what did the mathematician do to practice over winter break answer key

Go through theenVision Math Common Cadre Class 4 Respond Fundamental Topic ii Fluently Add and Subtract Multi-Digit Whole Numbers regularly and ameliorate your accuracy in solving questions.

enVision Math Common Core quaternary Grade Answers Key Topic 2 Fluently Add and Subtract Multi-Digit Whole Numbers

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

enVision STEM Projection: The World'southward Fastest Vehicles
Do Research Since 1970, the speed tape has been broken many times. Use the Internet or other sources to notice v vehicles that can get faster than ane,000 kilometers per hour.
Journal: Write a Report Include what you found. Also in your written report:

• Make a table that includes the type of vehicle, whether the vehicle moves on state, h2o, or in space, and the speed of the vehicle.
• Employ place value to find the fastest and the slowest vehicle in your tabular array.
• Calculate the difference between the speeds of two of the vehicles in your table.

Review What You Know

Vocabulary
Cull the all-time term from the box. Write it on the bare.

• equation
• estimate
• period
• rounding

Question 1.
An __________ is an judge number or respond.
Answer:
An estimate is an apporoximate number or reply.

Question 2.
A procedure that determines which multiple of x, 100, 1,000, and so on a number is closest to is called _________.
Answer:
A procedure that determines which multiple of 10, 100, 1000, and And then on a number is closest to is called rounding.

Question iii.
A number sentence that uses the equal sign (=) to show two expressions have the same value is an __________.
Answer:
A number judgement that uses the equal sign(=) to bear witness ii expressions have the same value is an equation.

Addition Facts and Mental Math

Notice each sum.
Question 4.
four + six
Reply:
four + 6 = x

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

Explanation:
The sum of vii and five is 12.

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

Explanation:
The sum of 29 and 8 is 37.

Question vii.
14 + 5
Reply:
xiv + v = 19

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

Explanation:
The sum of xiii and 7 is 20.

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

Question ten.
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 – three
Reply:
27 – three = 24

Question fourteen.
six – 4
Answer:
half dozen – 4 = ii

Question xv.
15 – 8
Answer:
15 – eight = vii

Question sixteen.
eleven – 8
Answer:
eleven – 8 = 3

Explanation:
The divergence between xi 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 ix.

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

Explanation:
The difference between 416 and 404 is 12.

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

Explanation:
The difference between 220 and 205 is xv.

Question 21.
148 – 106
Respond:
148 – 106 = 132

Explanation:
The deviation 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 m?

Answer:
The dominion for rounding to the nearest x thousand is to await at the last four digits.If the last four digits are  5000 or greater, then nosotros round our ten thousands digit up, and if it is less than 5000, and then we proceed our 10 thousands digit the same.
So, 843,000 rounds downs to 840000.

Selection a Project

PROJECT 2A
What are the largest cities in your domicile country?
Project: Map the Population of Your State's Largest Cities

Projection 2B
How did the U.s. get a nation?
Project: Write a Report on U.Due south. Expansion

PROJECT 2C
How exercise the sizes of the planets compare to the size of Globe?
Project: Make a Model of the Solar Organization

Projection 2D
How high is high?
Projection: Compare Mount Elevations

Lesson 2.1 Finding Sums and Differences with Mental Math

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

Expect Dorsum! Construct Arguments How could yous use mental math to solve 1,289 + 1,566? 1,034 + ane,566? How is the thinking unlike?

Essential Question
How Tin can You lot Use Mental on Math to Solve Problems?

Visual Learning Bridge
Katy'southward dad washes windows at i of the tallest buildings in Miami, the Four Seasons Hotel. He worked Saturdays in Oct 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 $two,595 in Oct.
+five+10 +80 +500 +two,000
Make 10

Break apart ane,985 to become a number that makes a ten, hundred, or thousand when added to ii,595. Then, use the Associative Property of Addition to change the grouping.
1,985 + 2,595
= (i,580 + 405) + 2,595
= 1,580 + (405 + ii,595)
= 1,580 + 3,000
= four,580
Katy'southward dad earned $four,580.

Add On
Break i addend apart and add together on.

You can start with either addend because of the Commutative Property of Addition.

Katy'due south dad earned $4,580.

