of this line to the nearest fourth inch.

Answer:
Length = 3¾ inches
Explanation:

Question 2.
Describe how you would show this measurement on a line plot.
Answer:

Do You Know How?
Question 3.
Draw a line plot to show the data.

Answer:

Question 4.
Measure your pencil to the nearest fourth inch. Show the length on your line plot.
Answer:
length of pencil : 3 \(\frac{3}{4}\)

Independent Practice

Question 5.
Daisy measured the lengths of her toy dinosaurs to the nearest fourth inch. She listed the lengths. Make a line plot to show the data.
1\(\frac{2}{4}\) in., 2\(\frac{1}{4}\) in., 1 in., 1\(\frac{2}{4}\) in., 1\(\frac{3}{4}\) in.
Answer:

Question 6.
Measure the lengths of the toy dinosaurs at the right to the nearest fourth inch. Write the length for each toy. Show the lengths on your line plot.
Answer:
length of toy 1 : 1\(\frac{2}{4}\) in.
length of toy 2 : 2\(\frac{1}{4}\) in.
length of toy 3 : 1 in.
length of toy 4 : 1\(\frac{2}{4}\) in.
length of toy 5 : 1\(\frac{3}{4}\) in.

Problem Solving

In 7 and 8, use the line plot at the right.

Question 7.
Arty made a line plot to show the number of inches that different snails crawled in a 5-minute race. What was the most common distance that the snails crawled?
Answer:
the most common distance that the snails crawled is 9 \(\frac{1}{4}\) inches

Question 8.
Higher Order Thinking How many more snails crawled a length more than 8\(\frac{3}{4}\) inches than a length less than 8\(\frac{3}{4}\) inches?
Answer:
snails that crawled length less than 8\(\frac{3}{4}\) inches are : 6
snails that crawled length more than 8\(\frac{3}{4}\) inches are : 19
difference : 19 – 6 = 13 snails
13 more snails crawled a length more than 8\(\frac{3}{4}\) inches than a length less than 8\(\frac{3}{4}\) inches

Question 9.
Measure the lengths of 10 classroom objects to the nearest fourth inch. Choose objects that are between 1 and 5 inches long. Record your measurements.
Answer:

Question 10.
On grid paper, draw a line plot to show your data from Exercise 9.
Answer:

Question 11.
Jackson bought 5 books that cost $7 each. How much change did he get from $40?
Answer:
Jackson got $5 change.
Explanation:
Cost of each book = $7
Cost of 5 books = 5×7
Total cost of 5 books =$35
Total amount paid = $40
Total change he received = 40-35
= $5.

Question 12.
Use Structure Use the digits 2, 6, and 8 to make as many 3-digit numbers as you can. Use place value to arrange the numbers in order from least to greatest.
Answer:
H     T     U
2     6      8
2     8      6
6     2      8
6     8      2
8     2      6
8     6      2
Assessment Practice

Question 13.
Tonya is making headbands. She recorded the lengths of all the blue bows she purchased for the headbands. Tonya also purchased 4 red bows with lengths of 1 inch, 1\(\frac{1}{4}\) inches, 1\(\frac{2}{4}\) inches, and 1\(\frac{2}{4}\) inches. Record the lengths of Tonya’s red bows in the line plot.

Answer:
Red bows are : 1 inch , 1\(\frac{1}{4}\) inches, 1\(\frac{2}{4}\) inches, and 1\(\frac{2}{4}\) inches.
so there are 4 red bows.

Lesson 12.8 Problem Solving

Make Sense and Persevere
Solve & Share
Marcus, Mariah, and Tony painted a mural. They divided it into equal parts. Marcus painted 2 parts, Mariah painted 3 parts, and Tony painted the rest. What fraction of the mural did each student paint?
This problem may have missing or extra information. If information you need is missing, make up some reasonable information and then solve the problem.
I can … make sense of problems and keep working if I get stuck.

