Estimate Sums
Name
4.2
?
Number and Operations—3.4.B MATHEMATICAL PROCESSES 3.1.C, 3.1.D
Estimate Sums
Essential Question
How can you use compatible numbers and rounding to estimate sums?
Unlock Unlock the the Problem Problem The table shows how many dogs went to Pine Lake Dog Park during the summer months. About how many dogs went to the park during June and August? You can estimate to find about how many or about how much. An estimate is a number close to an exact amount.
Pine Lake Dog Park Month
Number of Dogs
June
432
July
317
August
489
One Way Use compatible numbers. Compatible numbers are numbers that are easy to compute mentally and are close to the real numbers. 432 →
425
+ 489 → __
+ 475 __
Math Talk Mathematical Processes
Will the sum of the compatible numbers 425 and 475 be greater than or less than the exact sum? Explain.
© Houghton Mifflin Harcourt Publishing Company
So, about __ dogs went to Pine Lake Dog Park during June and August. 1.
What other compatible numbers could you have used?
2.
About how many dogs went to the park during July and August? What compatible numbers could you use to estimate?
Module 4
107
Another Way Use place value to round. 432 + 489 =
Math Talk
■
Mathematical Processes
First, find the place to which you want to round. Round both numbers to the same place. The greatest place value of 432 and 489 is hundreds. Round each number to the nearest hundred.
How would you round 432 and 489 to the nearest ten? What would be the estimated sum? Explain.
Find the sum of the rounded numbers. 400 + 500 = _
Share Share and and Show Show Estimate the sum. Use compatible numbers.
1.
47 + 23 _
2.
→ →
Use rounding. →
304 + 494 __
+ 25 _
→
300 + __
Use rounding or compatible numbers to estimate the sum. 3.
6.
421 + 218 + __ —
4.
267 + 517 + __ —
7.
369 + 480 __ 465 + 478 __
5.
+ — 8.
+ —
27 + 78 _
+ —
278 + 369 + __ —
9.
Multi-Step Green Lawn Service ordered 186 bags of top soil and 462 bags of fertilizer. Estimate to the nearest hundred how many bags Green Lawn Service ordered. Justify your answer.
108
© Houghton Mifflin Harcourt Publishing Company
Problem Problem Solving Solving
Name
Problem Problem Solving Solving Use the table for 10–13. 10.
11.
About how many pet bowls were sold in June and July altogether?
Dan’s Pet Supplies Sold Pet Bowls
Bags of Pet Food
June
91
419
July
57
370
August
76
228
Month
What’s the Question? The answer is about 800.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Image Source/Alamy Images
Write Math 12.
Multi-Step Dan estimated the lowest monthly sales of both pet bowls and bags of pet food to be about 300. What month had the lowest sales? Explain.
13.
Multi-Step Dan said the total number of bags of pet food sold in June, July, and August was about 1,000. How did Dan estimate? Explain.
Show Your Work
Module 4 • Lesson 2
109
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble for the correct answer choice.
15.
16.
Use Tools The table shows the number of steps from bottom to top for each pyramid. Which of these statements shows the best estimate of how many steps there are in both pyramids? A
5 + 100 = 105
C
10 + 90 = 100
B
0 + 75 = 75
D
6 + 95 = 101
Pyramid Djoser Chichen Itzá
110
6 91
Lea and Josh used sugar cubes to build a model of a pyramid. First, they glued 196 cubes to make a square base. Next, they used 144 cubes to make the first step. Which is the best estimate of the number of sugar cubes Lea and Josh used to build the first two steps of their pyramid? A
440
C
220
B
300
D
400
Multi-Step The height of the Great Pyramid of Giza is about 481 feet. The length of one side of its base is 755 feet. What is the best estimate of the sum of the height and length? A
1,000 feet
C
1,300 feet
B
1,100 feet
D
1,500 feet
TEXAS Test Prep 17.
Number of Steps
Tracy ordered 325 toys and 165 bags of food for her new pet store. Which is the best estimate of the total number of items Tracy ordered? A
700
C
400
B
500
D
600
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Alistair Laming/Alamy
14.