Use Compensation
Add together xv to one,985. Then subtract 15 from 2,595 to recoup. Calculation 15 and subtracting 15 is the same as calculation zero. Adding zero doesn't alter the sum because of the Identity Property of Addition.
1,985 + 2,595
= (one,985 + 15) + (two,595 – 15)
= 2,000 + 2,580
= 4,580
Katy's dad earned $4,580.

Convince Me! Apply Structure How could y'all brand ten past breaking apart ii,595?

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

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

Find how much you lot counted up.
five + x + 595 = 610

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

Utilize Bounty
Adding the same corporeality to both numbers in a subtraction problem doesn't change the difference.
1,990
two,510
(2,595 + 15) – (1,985 + 15)
= 2,610 – ii,000
= 610

Guided Exercise

Do You Empathize?
Question 1.
Explicate how to find 2,987 + four,278 with mental math. What property does your strategy apply?
Answer:
7265

Caption:
Use Compensation
Add 13 to 2,987. Then subtract 13 from 4278 to compensate. Adding xiii and subtracting 13 is the same as adding zero. Adding naught doesn't alter 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.

Practise You Know How?
For 2-4, utilise mental math strategies to solve.
Question two.
6,794 – 999
Answer:

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

Question 3.
4,505 + 3,515
Respond:
7620

Caption:
Make Ten

Suspension apart 4505 to get a number that makes a ten, hundred, or g 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 autonomously 9100 to get a number that makes a x, hundred, or thousand when added to 2130 and 900. Then, use the Associative Belongings of Add-on to alter the grouping.
9100 + 2130 + 900
=(9000+100) + 2130 + 900
=9000 + (100+900) + 2130
=9000 + grand + 2130
=10000 + 2130
=12130
Therefore, the sum of 9100, 2130 and 900 is 12130.

Independent Exercise

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

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

Question half dozen.
1,225 + 975
Answer:
2200

Explanation:
Use Compensation
Add 75 to 1,225. Then subtract 75 from 975 to recoup. Adding 15 and subtracting 15 is the same every bit calculation zero. Adding nothing doesn't alter the sum considering of the Identity Property of Addition.
one,225 + 975
= (1225 + 75) + (975 – 75)
= 1300 + 900
= 2200
The sum of 1225 and 975 is 2200.

Question 7.
v,491 – 2,860
Answer:

Explanation:
40+60+2491=2591
The departure 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 ix.
8,375 + 31,145
Answer:
39520

Caption:
Brand Ten

Break apart 8375 to get a number that makes a ten, hundred, or 1000 when added to 31145. And so, 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:
Brand Ten

Break autonomously 23100 to get a number that makes a x, hundred, or thousand when added to 74900. Then, use the Associative Property of Addition to change the group.
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, employ the table at the correct.

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

Question 12.
Circular the state surface area of the country with the to the lowest degree number of square miles to the nearest 10 thousand.
Answer:

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

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

Question 15.
Higher Guild Thinking Is Kelly's respond correct? What fault did she brand?
Kelly's Work
v,356 + 2,398
= (5,356 + ii) +(2,398 + two)
5,358 + two,400 = vii,758
Answer:
Kelly'southward piece of work is wrong.her error is she has to add and subtract the number if the question is to find the sum.

Explanation:
Add and decrease same number, the respond will non differ.
(5356-two) + (2398+2)
5354 + 2400
7754
Therefore 5356 + 2398 = 7754.

Assessment Exercise

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

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

Question 17.
Utilize mental math to find five,280 – 1,997.
A. 3,177
B. 3,180
C. 3,277
D. 3,283
Answer:
D.3283

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

Lesson 2.ii Estimate Sums and Differences

Solve & Share
A manufacturer in Detroit produces three new cars that weigh 6,127 pounds, iv,652 pounds, and iii,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 whatsoever way y'all choose.
I tin can … apply rounding and identify value to estimate sums and differences.

Answer:

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

Await Back! Why can you solve the problem using but an estimate rather than finding the exact weight of the iii cars?

Essential Question
How Tin You Approximate Sums and Differences of Whole Numbers?
Answer:
Nosotros can estimate the sums and deviation 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. Nigh how many more than books were checked out than magazines and movies combined?

Estimate: Round to the nearest g.
Notice the number of magazines and movies.

