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

Variant 1 easy

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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.

2 · Planchoose the strategy

#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.

3 · Execute4 carry out the plan

1Distance of 48,000 from 50,000

#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.

2Distance of 51,000 from 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.

3Distance of 50,300 from 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.

4Compare the gaps

#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

4 · Reviewdoes it hold up?

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.

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

Standardsmin 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.

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

Variant 2 easy

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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.

2 · Planchoose the strategy

#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.

3 · Execute4 carry out the plan

1Distance of 99,000 from 100,000

#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.

2Distance of 101,200 from 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.

3Distance of 100,400 from 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.

4Compare the gaps

#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

4 · Reviewdoes it hold up?

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.

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

Standardsmin 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.

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

Variant 3 easy

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

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

Your answer

Variant 4 medium

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

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

Your answer

Variant 5 medium

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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.

2 · Planchoose the strategy

#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.

3 · Execute4 carry out the plan

1Distance of 29,000 from 30,000

#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.

2Distance of 30,600 from 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.

3Distance of 30,150 from 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.

4Compare the gaps

#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

4 · Reviewdoes it hold up?

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

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

Standardsmin 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.

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

Variant 6 medium

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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.

2 · Planchoose the strategy

#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.

3 · Execute4 carry out the plan

1Distance of 14,500 from 15,000

#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.

2Distance of 15,700 from 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.

3Distance of 15,100 from 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.

4Compare the gaps

#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

4 · Reviewdoes it hold up?

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

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

Standardsmin 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.

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

Variant 7 medium

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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.

2 · Planchoose the strategy

#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.

3 · Execute4 carry out the plan

1Distance of 9,700 from 10,000

#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.

2Distance of 10,300 from 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.

3Distance of 10,050 from 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.

4Compare the gaps

#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

4 · Reviewdoes it hold up?

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

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

Standardsmin 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.

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

Variant 8 hard

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

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

Your answer

Variant 9 hard

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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.

2 · Planchoose the strategy

#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.

3 · Execute4 carry out the plan

1Distance of 8,800 from 10,000

#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.

2Distance of 10,500 from 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.

3Distance of 10,100 from 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.

4Compare the gaps

#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

4 · Reviewdoes it hold up?

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

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

Standardsmin 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.

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

Variant 10 hard

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

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

Your answer

Show solution

1 · Understandwhat's really being asked

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.

2 · Planchoose the strategy

#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.

3 · Execute4 carry out the plan

1Distance of 19,500 from 20,000

#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.

2Distance of 20,800 from 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.

3Distance of 20,200 from 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.

4Compare the gaps

#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

4 · Reviewdoes it hold up?

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

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

Standardsmin 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.

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

Locate and compare numbers on a number line · 10 practice problems

Generated variants — 10

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