Practice · Locate and compare numbers on a number line · Sensim Math

Variant 1 answer: 5,050

Which of the following numbers is closest to $5{,}000$ ? Write it.

$4{,}800 \qquad 5{,}400 \qquad 5{,}050$

Show solution

Understand

Of the numbers 4,800, 5,400, 5,050, decide which one is nearest to 5,000.

Givens

The numbers are 4,800, 5,400, 5,050.
The target is 5,000.

Unknowns

Which number is closest to 5,000

Constraints

'Closest' means the smallest distance (difference) from the target.

Plan

#1 Draw a Diagram · also uses: #6 Guess and Check

Picture the numbers on a number line around 5,000 and measure how far each is from 5,000; the one with the smallest gap is closest.

Execute

#1 Draw a Diagram 4.NBT.A.2

4,800 is below 5,000 by 5,000 - 4,800 = 200.

5{,}000 - 4{,}800 = 200

On the number line 4,800 sits to the left of 5,000.

#1 Draw a Diagram 4.NBT.A.2

5,400 is above 5,000 by 5,400 - 5,000 = 400.

5{,}400 - 5{,}000 = 400

On the number line 5,400 sits to the right of 5,000.

#1 Draw a Diagram 4.NBT.A.2

5,050 is above 5,000 by 5,050 - 5,000 = 50.

5{,}050 - 5{,}000 = 50

On the number line 5,050 sits to the right of 5,000.

#6 Guess and Check 4.NBT.A.2

The distances are 200, 400, 50. The smallest is 50, so 5,050 is closest to 5,000.

50 < 200 < 400

The smallest gap wins.

Answer: 5,050

Review

5,050 differs from 5,000 by only 50, less than the other gaps (200, 400), so 5,050 being closest is correct.

Make a systematic list (tool 2): write each number with its distance from the target and read off the smallest.

Standards · min grade 4

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Comparing the distances of each number from 5,000.

💡 This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!

Variant 2 answer: 50,300

Which of the following numbers is closest to $50{,}000$ ? Write it.

$48{,}000 \qquad 51{,}000 \qquad 50{,}300$

Show solution

Understand

Of the numbers 48,000, 51,000, 50,300, decide which one is nearest to 50,000.

Givens

The numbers are 48,000, 51,000, 50,300.
The target is 50,000.

Unknowns

Which number is closest to 50,000

Constraints

'Closest' means the smallest distance (difference) from the target.

Plan

#1 Draw a Diagram · also uses: #6 Guess and Check

Picture the numbers on a number line around 50,000 and measure how far each is from 50,000; the one with the smallest gap is closest.

Execute

#1 Draw a Diagram 4.NBT.A.2

48,000 is below 50,000 by 50,000 - 48,000 = 2,000.

50{,}000 - 48{,}000 = 2{,}000

On the number line 48,000 sits to the left of 50,000.

#1 Draw a Diagram 4.NBT.A.2

51,000 is above 50,000 by 51,000 - 50,000 = 1,000.

51{,}000 - 50{,}000 = 1{,}000

On the number line 51,000 sits to the right of 50,000.

#1 Draw a Diagram 4.NBT.A.2

50,300 is above 50,000 by 50,300 - 50,000 = 300.

50{,}300 - 50{,}000 = 300

On the number line 50,300 sits to the right of 50,000.

#6 Guess and Check 4.NBT.A.2

The distances are 2,000, 1,000, 300. The smallest is 300, so 50,300 is closest to 50,000.

300 < 1{,}000 < 2{,}000

The smallest gap wins.

Answer: 50,300

Review

50,300 differs from 50,000 by only 300, less than the other gaps (2,000, 1,000), so 50,300 being closest is correct.

Make a systematic list (tool 2): write each number with its distance from the target and read off the smallest.

Standards · min grade 4

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Comparing the distances of each number from 50,000.

💡 This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!

Variant 3 answer: 100,400

Which of the following numbers is closest to $100{,}000$ ? Write it.

$99{,}000 \qquad 101{,}200 \qquad 100{,}400$

Show solution

Understand

Of the numbers 99,000, 101,200, 100,400, decide which one is nearest to 100,000.

Givens

The numbers are 99,000, 101,200, 100,400.
The target is 100,000.

Unknowns

Which number is closest to 100,000

Constraints

'Closest' means the smallest distance (difference) from the target.

Plan

#1 Draw a Diagram · also uses: #6 Guess and Check

Picture the numbers on a number line around 100,000 and measure how far each is from 100,000; the one with the smallest gap is closest.

Execute

#1 Draw a Diagram 4.NBT.A.2

99,000 is below 100,000 by 100,000 - 99,000 = 1,000.