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

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

Decrease the number of magazines and movies from the rounded number of books.
12,600 – half dozen,400 = half dozen,200
Most 6,200 more than 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 departure between the number of books and the number of these other materials is greater than 6,500. Which of the estimates to a higher place should you lot apply to help her make her determination? Explain.

Another Case!
Decide if each computation is reasonable.
Y'all can utilize an estimate to decide whether or not an exact answer is reasonable.
39,482 + 26,357 = 65,839
39,482 + 26,357 is almost 40,000 + 26,000 = 66,000
The sum, 65,839, is reasonable because information technology is close to the estimate of 66,000.

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

Guided Practice

Do You Understand?
Question 1.
Is 2,793 a reasonable difference for 6,904 – four,111? Explicate.
Answer:

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

Do You lot Know How?
For two-four, judge each sum or difference.
Question ii.

Respond:

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

Question 3.

Answer:

Caption:
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, guess each sum or divergence.
Question v.

Respond:

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

Question vi.

Answer:

Caption:
When rounded to the nearest hundreds,
The estimated deviation 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:

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

Question ten.

Answer:

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

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

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

Question 12.
9,668 – ii,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.

Trouble 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 Uncomplicated and Kwame Charter School? Explain.

Answer:

Caption:
When rounded to the nearest hundreds,
The estimated sum is 3000.
Therefore, every bit 2,981 is close to 3000, information technology is reasonable for the total number of students at Wilson Elementary and Kwame Charter School

Question 15.
enVision® Stalk 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. Nearly how much faster is one satellite than the other? Explain how to approximate.
Reply:

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

Question 16.
Critique Reasoning Elle says, "When rounding to the nearest g, 928,674 rounds to 930,000." Do yous hold? Explain.
Answer:
No, I don't agree with Elle as she rounded of to the nearest then thousands rather tha nearest thousand.
The nearest m for 928674 is 929000.
When we circular of o the nearest thousand we have to wait at the last three digits and if information technology 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 cyberspace m than the digit in thousands place.

Question 17.
Higher Order Thinking A football squad needs to sell at to the lowest degree 20,000 tickets to ii games to comprehend 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 reply.
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
Equally both sums are same or close to 20000.
Therefore, the team could sell enough ticketsto embrace their expenses.

Assessment Practice

Question 18.
Concluding week, Mallory flew 2 round trips. They were iii,720 miles and 5,985 miles. Which is the best estimate of the full distance Mallory flew?
A. 11,000 miles
B. 9,700 miles
C. 8,700 miles
D. viii,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 all-time estimate.

Question nineteen.
Utilise estimation to determine which is a reasonable divergence.
38,041 – 19,558
A. 21,374
B. 20,973
C. 18,473
D. xvi,483
Answer:
C.18473

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

Lesson 2.three Add Whole Numbers

Solve & Share
Students collect empty plastic h2o bottles to recycle. How many bottles were collected in the offset two months? How many bottles were nerveless in all three months? Solve this problem using any strategy you choose.
I can … connect place-value concepts to using addition algorithms.

Expect Back! When calculation, how do you know when at that place are enough tens to make one hundred?

Essential Question
How Practise You Add Whole Numbers Efficiently?

Visual Learning Span
The Florida Legislature set a statewide recycling goal. To aid encounter this goal, Kennedy Elementary school students nerveless paper. 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 Construction in the trouble above, when yous add fractional sums you can add the ones commencement or the hundreds. Can you do the same when you add using the standard algorithm?

Guided Practice

Practise You Sympathise?
Question 1.
When you identify a 1 above the tens values, what does information technology mean?
Reply:
If i place 1 above the tens values it ways that i regrouped ones.

Question 2.
When y'all place a 1 above the hundreds values, what does it hateful?
Reply:
If i place one in a higher place the hundreds values it means that i regouped tens.

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

Answer:

Explanation:
The sum of 378 and 557 is 935.

Detect each sum using the strategy you lot cull.
Question 4
a.

Answer:

Explanation:
The sum of 678 and 253 is 931.

b.

Answer:

Caption:
The sum of 325 and 256 is 581.

c.

Answer:

Explanation:
The sum of 185 and 253 is 438.

Independent Practice

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

Answer:

Explanation:
The sum of 148 and 157 is 305.

Question 6.

