## 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

Answer:

0 **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

Answer:

0 **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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

8400 **8****450 ** 8500

Explanation:

given

The starting number 8400

The ending number 8500

The half way point of 8400 and 8500 is **8****450**.

Question 34.

580 590

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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 _______________.

Answer:

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 _______________.

Answer:

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 _______________.

Answer:

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 _______________.

Answer:

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 _______________.

Answer:

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 _______________.

Answer:

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.

Answer:

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

Answer:

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.

Answer:

b. Round to the nearest hundred thousands.

Answer:

### 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

Answer:

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

Answer:

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 ≈ ___________

Answer:

b. 999,765 ≈ ___________

Answer:

Question 3.

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

257,098 + 548,765 ≈ ___________

Answer:

### 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 _______________.

Answer:

b. 51,988 rounded to the nearest ten thousand is _______________.

Answer:

c. 105,159 rounded to the nearest ten thousand is _______________.

Answer:

Question 2.

a. 867,000 rounded to the nearest hundred thousand is _______________.

Answer:

b. 767,074 rounded to the nearest hundred thousand is _______________.

Answer:

c. 629,999 rounded to the nearest hundred thousand is _______________.

Answer:

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.

Answer:

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

Answer:

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.

Answer:

b. Round to the nearest hundred thousand.

Answer: