## Engage NY Eureka Math 4th Grade Module 1 Lesson 8 Answer Key

### Eureka Math Grade 4 Module 1 Lesson 8 Sprint Answer Key

A
Find the Midpoint  Question 1.
0 10
5 10

Explanation:
given
The starting number 0
The ending number 10
The half way point of 0 and 10 is 5.
So, the mid point of 0 and 10 is 5.

Question 2.
0 100
50 100

Explanation:
given
The starting number 0
The ending number 100
The half way point of 0 and 100 is 50.
So, the mid point of 0 and 100 is 50.

Question 3.
0 1000
0 500 1000

Explanation:
given
The starting number 0
The ending number 1000
The half way point of 0 and 1000 is 500.
So, the mid point of 0 and 1000 is 500.

Question 4.
10 20
10  15  20

Explanation:
given
The starting number 10
The ending number 20
The half way point of 10 and 20 is 15.

Question 5.
100 200
100  150 200

Explanation:
given
The starting number 100
The ending number 200
The half way point of 100 and 200 is 150.

Question 6.
1000 2000
1000  1500 2000

Explanation:
given
The starting number 1000
The ending number 2000
The half way point of 1000 and 2000 is 1500.

Question 7.
30 40
30  35  40

Explanation:
given
The starting number 30
The ending number 40
The half way point of 30 and 40 is 35.

Question 8.
300 400
300  350  400

Explanation:
given
The starting number 300
The ending number 400
The half way point of 300 and 400 is 350..

Question 9.
400 500
400  450  500

Explanation:
given
The starting number 400
The ending number 500
The half way point of 400 and 500 is 450.

Question 10.
20 30
20  25  30

Explanation:
given
The starting number 20
The ending number 30
The half way point of 20 and 30 is 25.

Question 11.
30 40
30  35  40

Explanation:
given
The starting number 30
The ending number 40
The half way point of 30 and 40 is 35.

Question 12.
40 50
40  45 50

Explanation:
given
The starting number 40
The ending number 50
The half way point of 40 and 50 is 45.

Question 13.
50 60
50  55  60

Explanation:
given
The starting number 50
The ending number 60
The half way point of 50 and 60 is 55.

Question 14.
500 600
500  550 600
Explanation:
given
The starting number 500
The ending number 600
The half way point of 500 and 600 is 550.

Question 15.
5000 6000
5000    5500  6000
Explanation:
given
The starting number 5000
The ending number 6000
The half way point of 5000 and 6000 is 5500.

Question 16.
200 300
200  250  300
Explanation:
given
The starting number 200
The ending number 300
The half way point of 200 and 300 is 250.

Question 17.
300 400
300  350 400
Explanation:
given
The starting number 300
The ending number 400
The half way point of 300 and 400 is 350.

Question 18.
700 800
700 750  800
Explanation:
given
The starting number 700
The ending number 800
The half way point of 700 and 800 is 750.

Question 19.
5700 5800
5700  5750  5800

Explanation:
given
The starting number 5700
The ending number 5800
The half way point of 5700 and 5800 is 5750.

Question 20.
70 80
70  75  80
Explanation:
given
The starting number 70
The ending number 80
The half way point of 70 and 80 is 75.
So, the mid point of 70 and 80 is 75.

Question 21.
670 680
670  675 680

Explanation:
given
The starting number 670
The ending number 680
The half way point of 670 and 680 is 675.

Question 22.
6700 6800
6700  6750 6800

Explanation:
given
The starting number 6700
The ending number 6800
The half way point of 6700 and 6800 is 6750.

Question 23.
6000 7000
6000   6500  7000

Explanation:
given
The starting number 6000
The ending number 7000
The half way point of 6000 and 7000 is 6500.

Question 24.
600 700
600   650  700
Explanation:
given
The starting number 600
The ending number 700
The half way point of 600 and 700 is 650.

Question 25.
60 70
60  65  70

Explanation:
given
The starting number 60
The ending number 70
The half way point of 60 and 70 is 65.

Question 26.
260 270
260   265  270

Explanation:
given
The starting number 260
The ending number 270
The half way point of 260 and 270 is 265.

Question 27.
9260 9270
9260   9265  9270

Explanation:
given
The starting number 9260
The ending number 9270
The half way point of 9260 and 9270 is 9265.

Question 28.
80 90
80   85  90

Explanation:
given
The starting number 80
The ending number 90
The half way point of 80 and 90 is 85.

Question 29.
90 100
90   95  100

Explanation:
given
The starting number 90
The ending number 100
The half way point of 90 and 100 is 95.

Question 30.
990 1000
990   995 1000

Explanation:
given
The starting number 990
The ending number 1000
The half way point of 990 and 1000 is 995.

Question 31.
9990 10,000
9990   9995 10,000

Explanation:
given
The starting number 9990
The ending number 10,000
The half way point of 9990 and 10,000 is 9995.

Question 32.
440 450
440   445 450

Explanation:
given
The starting number 440
The ending number 450
The half way point of 440 and 450 is 445.

Question 33.
8300 8400
8300  8350 8400

Explanation:
given
The starting number 8300
The ending number 8400
The half way point of 8300 and 8400 is 8350.

Question 34.
680 690
680  685  690

Explanation:
given
The starting number 680
The ending number 690
The half way point of 680 and 690 is 685.

Question 35.
9400 9500
9400   9450  9500

Explanation:
given
The starting number 9400
The ending number 9500
The half way point of 9400 and 9500 is 9450.

Question 36.
3900 4000
3900   3950  4000

Explanation:
given
The starting number 3900
The ending number  4000
The half way point of 3900 and 4000 is 3950.

Question 37.
2450 2460
2450   2455  2460

Explanation:
given
The starting number 2450
The ending number 2460
The half way point of 2450 and 2460 is 2455.

Question 38.
7080 7090
7080  7085 7090

Explanation:
given
The starting number 7080
The ending number 7090
The half way point of 7080 and 7090 is 7085.

Question 39.
3200 3210
3200  3205  3210

Explanation:
given
The starting number 3200
The ending number 3210
The half way point of 3200 and 3210 is 3205.

Question 40.
8630 8640
8630  8635  8640

Explanation:
given
The starting number 8630
The ending number 8640
The half way point of 8630 and 8640 is 8635.

Question 41.
8190 8200
8190  8195  8200

Explanation:
given
The starting number 8190
The ending number 8200
The half way point of 8190 and 8200 is 8195.

Question 42.
2510 2520
2510    2515  2520

Explanation:
given
The starting number 2510
The ending number 2520
The half way point of 2510 and 2520 is 2515.

Question 43.
4890 4900
4890  4895  4900

Explanation:
given
The starting number 4890
The ending number 4900
The half way point of 4890 and 4900 is 4895.

Question 44.
6660 6670
6660  6665  6670

Explanation:
given
The starting number 6660
The ending number 6670
The half way point of 6660 and 6670 is 6665.

B
Find the Midpoint  Question 1.
10 20
10  15  20

Explanation:
given
The starting number 10
The ending number 20
The half way point of 10 and 20 is 15.

Question 2.
100 200
100  150  200

Explanation:
given
The starting number 100
The ending number 200
The half way point of 100 and 200 is 150.

Question 3.
1000 2000
1000   1500  2000

Explanation:
given
The starting number 1000
The ending number 2000
The half way point of 1000 and 2000 is 1500.

Question 4.
20 30
20  25  30

Explanation:
given
The starting number 20
The ending number 30
The half way point of  20 and 30 is 25.

Question 5.
200 300
200  250  300

Explanation:
given
The starting number 200
The ending number 300
The half way point of 200 and 300 is 250.

Question 6.
2000 3000
2000  2500 3000

Explanation:
given
The starting number 2000
The ending number 3000
The half way point of 2000 and 3000 is 2500.

Question 7.
40 50
40  45 50

Explanation:
given
The starting number 40
The ending number 50
The half way point of 40 and 50 is 45.

Question 8.
400 500
400  450  500

Explanation:
given
The starting number 400
The ending number 500
The half way point of 400 and 500 is 450.

Question 9.
500 600
500  550  600

Explanation:
given
The starting number 500
The ending number 600
The half way point of 500 and 600 is 550.

Question 10.
30 40
30  35  40

Explanation:
given
The starting number 30
The ending number 40
The half way point of 30 and 40 is 35.

Question 11.
40 50
40  45  50

Explanation:
given
The starting number 40
The ending number 50
The half way point of 40 and 50 is 45.

Question 12.
50 60
50  55  60

Explanation:
given
The starting number 50
The ending number 60
The half way point of 50 and 60 is 55.

Question 13.
60 70
60  65  70

Explanation:
given
The starting number 60
The ending number 70
The half way point of 60 and 70 is 65.

Question 14.
600 700
600  650  700

Explanation:
given
The starting number 600
The ending number 700
The half way point of 600 and 700 is 650.

Question 15.
6000 7000
6000  6500 7000

Explanation:
given
The starting number 6000
The ending number 7000
The half way point of 6000 and 7000 is 6500.

Question 16.
300 400
300   350  400

Explanation:
given
The starting number 300
The ending number 400
The half way point of 300 and 400 is 350.