Reply:

Explanation:
The sum of 389 and 461 is 850.

Question seven.

Reply:

Explanation:
The sum of 365 and 458 is 823.

Question viii.

Respond:

Explanation:
The sum of 126 and 138 is 264.

Question 9.

Answer:

Explanation:
The sum of 371 and 454 is 825.

Question ten.

Reply:

Explanation:
The sum of 357 and 498 is 855.

Question xi.
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:

Caption:
The sum of 375 and 548 is 923.

Question 14.
718 + 865
Reply:

Explanation:
The sum of 718 and 865 is 1583.

Question fifteen.
909 + 624
Reply:

Explanation:
The sum of 909 and 624 is 1533.

Question 16.
129 + 587
Reply:

Caption:
The sum of 129 and 587 is 716.

Trouble Solving

Question 17.
Construct Arguments Harmony solved this trouble using the standard algorithm, but she made an fault. What was her error, and how tin can she set information technology?

Answer:

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

Question 18.
Higher Guild Thinking For which problems would y'all use a mental strategy or the standard algorithm to solve? Explain.
499 + 121
827 +385
175 + 325
Reply:
I use mental strategy to solve 499+121 and 175+325 as the number in hundreds place is small and information technology is easy to slove mentally, I utilize standard algorithm to solve 827+385 every bit the number in hundreds place is big.

Question 19.
A Trivial League team played a doubleheader (two back-to-back baseball game games). The start game lasted 155 minutes. The 2d game lasted 175 minutes. At that place was a thirty-minute break between games. What was the total fourth dimension of the doubleheader?
Answer:

Explanation:
A Fiddling League squad played a doubleheader, The offset game lasted 155 minutes. The second game lasted 175 minutes. In that location 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 = i,288
☐ 735 + 298 = 1,033
☐ 912 + 198 = one,010
Reply:

Explanation:
The marked sums are correct.

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

Answer:

Explanation:
To observe the missing number start decrease 1004 and 659, we get 345 equally the answer.The missing tens is iv.

Lesson two.4 Add together Greater Numbers

Solve & Share
Erica's class collected 4,219 bottles for the recycling center. Ana'south grade collected three,742 bottles. Leon'due south class collected four,436 bottles. How many bottles did the three classes collect? Solve this problem any style you lot choose.
I tin … utilize the standard algorithm and place value to add multi-digit numbers.

Wait Back! Generalize Which backdrop permit you to change the order and grouping of numbers to add? How did yous use these properties?

Essential Question
infant 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:
xx,000 + 4,595 = 24,595

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

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

The remodeled stadium will take 43,850 seats.
Yous can add together two or more numbers when you line upwards 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 shut to the estimate of 44,000, so the respond is reasonable.

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

Another Instance!
Find 30,283 + 63,423 + half dozen,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 gauge of 100,000.

Guided Practices

Do You Understand?
Question 1.
When calculation 36,424 and 24,482, why is in that location 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 ii.
Scientific discipline-volunteer teams itemize 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.

Practise You Know How?
For 3-6, observe each sum. Cheque that your answer is reasonable.
Question iii.

Answer:

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

Question iv.

Answer:

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

Question v.

Answer:

Caption:
The sum of 3258 and 1761 is 5019.Answer is reasonable as the approximate 5100 is close to the reply.

Question 6.

Reply:

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

Independent Exercise

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

Question seven.

Answer:

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

Question viii.

Reply:

Explanation:
The sum of 275558 and 605131 is 880689.Respond is reasonable as the gauge 881000 is close to the reply.

Question 9.

Respond:

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

Question 10.

Answer:

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

Question 11.

Answer:

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

Question 12.

Answer:

Caption:
The sum of 5555 and 7412 is 12967.Respond is reasonable equally the estimate 13000 is close to the reply.

Question xiii.

Respond:

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

Question 14.

Reply:

Explanation:
The sum of 30080 and 19187 is 49267.Answer is reasonable equally the estimate 49000 is shut 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:

Caption:
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 side by side week, 47,684 people read her 2nd post. Aubrey'southward tertiary mail service had 41,582 readers. What is the total number of readers?
Respond:

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

Question eighteen.
Write the number name for 21,604.
Answer:
Number proper name of 21604 is Twenty ane thousand six hundred four.