100{,}000 - 99{,}000 = 1{,}000

On the number line 99,000 sits to the left of 100,000.

#1 Draw a Diagram 4.NBT.A.2

101,200 is above 100,000 by 101,200 - 100,000 = 1,200.

101{,}200 - 100{,}000 = 1{,}200

On the number line 101,200 sits to the right of 100,000.

#1 Draw a Diagram 4.NBT.A.2

100,400 is above 100,000 by 100,400 - 100,000 = 400.

100{,}400 - 100{,}000 = 400

On the number line 100,400 sits to the right of 100,000.

#6 Guess and Check 4.NBT.A.2

The distances are 1,000, 1,200, 400. The smallest is 400, so 100,400 is closest to 100,000.

400 < 1{,}000 < 1{,}200

The smallest gap wins.

Answer: 100,400

Review

100,400 differs from 100,000 by only 400, less than the other gaps (1,000, 1,200), so 100,400 being closest is correct.

Make a systematic list (tool 2): write each number with its distance from the target and read off the smallest.

Standards · min grade 4

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Comparing the distances of each number from 100,000.

💡 This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!

Variant 4 answer: 15,100

Which of the following numbers is closest to $15{,}000$ ? Write it.

$14{,}500 \qquad 15{,}700 \qquad 15{,}100$

Show solution

Understand

Of the numbers 14,500, 15,700, 15,100, decide which one is nearest to 15,000.

Givens

The numbers are 14,500, 15,700, 15,100.
The target is 15,000.

Unknowns

Which number is closest to 15,000

Constraints

'Closest' means the smallest distance (difference) from the target.

Plan

#1 Draw a Diagram · also uses: #6 Guess and Check

Picture the numbers on a number line around 15,000 and measure how far each is from 15,000; the one with the smallest gap is closest.

Execute

#1 Draw a Diagram 4.NBT.A.2

14,500 is below 15,000 by 15,000 - 14,500 = 500.

15{,}000 - 14{,}500 = 500

On the number line 14,500 sits to the left of 15,000.

#1 Draw a Diagram 4.NBT.A.2

15,700 is above 15,000 by 15,700 - 15,000 = 700.

15{,}700 - 15{,}000 = 700

On the number line 15,700 sits to the right of 15,000.

#1 Draw a Diagram 4.NBT.A.2

15,100 is above 15,000 by 15,100 - 15,000 = 100.

15{,}100 - 15{,}000 = 100

On the number line 15,100 sits to the right of 15,000.

#6 Guess and Check 4.NBT.A.2

The distances are 500, 700, 100. The smallest is 100, so 15,100 is closest to 15,000.

100 < 500 < 700

The smallest gap wins.

Answer: 15,100

Review

15,100 differs from 15,000 by only 100, less than the other gaps (500, 700), so 15,100 being closest is correct.

Make a systematic list (tool 2): write each number with its distance from the target and read off the smallest.

Standards · min grade 4

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Comparing the distances of each number from 15,000.

💡 This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!

Variant 5 answer: 10,100

Which of the following numbers is closest to $10{,}000$ ? Write it.

$8{,}800 \qquad 10{,}500 \qquad 10{,}100$

Show solution

Understand

Of the numbers 8,800, 10,500, 10,100, decide which one is nearest to 10,000.

Givens

The numbers are 8,800, 10,500, 10,100.
The target is 10,000.

Unknowns

Which number is closest to 10,000

Constraints

'Closest' means the smallest distance (difference) from the target.

Plan

#1 Draw a Diagram · also uses: #6 Guess and Check

Picture the numbers on a number line around 10,000 and measure how far each is from 10,000; the one with the smallest gap is closest.

Execute

#1 Draw a Diagram 4.NBT.A.2

8,800 is below 10,000 by 10,000 - 8,800 = 1,200.

10{,}000 - 8{,}800 = 1{,}200

On the number line 8,800 sits to the left of 10,000.

#1 Draw a Diagram 4.NBT.A.2

10,500 is above 10,000 by 10,500 - 10,000 = 500.

10{,}500 - 10{,}000 = 500

On the number line 10,500 sits to the right of 10,000.

#1 Draw a Diagram 4.NBT.A.2

10,100 is above 10,000 by 10,100 - 10,000 = 100.

10{,}100 - 10{,}000 = 100

On the number line 10,100 sits to the right of 10,000.

#6 Guess and Check 4.NBT.A.2

The distances are 1,200, 500, 100. The smallest is 100, so 10,100 is closest to 10,000.

100 < 500 < 1{,}200

The smallest gap wins.

Answer: 10,100

Review

10,100 differs from 10,000 by only 100, less than the other gaps (1,200, 500), so 10,100 being closest is correct.

Make a systematic list (tool 2): write each number with its distance from the target and read off the smallest.