Thinking Habits
Be a good thinker! These questions can help you.

• What do I need to find?
• What do I know?
• What’s my plan for solving the problem?
• What else can I try if I get stuck?
• How can I check that my solution makes sense?
  

Look Back! Make Sense and Persevere What information was not given in the problem? How did you still solve the problem?
Answer:
The number of parts the mural is divided into was not given
Additional information:
Marcus, Mariah, and Tony painted a mural. They divided it into 8 equal parts. Marcus painted 2 parts, Mariah painted 3 parts, and Tony painted the rest. What fraction of the mural did each student paint?
Answer:
Marcus painted 2 parts
Mariah painted 3 parts
and Tony painted the rest
= 8 – ( 2 + 3 )
= 8 – 5
= 3 parts
Tony painted 3 parts
Marcus painted  :  \(\frac{2}{8}\)
Mariah painted  :  \(\frac{3}{8}\)
Tony painted      :  \(\frac{3}{8}\)

Essential Question
How Can You Make Sense of a Problem and Persevere in Solving It?
Answer:
The meaning of a problem and looking for entry points to its solution. Helps to analyze givens, constraints, relationships, and goals.

Suki divides her garden into 6 equal parts. She plants daisies, roses, and violets. It takes Suki 1 hour to plant the flowers. She plants daisies in 1 part, roses in 2 parts, and violets in the rest of the garden.
In what fraction of the garden does Suki plant violets?

What is a good plan for solving the problem?
I need to make sense of the given information. I need to think about what I can use to help me solve the problem.

How can I make sense of and solve this problem?
Answer:
I can…..

• identify the quantities given.
• understand which quantities are needed to solve the problem.
• choose and implement an appropriate strategy.
• check to be sure my work and answer make sense.
  Explanation:

The information about 1 hour to plant the flowers is not needed to solve the problem.
I can use a picture to help make sense.
1 equal part for daisies is \(\frac{1}{6}\) of the whole.
2 equal parts for roses is \(\frac{2}{6}\) of the whole.
There are 3 equal parts left for violets.

3 copies of \(\frac{1}{6}\) is \(\frac{3}{6}\).
So, Suki plants violets in \(\frac{3}{6}\) of the garden.

Convince Me! Make Sense and Persevere How can you check to make sure the work and answer given above make sense?
Answer:
Total number of parts garden is divided into is: 6 parts
Daisies are planted in 1 part [ 1/6 fraction]
Roses are planted in 2 parts [ 2/6 fraction]
So Suki plants violets in 3 parts as :
1 + 2 = 3
6 – 3  = 3 parts
3/6 unit fraction.

Guided Practice

Make Sense and Persevere Keira and Matt cut a sandwich into 4 equal parts. They each ate 1 part. Keira is 9 years old. Matt is the same age as Keira. What fraction of the sandwich is not eaten?

Question 1.
Is there any missing or extra information? Explain.
Answer:
Missing information : none
Extra information : the ages of Keira and Matt are given [we don’t need their ages to determine the parts of the sandwich left]

Question 2.
What do you need to find before you can determine how much of the sandwich is left?
Answer:
We don’t need to find the any other information as all the needed information is given in the question

Question 3.
Solve the problem. If information you need is missing, make up some reasonable information for the problem.
Answer:
The sandwich is divided into 4 equal parts
Keira and Matt each ate one part so total parts eaten : 2 parts
number of parts left is : 4- 2 = 2 parts

Independent Practice

Make Sense and Persevere Marni planted a vegetable garden. She put lettuce in 1 part, carrots in 4 parts, and broccoli in the rest of her garden. In what fraction of the garden did Marni plant broccoli?
Question 4.
Is there any missing or extra information?
Answer:
Missing information : the question did not specify the number of the parts Marni’s garden is divided into
Extra information : none