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

Respond:
The right sum is 872879.

Explanation:
The sum of 638528 and 234351 is 872879.
The error is regrouping 8 and iv thousands equally i 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'southward reply reasonable? Explain.
Answer:

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

Question 21.
Make Sense and Persevere In that location were 130,453 pairs of skates rented at an ice rink in one year. The next yr, 108,626 pairs were rented. The post-obit year 178,119 pairs were rented. How many pairs were rented during the busiest two years? How many pairs were rented during all 3 years?
Respond:

Caption:
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.
☐ v,742 + 8,353 = xiv,095
☐ nine,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 add-on expressions that accept a sum of 89,405.
☐ 78,487 + 7,998
☐ 79,562 + 9,843
☐ 2,222 + 77,183
☐ 52,514 + 36,891
☐ six,573 + 82,832
Respond:

Lesson 2.five Decrease 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 trouble using any strategy you cull.
I tin can … connect place-value concepts to using the standard algorithm for subtraction

Wait Dorsum! How can you use properties to find the number of rooms not rented?

Essential Question
How Tin 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 exercise you lot need to regroup to subtract 483 – 295? Explicate.

Guided Practice

Practise You lot Empathize?
Question 1.
To decrease 859 – 583, how do y'all regroup 8 hundreds 5 tens?
Answer:

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

Question ii.
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 Y'all Know How?
In 3-half-dozen, subtract. Use an estimate to bank check that your answer is reasonable.
Question 3.

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

Explanation:
The deviation of 154 and 89 is 65.
The difference 65 is reasonable equally information technology is close to the estimated deviation lx.

Question 4.

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

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

Question v.

Reply:
Judge: 915 — 920, 288 — 290
920-290=630

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

Question 6.

Reply:
Approximate: 743 — 740, 694 — 690
740-690=l

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 seven-18, decrease. Utilise an estimate to cheque that your reply is reasonable.
Question 7.

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

Explanation:
The deviation of 289 and 145 is 144.
The divergence 144 is reasonable equally information technology is shut to the estimated divergence 140.

Question 8.

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

Caption:
The difference of 326 and 184 is 142.
The difference 142 is reasonable every bit information technology is close to the estimated departure 150.

Question 9.

Answer:
Approximate: 736 — 740, 218 — 220
740-220=520

Caption:
The divergence of 736 and 218 is 518.
The difference 518 is reasonable equally information technology is close to the estimated deviation 520.

Question 10.

Reply:
Judge: 525 — 530, 267 — 270
530-270=260

Explanation:
The difference of 525 and 267 is 258.
The divergence 258 is reasonable as information technology is shut to the estimated deviation 250.

Question 11.

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

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

Question 12.

Answer:
Approximate: 847 — 850, 387 — 390
850-390=460

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

Question xiii.

Answer:
Guess: 475 — 480, 98 — 100
480-100=380

Caption:
The departure of 475 and 98 is 377.
The difference 377 is reasonable as information technology is close to the estimated difference 380.

Question fourteen.

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

Caption:
The difference of 826 and 184 is 642.
The difference 642 is reasonable as it is close to the estimated departure 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 information technology is shut to the estimated difference 720.

Question xvi.
167 – 79
Respond:

Explanation:
The difference of 167 and 79 is 88.

Question 17.
284 – 167
Answer:

Explanation:
The departure of 284 and 167 is 117.

Question 18.
817 – 548
Reply:

Caption:
The difference of 817 and 548 is 269.

Problem Solving

Question 19.
How much greater is the surface area of Hernando Canton than Spousal relationship County?

Respond:

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

Question xx.
Make Sense and Persevere How much greater is the area of Monroe County than the expanse of Union County and Hernando County combined? Explain.
Answer:
The expanse of spousal relationship 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 Wedlock County and Hernando County combined.

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

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

Question 22.
College Gild Thinking What mistake did Leon make? What is the correct deviation?

Answer:

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

Assessment Do

Question 23.
What is the difference?

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

Explanation:
The departure of 724 and 459 is 265.

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

Answer:

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

Lesson two.six Decrease Greater Numbers

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

Expect Back! Guess the difference in the areas of the two states. Is your reply shut to this judge?

Essential Question
How Do You lot Decrease Greater Numbers Efficiently?