H o mewo rk and Practice
4.2
Number and Operations—3.4.B MATHEMATICAL PROCESSES 3.1.C, 3.1.D
Name
Estimate Sums
Use rounding or compatible numbers to estimate the sum. 1.
18 + 53
2.
37 + 52
3.
345 + 223
4.
509 + 478
5.
642 + 212
6.
109 + 688
8.
Elena drove 245 miles last week and 222 miles this week. She estimated that she drove about 475 miles in both weeks. How did Elena estimate?
Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
7.
Seth bought a pair of sneakers for $48 and a jacket for $64. Explain how you can estimate to find the total amount that he spent for the sneakers and jacket.
Module 4 • Lesson 2 111
TEXAS Test Prep
Lesson Lesson Check Check Fill in the bubble completely to show your answer.
11.
12.
112
Cal has $42. He gets $25 from his grandparents for his birthday. Which of these statements shows the best estimate of the amount of money Cal has now?
10.
Mr. Avery’s class made $118 for the fundraiser. Mrs. Bolero’s class made $189 for the fundraiser. Which of these statements shows the best estimate of the total amount both classes raised?
A
$50 + $30 = $80
B
$50 + $20 = $70
A
$100 + $200 = $300
C
$40 + $40 = $80
B
$125 + $150 = $275
D
$40 + $25 = $65
C
$100 + $100 = $200
D
$200 + $200 = $400
Which is the best estimate of the total number of students in kindergarten and first grade at Wayside Elementary School?
Students at Wayside Elementary School Grade
Number of Students
Kindergarten
187
First Grade
203
Second Grade
382
400
Third Grade
238
500
Fourth Grade
178
A
350
B
300
C D
Multi-Step Which is the best estimate of the total number of students in second, third, and fourth grade at Wayside Elementary School?
13.
Multi-Step Which is the best estimate of the total number of students in all grades at Wayside Elementary School?
A
500
A
900
B
400
B
1,200
C
700
C
1,100
D
800
D
1,000
© Houghton Mifflin Harcourt Publishing Company
9.
4.2
?
Number and Operations—3.4.B MATHEMATICAL PROCESSES 3.1.C, 3.1.D
Estimate Sums
Essential Question
How can you use compatible numbers and rounding to estimate sums?
Unlock Unlock the the Problem Problem The table shows how many dogs went to Pine Lake Dog Park during the summer months. About how many dogs went to the park during June and August? You can estimate to find about how many or about how much. An estimate is a number close to an exact amount.
Pine Lake Dog Park Month
Number of Dogs
June
432
July
317
August
489
One Way Use compatible numbers. Compatible numbers are numbers that are easy to compute mentally and are close to the real numbers. 432 →
425
+ 489 → __
+ 475 __
Math Talk Mathematical Processes
Will the sum of the compatible numbers 425 and 475 be greater than or less than the exact sum? Explain.
© Houghton Mifflin Harcourt Publishing Company
So, about __ dogs went to Pine Lake Dog Park during June and August. 1.
What other compatible numbers could you have used?
2.
About how many dogs went to the park during July and August? What compatible numbers could you use to estimate?
Module 4
107
Another Way Use place value to round. 432 + 489 =
Math Talk
■
Mathematical Processes
First, find the place to which you want to round. Round both numbers to the same place. The greatest place value of 432 and 489 is hundreds. Round each number to the nearest hundred.
How would you round 432 and 489 to the nearest ten? What would be the estimated sum? Explain.
Find the sum of the rounded numbers. 400 + 500 = _
Share Share and and Show Show Estimate the sum. Use compatible numbers.
1.
47 + 23 _
2.
→ →
Use rounding. →
304 + 494 __
+ 25 _
→
300 + __
Use rounding or compatible numbers to estimate the sum. 3.
6.
421 + 218 + __ —
4.
267 + 517 + __ —
7.
369 + 480 __ 465 + 478 __
5.
+ — 8.
+ —
27 + 78 _
+ —
278 + 369 + __ —
9.
Multi-Step Green Lawn Service ordered 186 bags of top soil and 462 bags of fertilizer. Estimate to the nearest hundred how many bags Green Lawn Service ordered. Justify your answer.
108
© Houghton Mifflin Harcourt Publishing Company
Problem Problem Solving Solving
Name
Problem Problem Solving Solving Use the table for 10–13. 10.