Standards · min grade 4

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Comparing the distances of each number from 10,000.

💡 This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!

Variant 6 answer: 1,020

Which of the following numbers is closest to $1{,}000$ ? Write it.

$970 \qquad 1{,}080 \qquad 1{,}020$

Show solution

Understand

Of the numbers 970, 1,080, 1,020, decide which one is nearest to 1,000.

Givens

The numbers are 970, 1,080, 1,020.
The target is 1,000.

Unknowns

Which number is closest to 1,000

Constraints

'Closest' means the smallest distance (difference) from the target.

Plan

#1 Draw a Diagram · also uses: #6 Guess and Check

Picture the numbers on a number line around 1,000 and measure how far each is from 1,000; the one with the smallest gap is closest.

Execute

#1 Draw a Diagram 4.NBT.A.2

970 is below 1,000 by 1,000 - 970 = 30.

1{,}000 - 970 = 30

On the number line 970 sits to the left of 1,000.

#1 Draw a Diagram 4.NBT.A.2

1,080 is above 1,000 by 1,080 - 1,000 = 80.

1{,}080 - 1{,}000 = 80

On the number line 1,080 sits to the right of 1,000.

#1 Draw a Diagram 4.NBT.A.2

1,020 is above 1,000 by 1,020 - 1,000 = 20.

1{,}020 - 1{,}000 = 20

On the number line 1,020 sits to the right of 1,000.

#6 Guess and Check 4.NBT.A.2

The distances are 30, 80, 20. The smallest is 20, so 1,020 is closest to 1,000.

20 < 30 < 80

The smallest gap wins.

Answer: 1,020

Review

1,020 differs from 1,000 by only 20, less than the other gaps (30, 80), so 1,020 being closest is correct.

Make a systematic list (tool 2): write each number with its distance from the target and read off the smallest.

Standards · min grade 4

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Comparing the distances of each number from 1,000.

💡 This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!

Variant 7 answer: 20,200

Which of the following numbers is closest to $20{,}000$ ? Write it.

$19{,}500 \qquad 20{,}800 \qquad 20{,}200$

Show solution

Understand

Of the numbers 19,500, 20,800, 20,200, decide which one is nearest to 20,000.

Givens

The numbers are 19,500, 20,800, 20,200.
The target is 20,000.

Unknowns

Which number is closest to 20,000

Constraints

'Closest' means the smallest distance (difference) from the target.

Plan

#1 Draw a Diagram · also uses: #6 Guess and Check

Picture the numbers on a number line around 20,000 and measure how far each is from 20,000; the one with the smallest gap is closest.

Execute

#1 Draw a Diagram 4.NBT.A.2

19,500 is below 20,000 by 20,000 - 19,500 = 500.

20{,}000 - 19{,}500 = 500

On the number line 19,500 sits to the left of 20,000.

#1 Draw a Diagram 4.NBT.A.2

20,800 is above 20,000 by 20,800 - 20,000 = 800.

20{,}800 - 20{,}000 = 800

On the number line 20,800 sits to the right of 20,000.

#1 Draw a Diagram 4.NBT.A.2

20,200 is above 20,000 by 20,200 - 20,000 = 200.

20{,}200 - 20{,}000 = 200

On the number line 20,200 sits to the right of 20,000.

#6 Guess and Check 4.NBT.A.2

The distances are 500, 800, 200. The smallest is 200, so 20,200 is closest to 20,000.

200 < 500 < 800

The smallest gap wins.

Answer: 20,200

Review

20,200 differs from 20,000 by only 200, less than the other gaps (500, 800), so 20,200 being closest is correct.

Make a systematic list (tool 2): write each number with its distance from the target and read off the smallest.

Standards · min grade 4

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Comparing the distances of each number from 20,000.

💡 This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!

Variant 8 answer: 10,050

Which of the following numbers is closest to $10{,}000$ ? Write it.

$9{,}700 \qquad 10{,}300 \qquad 10{,}050$

Show solution

Understand

Of the numbers 9,700, 10,300, 10,050, decide which one is nearest to 10,000.

Givens

The numbers are 9,700, 10,300, 10,050.
The target is 10,000.

Unknowns

Which number is closest to 10,000

Constraints

'Closest' means the smallest distance (difference) from the target.

Plan

#1 Draw a Diagram · also uses: #6 Guess and Check

Picture the numbers on a number line around 10,000 and measure how far each is from 10,000; the one with the smallest gap is closest.

Execute

#1 Draw a Diagram 4.NBT.A.2

9,700 is below 10,000 by 10,000 - 9,700 = 300.

10{,}000 - 9{,}700 = 300

On the number line 9,700 sits to the left of 10,000.