Question 5.
Solve the problem. If information you need is missing, make up some reasonable information for the problem.
Answer:
Additional information : Marni’s garden is divided into 8 parts. She put lettuce in 1 part, carrots in 4 parts, and broccoli in the rest of her garden. In what fraction of the garden did Marni plant broccoli?
Answer:
fraction in which broccoli is planted : 3/8
Explanation:
Total number of parts Marni’s garden is divided into is 8 parts
lettuce : 1 part
carrots : 4 parts
broccoli : 8 – (1 + 4)
.             : 8 – 5 = 3
fraction in which broccoli is planted : 3/8

Question 6.
Can you use a different number of parts and still solve the problem? Explain.
Answer:
yes
Explanation :
If Total number of parts Marni’s garden is divided into is 6 parts
lettuce : 1 part
carrots : 4 parts
broccoli : 6 – (1 + 4)
.             : 6 – 5 = 1
fraction in which broccoli is planted : 1/8

Problem Solving

Performance Task
Sports Day
Green School divides its school gym into 8 equal parts for a sports day. Basketball is in 2 parts, soccer is in 1 part, and volleyball and tennis are in the rest.

Question 7.
Make Sense and Persevere The gym teacher wants to know what fraction of the gym is used for tennis. What missing information do you need to solve the problem?
Answer:
School gym is divides into 8 equal parts.
Tennis and Volleyball not clearly mentioned, these two are missing information do you need to solve the problem.

In 8 and 9, draw a picture to represent the number of parts in each plan.
Question 8.
Reasoning What fraction of the gym would be used for tennis if 2 parts were for volleyball?

Answer: 3 parts

Explanation:
if 2 parts were used for volleyball , three parts used for tennis

Question 9.
Reasoning What fraction of the gym would be used for tennis if 3 parts were used for volleyball?
Answer: 2 PARTS

Explanation : if 3 parts were used for volleyball , two parts used for tennis as shown in that above picture

Question 10.
Construct Arguments To have the same fraction for tennis as for basketball, which plan, Exercise 8 or 9, should be used? Justify your answer.
Answer:
plan 9 should be used
Explanation:
for tennis and basket ball to be equal we need to have equal number of parts for tennis and basket ball
in question 9 plan tennis and basket ball both are takin a space of 2 parts
whereas in question 8 plan tennis is taking up more space than that of basket ball
so,
for tennis and basket ball to be equal we need to have equal number of parts for tennis and basket ball

Topic 12 Fluency Practice Activity

Follow the path
Shade a path from START to FINISH. Follow the sums and differences where the digit in the hundreds place is greater than the digit in the tens place. You can only move up, down, right, or left.
I can … add and subtract within 1,000.

Answer :

Topic 12 Vocabulary Review

Understand Vocabulary
Word List

• denominator
• fraction
• line plot
• nearest fourth inch
• nearest half inch
• numerator
• unit fraction

Question 1.
Circle each unit fraction.
\(\frac{1}{4}\)
\(\frac{3}{8}\)
\(\frac{1}{6}\)
\(\frac{1}{8}\)
\(\frac{2}{3}\)
Answer:

Question 2.
Circle each fraction where 6 is the denominator.
\(\frac{3}{6}\)
\(\frac{6}{8}\)
\(\frac{1}{6}\)
\(\frac{5}{6}\)
\(\frac{4}{8}\)
Answer:

Question 3.
Circle each fraction where 4 is the numerator.
\(\frac{2}{4}\)
\(\frac{4}{8}\)
\(\frac{1}{4}\)
\(\frac{3}{4}\)
\(\frac{4}{6}\)
Answer:

Question 4.
Circle the lengths that could be measurements to the nearest half inch.
2\(\frac{1}{2}\) in.
4 in.
3\(\frac{3}{4}\) in.
7\(\frac{1}{4}\) in.
6 in.
Answer:

Question 5.
Circle the lengths that could be measurements to the nearest fourth inch.
8\(\frac{3}{4}\) in.
1\(\frac{1}{4}\) in.
11 in.
7\(\frac{1}{4}\) in.
6 in.
Answer:

Write always, sometimes, or never.
Question 6.
The numerator in a fraction is _?_ greater than the denominator. _________
Answer:
Some times
Explanation:
In a proper fraction, the numerator is sometimes more than the denominator.
Question 7.
A fraction ? _ has a numerator and denominator. __________
Answer:
Always
Explanation:
A fraction represents a part of a whole or any number of equal parts.
For example, one-half, eight-fifths, three-quarters.
Question 8
A line plot_?_ shows measurements of lengths. _________
Answer:
Never
Explanation:
A Line plot can be defined as a graph that displays data as points or check marks above a number line, showing the frequency of each value.

Question 9.
Use at least 2 terms from the Word List to explain how to find the unit fraction of the shape shown below.

Answer:
1/6
Explanation:
A unit fraction is any fraction with 1 as its numerator (top number), and a whole number for the denominator (bottom number).
If we divide the hexagon into 6 equal parts
then each part will be one part of the six parts
that is 1/6

Topic 12 Reteaching

Set A pages 437-440

This is one way to divide a whole into fourths.

Because each of the 4 parts has the same area, each part is one fourth of the whole.
You can write this fraction as \(\frac{1}{4}\)
A unit fraction represents one of the equal parts \(\frac{1}{4}\) is a unit fraction.

Remember that fractions can name equal parts of a whole.

In 1 and 2, draw lines to divide the shape into the given number of equal parts. Then write the fraction that represents 1 part.
Question 1.
6 equal parts

Answer:

Explanation:
total area of the figure : 12
12 divided into 6 parts is 12 ÷ 6 = 2

Question 2.
2 equal parts

Answer:

Explanation:
total area of the figure : 12
12 divided into 2 parts is 12 ÷ 2 = 6

Question 3.
Martin divides a shape into 3 equal parts. What unit fraction can he write to represent 1 part?
Answer:

Set B pages 441-444

What fraction of this rectangle is shaded?

The rectangle is divided into 8 equal parts. So, the unit fraction of the rectangle is \(\frac{1}{8}\).
In the whole rectangle, there are 8 parts of \(\frac{1}{8}\).
8 copies of \(\frac{1}{8}\) is \(\frac{8}{8}\)
For the shaded part there are 6 parts of \(\frac{1}{8}\).

6 copies of \(\frac{1}{8}\) is \(\frac{6}{8}\)
So, \(\frac{6}{8}\) of the rectangle is shaded.

Remember that you need to think about how many parts there are in all and how many parts are shaded.

In 1-4, write the unit fraction that represents each part of the whole. Next, write the number of shaded parts. Last, write the fraction of the whole that is shaded.
Question 1.

Answer:
Unit fraction = 1/3
Number of shaded part is one.
Fraction of whole that is shaded = 1/3
Question 2.

Answer:
Unit fraction = 5/6
Number of shaded parts are 5
Fraction of whole that is shaded = 5/6
Question 3.

Answer:
Unit fraction = 3/4
Number of shaded parts are 3
Fraction of whole that is shaded = 3/4

Question 4.

Answer:
Unit fraction = 2/4
Number of shaded parts are 2
Fraction of whole that is shaded = 2/4

Set C pages 445-448

This shape is \(\frac{2}{4}\) of a piece of fabric Tina used in a quilt. You can draw a picture and write a fraction to represent the whole piece of fabric.

\(\frac{2}{4}\) is 2 copies of \(\frac{1}{4}\)
Divide the piece of fabric into 2 equal parts.
4 copies of \(\frac{1}{4}\) makes \(\frac{4}{4}\). or 1 whole.

Remember that the denominator shows the total number of equal parts in a whole.

In 1 and 2, draw a picture and write a fraction to represent the whole.
Question 1.

Answer:

1 = 4/4

Question 2.

Answer:

1 = 8/8

Set D pages 449-452

You can show fractions on a number line.
The fraction \(\frac{5}{6}\) is labeled. What are the missing fractions?

First, find the unit fraction. The line is divided into six equal lengths. So, the number line shows sixths.
Each jump represents \(\frac{1}{6}\). So, the first tick mark is labeled \(\frac{1}{6}\). The second tick mark is labeled \(\frac{2}{6}\), and so on.
The missing fractions on the number line are \(\frac{1}{6}, \frac{2}{6}, \frac{3}{6}\), and \(\frac{4}{6}\)

Remember to first decide what unit fraction is shown on each number line.

In 1 and 2, write the missing fractions on each number line.
Question 1.

Answer:
1/4 and 3/4

Question 2.

Answer:
1/8 , 2/8 , 4/8 , 5/8 , 7/8

Question 3.
Divide the number line below into 3 equal parts and mark \(\frac{2}{3}\) on the line.

Answer:

Set E pages 453-456

Number lines can have fractions greater than 1.
The number line below is divided into thirds.
The denominator is 3 because the unit fraction is \(\frac{1}{3}\). The numerator shows how many copies of the unit fraction each point represents.

Remember that the numerator increases by 1 because each part of the number line is 1 more copy of the unit fraction.

Question 1.
The number line has equal lengths marked. Write the missing fractions.

Answer:
1/6 , 4/6 , 5/6 , 7/6 , 8/6

Question 2.
Divide the number line into fourths. Label each point.

Answer:

Set F pages 457-460

You can use a line plot to show data, such as lengths measured to the nearest half inch.
Steps to make a line plot:

• Draw a number line and choose a scale.
• The scale should show data values from the least to the greatest.
• Write a title for the line plot.
• Mark a dot for each value.
  

Remember to mark a dot for each length. Check your completed line plot against the data in the chart.

Question 1.
Draw a line plot to show the data.
Answer:

Question 2.
How many strings does Carl have in all?
Answer:
10 strings
Explanation:
2½ inch strings – 04
3 inch    strings – 03
3½ inch strings – 02
4 inch    strings – 01

Question 3.
Draw a line that is the same length as the most common string length.
Answer:
Most common string is 2½ inch

Set G pages 461-464

You can measure to different lengths, such as to the nearest fourth inch.
The closest fourth-inch mark to the end of the length of the rectangle is the 2\(\frac{1}{4}\)-inch mark.

The lengths can be shown on a line plot.

Remember to think about the scale of the line plot. It needs to include the least and greatest values.

Question 1.
Measure and record the lengths of 5 classroom objects to the nearest fourth inch. Use objects that are between 1 and 3 inches long.
Answer:
Eraser : 1.5 inches
Pencil :  2.7 inches
Pen Cap : 2.3 inches
Chalk : 2.3 inches
Sticker : 1 inch

Question 2.
Draw a line plot to show your data.
Answer:

Set H pages 465-468

Think about these questions to help you make sense and persevere in solving problems.
Thinking Habits

• What do I need to find?
• What do I know?
• What’s my plan for solving the problem?
• What else can I try if I get stuck?
• How can I check that my solution makes sense?
  

Remember to make sense of the problem by identifying the quantities. Then use what you know to solve.

Gavin divided his notebook into 8 equal parts. He plans to use 3 parts to take notes for math and 2 parts for reading. He has school from 8:30 A.M. to 3:30 P.M. What fraction of his notebook does he have left?
Question 1.
Is there any missing or extra information? Explain.
Answer:
Gavin divided his book into 8 equal parts
3 parts are used for math 3/8
2 parts are used for reading 2/8
The fraction of notebook he has left is :
3 + 2 = 5
8 – 5 = 3
The fraction of notebook he has left is 3/5

Question 2.
Solve the problem. If information you need is missing, make up some reasonable information for the problem. You can draw a picture to help.
Answer:
The missing information is:
3/8 part of the book was used for science

Topic 12 Assessment Practice

Question 1.
What fraction of the whole is colored green? What fraction of the whole is colored yellow?