Question 17.
400 500
400  450  500

Explanation:
given
The starting number 400
The ending number 500
The half way point of 400 and 500 is 450.

Question 18.
800 900
800  850  900

Explanation:
given
The starting number 800
The ending number 900
The half way point of 800 and 900 is 850.

Question 19.
5800 5900
5800  5850 5900

Explanation:
given
The starting number 5800
The ending number 5900
The half way point of 5800 and 5900 is 5850.

Question 20.
80 90
80  85 90

Explanation:
given
The starting number 80
The ending number 90
The half way point of 80 and 90 is 85.

Question 21.
680 690
680  685 690

Explanation:
given
The starting number 680
The ending number 690
The half way point of 680 and 690 is 685.

Question 22.
6800 6900
6800  6850 6900

Explanation:
given
The starting number 6800
The ending number 6900
The half way point of 6800 and 6900 is 6850.

Question 23.
7000 8000
7000  7500 8000

Explanation:
given
The starting number 7000
The ending number 8000
The half way point of 7000 and 8000 is 7500.

Question 24.
700 800
700  750 800

Explanation:
given
The starting number 700
The ending number 800
The half way point of 700 and 800 is 750.

Question 25.
70 80
70  75 80

Explanation:
given
The starting number 70
The ending number 80
The half way point of 70 and 80 is 75..

Question 26.
270 280
270  275 280

Explanation:
given
The starting number 270
The ending number 280
The half way point of 270 and 280 is 275.

Question 27.
9270 9280
9270  9275  9280

Explanation:
given
The starting number 9270
The ending number 9280
The half way point of 9270 and 9280 is 9275.

Question 28.
80 90
80  85  90

Explanation:
given
The starting number 80
The ending number 90
The half way point of 80 and 90 is 85.

Question 29.
90 100
90  95 100

Explanation:
given
The starting number 90
The ending number 100
The half way point of 90 and 100 is 95.

Question 30.
990 1000
990  995 1000

Explanation:
given
The starting number 990
The ending number 1000
The half way point of 990 and 1000 is 995.

Question 31.
9990 10,000
9990  9995 10,000

Explanation:
given
The starting number 9990
The ending number 10,000
The half way point of 9990  and 10,000 is 9995.

Question 32.
450 460
450  455  460

Explanation:
given
The starting number 450
The ending number 460
The half way point of 450 and 460 is 455 .

Question 33.
8400 8500
8400  8450  8500

Explanation:
given
The starting number 8400
The ending number 8500
The half way point of 8400 and 8500 is 8450.

Question 34.
580 590
580  585  590

Explanation:
given
The starting number 580
The ending number 590
The half way point of 580 and 590 is 585.

Question 35.
9500 9600
9500  9550  9600

Explanation:
given
The starting number 9500
The ending number 9600
The half way point of 9500 and 9600 is 9550.

Question 36.
2900 3000
2900  2950 3000

Explanation:
given
The starting number 2900
The ending number 3000
The half way point of 2900 and 3000 is 2950.

Question 37.
3450 3460
3450  3455 3460

Explanation:
given
The starting number 3450
The ending number 3460
The half way point of 3450 and 3460 is 3455.

Question 38.
6080 6090
6080  6085 6090

Explanation:
given
The starting number 6080
The ending number 6090
The half way point of 6080 and 6090 is 6085 .

Question 39.
4200 4210
4200  4205 4210

Explanation:
given
The starting number 4200
The ending number 4210
The half way point of 4200  and 4210 is 4205.

Question 40.
7630 7640
7630  7635 7640

Explanation:
given
The starting number 7630
The ending number 7640
The half way point of 7630 and 7640 is 7635.

Question 41.
7190 7200
7190  7195  7200

Explanation:
given
The starting number 7190
The ending number 7200
The half way point of 7190 and 7200 is 75.

Question 42.
3510 3520
3510  3515  3520

Explanation:
given
The starting number 3510
The ending number 3520
The half way point of 3510 and 3520 is 3515.

Question 43.
5890 5900
5890  5895  5900

Explanation:
given
The starting number 5890
The ending number 5900
The half way point of 5890 and 5900 is 5895.

Question 44.
7770 7780
7770    7775   7780
Explanation:
given
The starting number 7770
The ending number 7780
The half way point of 7770 and 7780 is 7775.

### Eureka Math Grade 4 Module 1 Lesson 8 Problem Set Answer Key

Complete each statement by rounding the number to the given place value. Use the number line to show your work.