#1 Draw a Diagram 4.NBT.A.2

10,300 is above 10,000 by 10,300 - 10,000 = 300.

10{,}300 - 10{,}000 = 300

On the number line 10,300 sits to the right of 10,000.

#1 Draw a Diagram 4.NBT.A.2

10,050 is above 10,000 by 10,050 - 10,000 = 50.

10{,}050 - 10{,}000 = 50

On the number line 10,050 sits to the right of 10,000.

#6 Guess and Check 4.NBT.A.2

The distances are 300, 300, 50. The smallest is 50, so 10,050 is closest to 10,000.

50 < 300 < 300

The smallest gap wins.

Answer: 10,050

Review

10,050 differs from 10,000 by only 50, less than the other gaps (300, 300), so 10,050 being closest is correct.

Make a systematic list (tool 2): write each number with its distance from the target and read off the smallest.

Standards · min grade 4

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Comparing the distances of each number from 10,000.

💡 This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!

Variant 9 answer: 30,150

Which of the following numbers is closest to $30{,}000$ ? Write it.

$29{,}000 \qquad 30{,}600 \qquad 30{,}150$

Show solution

Understand

Of the numbers 29,000, 30,600, 30,150, decide which one is nearest to 30,000.

Givens

The numbers are 29,000, 30,600, 30,150.
The target is 30,000.

Unknowns

Which number is closest to 30,000

Constraints

'Closest' means the smallest distance (difference) from the target.

Plan

#1 Draw a Diagram · also uses: #6 Guess and Check

Picture the numbers on a number line around 30,000 and measure how far each is from 30,000; the one with the smallest gap is closest.

Execute

#1 Draw a Diagram 4.NBT.A.2

29,000 is below 30,000 by 30,000 - 29,000 = 1,000.

30{,}000 - 29{,}000 = 1{,}000

On the number line 29,000 sits to the left of 30,000.

#1 Draw a Diagram 4.NBT.A.2

30,600 is above 30,000 by 30,600 - 30,000 = 600.

30{,}600 - 30{,}000 = 600

On the number line 30,600 sits to the right of 30,000.

#1 Draw a Diagram 4.NBT.A.2

30,150 is above 30,000 by 30,150 - 30,000 = 150.

30{,}150 - 30{,}000 = 150

On the number line 30,150 sits to the right of 30,000.

#6 Guess and Check 4.NBT.A.2

The distances are 1,000, 600, 150. The smallest is 150, so 30,150 is closest to 30,000.

150 < 600 < 1{,}000

The smallest gap wins.

Answer: 30,150

Review

30,150 differs from 30,000 by only 150, less than the other gaps (1,000, 600), so 30,150 being closest is correct.

Make a systematic list (tool 2): write each number with its distance from the target and read off the smallest.

Standards · min grade 4

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Comparing the distances of each number from 30,000.

💡 This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!

Variant 10 answer: 8,050

Which of the following numbers is closest to $8{,}000$ ? Write it.

$7{,}400 \qquad 8{,}300 \qquad 8{,}050$

Show solution

Understand

Of the numbers 7,400, 8,300, 8,050, decide which one is nearest to 8,000.

Givens

The numbers are 7,400, 8,300, 8,050.
The target is 8,000.

Unknowns

Which number is closest to 8,000

Constraints

'Closest' means the smallest distance (difference) from the target.

Plan

#1 Draw a Diagram · also uses: #6 Guess and Check

Picture the numbers on a number line around 8,000 and measure how far each is from 8,000; the one with the smallest gap is closest.

Execute

#1 Draw a Diagram 4.NBT.A.2

7,400 is below 8,000 by 8,000 - 7,400 = 600.

8{,}000 - 7{,}400 = 600

On the number line 7,400 sits to the left of 8,000.

#1 Draw a Diagram 4.NBT.A.2

8,300 is above 8,000 by 8,300 - 8,000 = 300.

8{,}300 - 8{,}000 = 300

On the number line 8,300 sits to the right of 8,000.

#1 Draw a Diagram 4.NBT.A.2

8,050 is above 8,000 by 8,050 - 8,000 = 50.

8{,}050 - 8{,}000 = 50

On the number line 8,050 sits to the right of 8,000.

#6 Guess and Check 4.NBT.A.2

The distances are 600, 300, 50. The smallest is 50, so 8,050 is closest to 8,000.

50 < 300 < 600

The smallest gap wins.

Answer: 8,050

Review

8,050 differs from 8,000 by only 50, less than the other gaps (600, 300), so 8,050 being closest is correct.

Make a systematic list (tool 2): write each number with its distance from the target and read off the smallest.

Standards · min grade 4

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Comparing the distances of each number from 8,000.

💡 This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!

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