Visual Learning Bridge
Three of the country'due south 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?
Observe the full expanse of Denali and Kenai Fjords.

Pace i
Detect 34,287 – 21,893.
Subtract the ones. Regroup if necessary

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

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

Pace 3
Operations that disengage each other are changed operations. Addition and subtraction have an inverse relationship. Add to cheque your answer.

Convince Me! Critique Reasoning The work shown is Non correct. What errors were made? Bear witness how to find the correct answer.

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

Guided Practise

Exercise You lot Understand?
Question 1.
In the subtraction trouble above, why was the null in the ten thousands place not written in the answer?
Respond:

Question 2.
The total land area of New Bailiwick of jersey is xix,047 square kilometers. Write and solve an equation to show how to find how much more than 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 than state surface area than New Jersey.

Do Yous Know How?
For 3-vi, subtract. Gauge to check whether your answers are reasonable.
Question iii.
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
Reply:
Guess:2200-1400=800

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

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

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

Question half dozen.
281,311 – 3,427
Answer:
Estimate: 281000-3000=278000

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

Independent Practice

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

Answer:
Judge: 82000-47000=35000

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

Question eight.

Answer:
Estimate: 654000-562000=92000

Explanation:
The divergence of 653642 and 562410 is 91232
The deviation 91232 is reasonable equally it is close to the estimate 92000.

Question 9.

Answer:
Estimate: 9000-4000=5000

Caption:
The difference of 9128 and 3753 is 5375
The divergence 5375 is reasonable as it is shut to the approximate 5000.

Question 10.

Answer:
Guess: 43000-8000=35000

Explanation:
The deviation of 42648 and 8169 is 34479
The difference 34479 is reasonable every bit it is close to the approximate 35000.

Question 11.

Reply:
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:
Gauge: 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 departure of 215714 and 176313 is 39401
The difference 39401 is reasonable as it is close to the approximate 40000.

Question 14.

Answer:
Estimate: 86000-74000=12000

Explanation:
The difference of 85968 and 74084 is 11884
The difference 11884 is reasonable equally information technology is close to the approximate 12000.

Trouble Solving

Question fifteen.
Reasoning A crayon visitor makes 87,491 bluish crayons, 36,262 blood-red crayons, and 25,063 gray crayons. How many more blue crayons are made than cerise and gray crayons combined?
Answer:
At that place are 61325 cerise and gray crayons combined


Explanation:
The departure of 87491 and 61325 is 26166.
Therefore there are 26166 mistiness crayons are fabricated more than red and gray crayons.

Question sixteen.
Number Sense Patrick subtracted four,832 – 2,322 and got 2,510. Is his difference reasonable? Explicate.
Answer:
Yes, Patrick's answer is reasonable.

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

Question 17.
College Gild Thinking Nadia found 9,476 – viii,185 using the algorithm shown. Show how to find one,784 – i,339 with Nadia's algorithm.
9,476 – eight,185 = i,000 + 300 – ten + 1
= one,291
Answer:
1784-1339 = 500-100+xl+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 off-white in 2019 than in 2017 and 2018 combined?

Answer:
193301 people attended the street fair in 2017 and 2018 combined

Explanation:
The divergence of 362839 and 169538 is 169538.
Therefore, 169538 more people attended the street off-white in 2019 than in 2017 and 2018 combined.

Question 19.
On Mon, from the peak of Mountain Kilimanjaro, a grouping of mountain climbers descended 3,499 anxiety. On Tuesday, they descended another 5,262 feet. How many feet did the mountain climbers descend after 2 days? How many more anxiety practise they have to descend to reach the lesser?

Answer:
8761 feet the mount climbers descend afterwards two days

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

Assessment Practice

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

Answer:


Caption:
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. xxx,986
C. 30,968
D. 30,000
Respond:
C.30968

Explanation:
The departure of 62179 and 31211 is 30968.

Lesson 2.vii Subtract Across Zeros

Solve & Share
London, England, is xv,710 kilometers from the South Pole. Tokyo, Nihon, is 13,953 kilometers from the S Pole. How much farther is London than Tokyo from the S Pole? Solve this trouble any manner you choose.
I can … apply the standard algorithm to decrease from numbers with zeros.