Answer:
3/6 fraction of the whole is colored green.
3/6 fraction of the whole is colored yellow.

Question 2.
Write a fraction to name the equal parts of the whole pizza. How many parts would you need to make two whole pizzas? Explain.

Answer:
Fraction name : 1/8
we need 16 parts to make 2 whole pizzas
Explanation:
1 pizza needs 8 parts to make 1 whole so we need 16 parts [8 + 8 = 16] to make 2 wholes

Question 3.
This line segment represents \(\frac{1}{3}\) of the distance from Mal’s house to the library. Which represents the whole distance and has an accurate explanation?

A. The line segment represents \(\frac{1}{3}\) the distance from Mal’s house to the library. So, the whole distance is 3 times as long.
B. The line segment represents \(\frac{1}{3}\) the distance from Mal’s house to the library. So, the whole distance is 2 times as long.
C. The line segment represents \(\frac{1}{3}\) the distance from Mal’s house to the library. So, the whole distance is 4 times as long.
D. The line segment represents the distance from Mal’s house to the library. So, the whole distance is the identical line segment.
Answer:
Option A
Explanation:
The line segment represents 1/3 the distance from Mal’s house to the library. So, the whole distance is 3 times as long.

Question 4.
Which point is at \(\frac{3}{6}\) on the number line?

A. Point A
B. Point B
C. Point C
D. Point D
Answer:
Point B

Question 5.
Which of the fractions would be to the right of 1 on a number line? Select all that apply.

Answer:
5/4

Question 6.
A. Draw a picture to show \(\frac{2}{4}\).
Answer:

B. Explain how you knew you had shaded the correct amount of your picture.
Answer:
Divide the circle into fourths and then shade 2 of the 4 parts blue

Question 7.
Jeremy put pepperoni on \(\frac{1}{2}\) of a pizza. He put olives on \(\frac{1}{3}\) of the pizza. What fraction of the pizza did NOT have pepperoni? What fraction of the pizza did NOT have olives?
Answer:
1/2 of the fraction did not have pepperoni.
2/3 of the fraction did not have olives.

Question 8.
One point on the number line below has been named with the fraction \(\frac{2}{4}\). Write a fraction for each of the other points shown.

Answer:

Question 9.
Explain how you know \(\frac{3}{3}\) represents a whole.
Answer:
Fraction 3/3 means 3 parts of 3 parts
Dividing 3 with 3 we get 1
So the fraction 3/3 is a whole 1

Question 10.
Jared folded a piece of paper 9 inches by 12 inches into sections as shown below. What fraction of the total area is in each section? Explain.

Answer:
Fraction of total Area is 36
Explanation:
Area of total paper = 9 x 12 = 108 sq.inches
The paper is divided into 3 equal part
Area of each part = 108 ÷ 3 = 36 sq.inches

Question 11.
How many \(\frac{2}{8}\)s do you need to get \(\frac{8}{8}\)?
Answer:
Four
Explanation:
we need four 2/8 fractions to get 8/8
2/8 + 2/8 + 2/8 + 2/8 = 8/8

Question 12.
Lane’s class is painting a mural with 6 equal parts. They spent 45 minutes painting on each of 2 days. On the first day, the class painted \(\frac{1}{6}\) of the mural. The next day, the class painted another \(\frac{1}{6}\) of the mural. How many \(\frac{1}{6}\) parts did the class paint in the two days?
A. 1
B. 2
C. 3
D. 4
Answer:
Option B
Explanation:
The class paints 1/6 part each day in d days the class paints 2/6 parts
1/6 – day 1
1/6 – day 2
By day 2 no of parts painted are 1/6 + 1/6 = 2/6

Question 13.
How many \(\frac{1}{8}\) s do you need to get \(\frac{5}{8}\)? Use the number line below for help.
A. 1
B. 3
C. 5
D. 8

Answer:
Option C
Explanation:
You need 5 yards to make 1/8 as 5/8

Question 14.
Which point represents 6 lengths of \(\frac{1}{8}\) on the number line? Explain.