Question 1.
a. 53,000 rounded to the nearest ten thousand is _______________.  Explanation:
Given 53,000
50,000 is the starting number and 60,000 is the end number.
The mid point of both is 55,000. Since the  number is less than the mid point the nearest ten thousand to 53,000 is 50,000
b. 42,708 rounded to the nearest ten thousand is _______________.  Explanation:
Given 42,708
The starting number of the number line 42,000
The ending number of the number line is 43,000
The mid point of both the numbers is 42,500 and the given number is 42,708 which is more than the mid point.So, the number is nearer to 43,000.
c. 406,823 rounded to the nearest ten thousand is _______________.  Explanation:
Given 406,823
The starting number of the number line 400,000
The ending number of the number line is 410,000
The mid point of both the numbers is 405,000 and the given number is 406,823 which is more than the mid point.So, the number is nearer to 410,000.

Question 2.
a. 240,000 rounded to the nearest hundred thousand is _______________.  Explanation:
Given 240,000
The starting number of the number line 200,000
The ending number of the number line is 300,000
The mid point of both the numbers is 250,000 and the given number is 240,000 which is less than the mid point.So, the number is nearer to 200,000.
b. 449,019 rounded to the nearest hundred thousand is _______________.  Explanation:
Given 449,019
The starting number of the number line is 400,000
The ending number of the number line is 500,000
The mid point of both the numbers is 450,000 and the given number is 449,019 which is less than the mid point.So, the number is nearest to 400,000.
c. 964,103 rounded to the nearest hundred thousand is _______________.  Explanation:
Given 964,103
The starting number of the number line 900,000
The ending number of the number line is 1,000,000
The mid point of both the numbers is 950,000 and the given number is 964,103 which is more than the mid point.So, the number is nearer to 1,000,000.
Question 3.
975,462 songs were downloaded in one day. Round this number to the nearest hundred thousand to estimate how many songs were downloaded in one day. Use a number line to show your work.
Given 975,462 songs
Round this number to the nearest hundred thousand Question 4.
This number was rounded to the nearest ten thousand. List the possible digits that could go in the thousands place to make this statement correct. Use a number line to show your work.
13_ ,644 ≈ 130,000
13_ ,644 ≈ 130,000
The possible digits could be 1 , 2 , 3 , 4 Question 5.
Estimate the difference by rounding each number to the given place value.
712,350 − 342,802
a. Round to the nearest ten thousands. b. Round to the nearest hundred thousands. ### Eureka Math Grade 4 Module 1 Lesson 8 Exit Ticket Answer Key

Question 1.
Round to the nearest ten thousand. Use the number line to model your thinking. a. 35,124 Explanation:
Given 35,124
The starting number of the number line 30,000
The ending number of the number line is 40,000
The mid point of both the numbers is 35,000 and the given number is 35,124 which is more than the mid point.So, the number is nearer to 40,000. b. 981,657 Explanation:
Given 981,657
The starting number of the number line 980,000
The ending number of the number line is 990,000
The mid point of both the numbers is 985,000 and the given number is 981,657 which is less than the mid point.So, the number is nearer to 980,000.

Question 2.
Round to the nearest hundred thousand. Use the number line to model your thinking. a. 89,678 ≈ ___________  b. 999,765 ≈ ___________ Question 3.
Estimate the sum by rounding each number to the nearest hundred thousand.
257,098 + 548,765 ≈ ___________ ### Eureka Math Grade 4 Module 1 Lesson 8 Homework Answer Key

Complete each statement by rounding the number to the given place value. Use the number line to show your work.

Question 1.
a. 67,000 rounded to the nearest ten thousand is _______________.  b. 51,988 rounded to the nearest ten thousand is _______________.  c. 105,159 rounded to the nearest ten thousand is _______________.  Question 2.
a. 867,000 rounded to the nearest hundred thousand is _______________.  b. 767,074 rounded to the nearest hundred thousand is _______________.  c. 629,999 rounded to the nearest hundred thousand is _______________.  Question 3.
491,852 people went to the water park in the month of July. Round this number to the nearest hundred thousand to estimate how many people went to the park. Use a number line to show your work.
Number of people went to the water park in the month of July are = 491,852 Approximately 500,000 people went to water park in the month of July.

Question 4.
This number was rounded to the nearest hundred thousand. List the possible digits that could go in the ten thousands place to make this statement correct. Use a number line to show your work.
1_9,644 ≈ 100,000
1_9,644 ≈ 100,000
The possible digits that could go in the ten thousand place to make the statement correct are 1, 2 , 3 , 4. Question 5.
Estimate the sum by rounding each number to the given place value.
164,215 + 216,088
a. Round to the nearest ten thousand.  