Await Back! Explain how you decided what functioning to use to detect how much farther London is than Tokyo from the South Pole.

Essential Question
How Do Yous Decrease Across Zeros?

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

Regroup.

Decrease.

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

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

Guided Do

Do You Sympathize?
Question 1.
Leesa used bounty to solve the problem on the previous page. She subtracted (half dozen,000 – 1) – (4,678 – one) = 5,999 – four,677 = 1,322. How could yous use Leesa'south approach to subtract 5,000 – 1,476?
Answer:
3524

Explanation:
Using Leesa's arroyo we tin can solve 5000-1476 past subrtacting ane 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 viii,593 kilometers from Oslo to Los Angeles. How many more kilometers was the flight to Lima?
Answer:

Do Yous Know How?
For three-eight, decrease.
Question 3.

Answer:

Question 4.

Respond:

Question v.

Answer:

Question 6.

Reply:

Question 7.
101,001 – viii,915
Answer:

Question eight.
9,050 – 3,461
Answer:

Independent Practice

For 9-23, decrease.
Approximate to check if your answer is reasonable.
Question 9.

Answer:

Question 10.

Answer:

Question xi.

Answer:

Question 12.

Respond:

Question thirteen.

Answer:

Question xiv.

Answer:

Question 15.

Respond:

Question 16.

Respond:

Question 17.

Answer:

Question 18.

Answer:

Question 19.

Answer:

Question 20.

Answer:

Question 21.
6,090 – 5,130
Answer:

Question 22.
xi,246 – nine,489
Respond:

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

Trouble Solving

Question 24.
Construct Arguments Will the departure betwixt 44,041 and 43,876 be greater or less than 1,000? Explicate.
Answer:

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

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

Question 26.
How many more hip-hop than state downloads were sold?
Respond:

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

Cess Practice

Question 28.
Select all the correct differences.
☐ v,000 – one,856 = 3,244
☐ ten,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.
Discover the difference.

A. 17,355
B. xx,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 bulldoze. They collected a total of iii,288 toys 1 week and 1,022 toys the side by side 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 virtually numbers to prove and explain how the two quantities of toys given to clemency are related.
I can … brand sense of quantities and relationships in problem situations.

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

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

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

Essential Question
How Tin can You Apply Quantitative Reasoning to Solve Bug?

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 blueish marlins. Each kid gets to aid counterbalance two marlins. How much more did Kara's marlins weigh than Carl's?

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

How can I employ reasoning to solve this problem?
I tin can

• identify the quantities I know.
• depict diagrams and write equations to bear witness relationships.
• connect the solution back to the real world trouble.

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

Kara's marlins weighed 299 pounds more than Carl'southward.

Convince Me! Reasoning Write a trouble that can exist solved using the bar diagram below. Write an equation to solve. Apply reasoning to retrieve about the meaning of each number earlier starting.

Guided Practice

Reasoning
A manufacturer shipped 12,875 fidget spinners one week and nine,843 of them were sold. The side by side 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 prove the relationships of the numbers in the trouble. Write and solve equations which could be used to find f, the spinners non sold the first week; south, 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 accept placed 8,361 stones, and they have 7,944 stones left. Do they take enough stones? How many more than stones do they need?

Use Exercises iii-v to answer the question.
Question three.
What quantities are given in the trouble, and what exercise the numbers mean?
Answer:

Question 4.
Complete the bar diagram to prove how to find s, the number of stones the builders accept in all. Then, write and solve an equation. Do they have plenty? Explicate.
Answer:

Question five.
Complete the bar diagram to show how to notice the difference, d, of how many more stones the builders demand. Then, write and solve an equation.

Answer:

Problem Solving

Performance Chore
Bird Migration Ornithology is the scientific written report of birds. Every year, some birds travel great distances, or migrate, to find nutrient and kickoff families. The table shows the distances five species of birds flew over one twelvemonth, every bit observed past an ornithologist. How much farther did the Arctic Tern wing than the Pectoral Short-Tailed Shearwater and the Pied Wheatear combined?

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

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

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

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

Answer:

Topic 2 Fluency Practice Activeness

Follow the Path
Shade a path from START to Cease. Follow the sums that are correct. You lot can but move upward, down, correct, or left.
I can.. add multi-digit whole numbers.