11.
About how many pet bowls were sold in June and July altogether?
Dan’s Pet Supplies Sold Pet Bowls
Bags of Pet Food
June
91
419
July
57
370
August
76
228
Month
What’s the Question? The answer is about 800.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Image Source/Alamy Images
Write Math 12.
Multi-Step Dan estimated the lowest monthly sales of both pet bowls and bags of pet food to be about 300. What month had the lowest sales? Explain.
13.
Multi-Step Dan said the total number of bags of pet food sold in June, July, and August was about 1,000. How did Dan estimate? Explain.
Show Your Work
Module 4 • Lesson 2
109
Mathematical Processes M Model ¥ Reason ¥ Communicate M
Daily Daily Assessment Assessment Task Task Fill in the bubble for the correct answer choice.
15.
16.
Use Tools The table shows the number of steps from bottom to top for each pyramid. Which of these statements shows the best estimate of how many steps there are in both pyramids? A
5 + 100 = 105
C
10 + 90 = 100
B
0 + 75 = 75
D
6 + 95 = 101
Pyramid Djoser Chichen Itzá
110
6 91
Lea and Josh used sugar cubes to build a model of a pyramid. First, they glued 196 cubes to make a square base. Next, they used 144 cubes to make the first step. Which is the best estimate of the number of sugar cubes Lea and Josh used to build the first two steps of their pyramid? A
440
C
220
B
300
D
400
Multi-Step The height of the Great Pyramid of Giza is about 481 feet. The length of one side of its base is 755 feet. What is the best estimate of the sum of the height and length? A
1,000 feet
C
1,300 feet
B
1,100 feet
D
1,500 feet
TEXAS Test Prep 17.
Number of Steps
Tracy ordered 325 toys and 165 bags of food for her new pet store. Which is the best estimate of the total number of items Tracy ordered? A
700
C
400
B
500
D
600
© Houghton Mifflin Harcourt Publishing Company • Image Credits: ©Alistair Laming/Alamy
14.
H o mewo rk and Practice
4.2
Number and Operations—3.4.B MATHEMATICAL PROCESSES 3.1.C, 3.1.D
Name
Estimate Sums
Use rounding or compatible numbers to estimate the sum. 1.
18 + 53
2.
37 + 52
3.
345 + 223
4.
509 + 478
5.
642 + 212
6.
109 + 688
8.
Elena drove 245 miles last week and 222 miles this week. She estimated that she drove about 475 miles in both weeks. How did Elena estimate?
Problem Problem Solving Solving
© Houghton Mifflin Harcourt Publishing Company
7.
Seth bought a pair of sneakers for $48 and a jacket for $64. Explain how you can estimate to find the total amount that he spent for the sneakers and jacket.
Module 4 • Lesson 2 111
TEXAS Test Prep
Lesson Lesson Check Check Fill in the bubble completely to show your answer.
11.
12.
112
Cal has $42. He gets $25 from his grandparents for his birthday. Which of these statements shows the best estimate of the amount of money Cal has now?
10.
Mr. Avery’s class made $118 for the fundraiser. Mrs. Bolero’s class made $189 for the fundraiser. Which of these statements shows the best estimate of the total amount both classes raised?
A
$50 + $30 = $80
B
$50 + $20 = $70
A
$100 + $200 = $300
C
$40 + $40 = $80
B
$125 + $150 = $275
D
$40 + $25 = $65
C
$100 + $100 = $200
D
$200 + $200 = $400
Which is the best estimate of the total number of students in kindergarten and first grade at Wayside Elementary School?
Students at Wayside Elementary School Grade
Number of Students
Kindergarten
187
First Grade
203
Second Grade
382
400
Third Grade
238
500
Fourth Grade
178
A
350
B
300
C D
Multi-Step Which is the best estimate of the total number of students in second, third, and fourth grade at Wayside Elementary School?
13.
Multi-Step Which is the best estimate of the total number of students in all grades at Wayside Elementary School?
A
500
A
900
B
400
B
1,200
C
700
C
1,100
D
800
D
1,000
© Houghton Mifflin Harcourt Publishing Company
9.