Answer:
Point D

Question 15.
Divide the circle into 8 equal parts. What fraction does each part represent?

Answer:

Each part represent1/8 fraction.

Question 16.
Seth drew \(\frac{2}{4}\) of a shape below. Draw a picture to show the whole shape and write a fraction to represent the whole.

Answer:

Explanation:
One whole is 4/4 that means to get 4/4 we need to have 2 parts of 2/4
As 2/4 + 2/4 = 4/4

Question 17.
Mara believes the point marked on the number line is \(\frac{2}{3}\). Is she correct? Explain.

Answer:
Mara is wrong
Explanation:
the markings of the fractions on the number line are not correct
[the markings are not even there is a lot of gap between 1/3 and 3/3]

Question 18.
Select all the sentences that describe this shape.

Answer:

Question 19.
Divide the number line into equal lengths. Then mark and label the given fraction.
6 equal lengths; \(\frac{5}{6}\)

Answer:

Explanation:
First divide the number line into 6 equal parts like in the picture below

Then mark the 5/6th point

Question 20.
Tony collects colored strings. The table shows the lengths of some of his strings.

A. Measure the lengths of Tony’s red and brown strings shown below to the nearest fourth inch.

Answer:
Red string     : 3     inches
Brown string : 2¾ inches

B. Draw a line plot to show the lengths of Tony’s 7 strings to the nearest fourth inch.
Answer:

Topic 12 Performance Task

Art Display
Three students, Zach, Allie, and Paige, are making an art display.

Use the Paint Colors list and the design at the right to answer Questions 1-4.
Question 1.
The display will be divided into 8 equal parts. Paint Colors Draw lines to show one way to do this. Then write the fraction that describes the the total shape that is represented by 1 equal part.
Paint Colors

• Allie is painting the blue parts.
• Paige is painting the red parts.
• Zach is painting the yellow parts.
•  Each student will paint at least 2 parts.
  

Answer:

1/8 part

Question 2.
Shade the parts blue, yellow, or red to show how many parts each student could paint. Write fractions to show how much of the total display Allie and Paige painted.
Answer:

• Allie is painting the 3 blue parts.      3/8
• Paige is painting the 3 red parts.      3/8
• Zach is painting the 2 yellow parts.

Question 3.
Divide the number line into the number of equal parts of the display. Then mark a dot to show the fraction of the display that Zach painted on the number line.

Answer:

Question 4.
Which fraction represents the whole display? Explain. Then mark a dot to show where this fraction is located on the number line above.
Answer:
8/8 is the whole fraction

Use the Ribbon Lengths diagram on the right and the Number of Ribbons table below to answer Question 5.

Question 5.
The students will use the ribbon lengths at the right in their display
Part A
Measure and record the lengths of each of these ribbons to the nearest fourth inch.
Answer:
RED Ribbon : 3¾
BLUE Ribbon : 3 2/4  [3½]
GREEN Ribbon : 3¼

Part B
The Number of Ribbons table shows how many of each color ribbon will be used. Draw a line plot to show this data.

Answer:

Question 6.
In order to complete the display, the students recorded the number of half-hour sessions they spent working together. The number line below is divided into equal parts. Each part represents half an hour. Write the missing fractions on the number line.

Answer:

enVision Math Common Core Grade 3 Answer Key

Practice with the help of enVision Math Common Core Grade 3 Answer Key Topic 9 Fluently Add and Subtract within 1,000 regularly and improve your accuracy in solving questions.

enVision Math Common Core 3rd Grade Answers Key Topic 9 Fluently Add and Subtract within 1,000

Essential Question: What are the 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 addition and 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.