Topic 2 Vocabulary Review

Understand Vocabulary
Word Listing

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

Question 1.
Circle the property of add-on shown past 126 + 0 = 126.
Associative
Commutative
Identity
Answer:

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

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

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

Answer:

Utilise 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.
Reply:

Topic 2 Reteaching

Fix A pages 37-twoscore

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

Retrieve 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 v.
47,676 – 16,521
Answer:

Question 6.
1,089 – 961
Answer:

Set up B pages 41-44

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

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

Remember that yous can circular numbers to any place when estimating sums and differences.

Estimate each sum or divergence.
Question one.
652,198 + 49,753
Answer:

Question 2.
8,352 – 3,421
Answer:

Question 3.
17,586 – 9,483
Answer:

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

Question 5.
1,440 – 933
Answer:

Question 6.
55,748 – 28,392
Answer:

Question 7.
4,981 + half-dozen,193
Answer:

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

Set up C pages 45-52

Find 72,438 + 6,854.

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

Call up to regroup if necessary when adding whole numbers.
Question i.

Respond:

Question ii.

Answer:

Question three.
215 + 8,823
Answer:

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

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

Question half dozen.
572,941 + 181,662
Answer:

Set D pages 53-threescore

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

The reply is reasonable.

Remember that you may need to regroup to subtract.

Question 1.

Answer:

Question 2.

Answer:

Question three.
41,542 – 32,411
Answer:

Question iv.
iv,978 – 2,766
Answer:

Question 5.
735,184 – 255,863
Answer:

Question half dozen.
44,558 – 22,613
Respond:

Set E pages 61-64

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

The answer is reasonable.

Remember yous may need to regroup more than one place at a time to subtract beyond zeros.
Question ane.

Answer:

Question 2.

Answer:

Question iii.
lxx,000 – 25,228
Answer:

Question 4.
560,043 – 312,562
Answer:

Question five.
8,052 – one,205
Answer:

Question 6.
20,008 – 16,074
Answer:

Set F pages 65-68

Retrieve virtually these questions to assistance 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 tin can I correspond a word problem using pictures, numbers, or equations?
  

Remember that you can draw a bar diagram and use it to reason near 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 unit in Brisbane, Australia.
Question ane.
Draw a bar diagram that shows the distance Raahil traveled to Brisbane.
Answer:

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

Topic 2 Cess Exercise

Question one.
The table shows the number of hot dogs Frank's hot dog stand up sold this weekend.

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

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

Question 2.
Find viii,000 – 6,280.
Respond:

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

Answer:

Question iv.
Notice the difference.

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

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

Question 6.
Find the departure. Then use improver to check your piece of work.

Answer:

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

Question eight.
Discover the sum.

Answer:

Question ix.
Sandra used improver properties to rewrite the equation below. Select all the equations Sandra might have written.
1,450 + 1,125 + i,050 = due north
☐ (ane,400 + 1,100 + one,000) + (fifty + 25 + 50) = n
☐ 1,450 + 1,050 = northward one,125 + 1,050 + 1,450 = due north
☐ 1,000 + 1,000 + 1,000 + 450 + 50 + 125 = one
☐ (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 detect how many more total birds Joe and Sara saw this twelvemonth than terminal year.
Reply:

B. Approximate how many more than birds were seen in the park this year than terminal year by rounding each number in the table and solving the problem. Use the judge to bank check if your answer to Office A is reasonable.
Answer:

Topic 2 Performance Task

Taking Inventory Jiao runs a wholesale art supply website. She fills majority orders for craft and hobby stores.
Question ane.
Employ the Wooden Beads table to answer the questions.
Part A
Crafts and Stuff ordered oak and ebony chaplet. Explicate 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 chaplet to Create. How much larger is the order for Create? Write and solve equations to notice j, the number of beads in the guild to Jill's Crafts; c, the number of chaplet in the club to Create; and d, the difference.
Answer:

Question ii.
Use the Drinking glass Beads table to answer the questions.
Part A
Write and solve an equation to prove how many drinking glass beads, b, Create will take if they social club the bubble and smoky chaplet.

Answer:

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

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

Respond:

Office B
Craftology orders the contumely and copper beads. After they arrive, the store sells 29,735 of them. How many beads does Craftology take left from their order? Testify your computations.
Answer:

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