← Locate and compare numbers on a number line · Repeating Cycle Patterns

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

4.NBT.A.2

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 50,300

Which of the following numbers is closest to 50,00050{,}000? Write it.

48,00051,00050,30048{,}000 \qquad 51{,}000 \qquad 50{,}300

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=2,00050{,}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=1,00051{,}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=30050{,}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<2,000300 < 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 answer: 100,400

Which of the following numbers is closest to 100,000100{,}000? Write it.

99,000101,200100,40099{,}000 \qquad 101{,}200 \qquad 100{,}400

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=1,000100{,}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=1,200101{,}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=400100{,}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<1,200400 < 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 answer: 8,050

Which of the following numbers is closest to 8,0008{,}000? Write it.

7,4008,3008,0507{,}400 \qquad 8{,}300 \qquad 8{,}050

Show solution
1 · Understandwhat's really being asked

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.
2 · Planchoose the strategy

#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.

3 · Execute4 carry out the plan

1Distance of 7,400 from 8,000

#1 Draw a Diagram 4.NBT.A.2
7,400 is below 8,000 by 8,000 - 7,400 = 600.
8,000−7,400=6008{,}000 - 7{,}400 = 600
On the number line 7,400 sits to the left of 8,000.

2Distance of 8,300 from 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=3008{,}300 - 8{,}000 = 300
On the number line 8,300 sits to the right of 8,000.

3Distance of 8,050 from 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=508{,}050 - 8{,}000 = 50
On the number line 8,050 sits to the right of 8,000.

4Compare the gaps

#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<60050 < 300 < 600
The smallest gap wins.
Answer: 8,050
4 · Reviewdoes it hold up?

8,050 differs from 8,000 by only 50, less than the other gaps (600, 300), so 8,050 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 8,000.
💡Takeaway. This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!
Variant 4 medium answer: 1,020

Which of the following numbers is closest to 1,0001{,}000? Write it.

9701,0801,020970 \qquad 1{,}080 \qquad 1{,}020

Show solution
1 · Understandwhat's really being asked

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.
2 · Planchoose the strategy

#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.

3 · Execute4 carry out the plan

1Distance of 970 from 1,000

#1 Draw a Diagram 4.NBT.A.2
970 is below 1,000 by 1,000 - 970 = 30.
1,000−970=301{,}000 - 970 = 30
On the number line 970 sits to the left of 1,000.

2Distance of 1,080 from 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=801{,}080 - 1{,}000 = 80
On the number line 1,080 sits to the right of 1,000.

3Distance of 1,020 from 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=201{,}020 - 1{,}000 = 20
On the number line 1,020 sits to the right of 1,000.

4Compare the gaps

#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<8020 < 30 < 80
The smallest gap wins.
Answer: 1,020
4 · Reviewdoes it hold up?

1,020 differs from 1,000 by only 20, less than the other gaps (30, 80), so 1,020 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 1,000.
💡Takeaway. This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!
Variant 5 medium answer: 30,150

Which of the following numbers is closest to 30,00030{,}000? Write it.

29,00030,60030,15029{,}000 \qquad 30{,}600 \qquad 30{,}150

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=1,00030{,}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=60030{,}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=15030{,}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<1,000150 < 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 answer: 15,100

Which of the following numbers is closest to 15,00015{,}000? Write it.

14,50015,70015,10014{,}500 \qquad 15{,}700 \qquad 15{,}100

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=50015{,}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=70015{,}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=10015{,}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<700100 < 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 answer: 10,050

Which of the following numbers is closest to 10,00010{,}000? Write it.

9,70010,30010,0509{,}700 \qquad 10{,}300 \qquad 10{,}050

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=30010{,}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=30010{,}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=5010{,}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<30050 < 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 answer: 5,050

Which of the following numbers is closest to 5,0005{,}000? Write it.

4,8005,4005,0504{,}800 \qquad 5{,}400 \qquad 5{,}050

Show solution
1 · Understandwhat's really being asked

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.
2 · Planchoose the strategy

#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.

3 · Execute4 carry out the plan

1Distance of 4,800 from 5,000

#1 Draw a Diagram 4.NBT.A.2
4,800 is below 5,000 by 5,000 - 4,800 = 200.
5,000−4,800=2005{,}000 - 4{,}800 = 200
On the number line 4,800 sits to the left of 5,000.

2Distance of 5,400 from 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=4005{,}400 - 5{,}000 = 400
On the number line 5,400 sits to the right of 5,000.

3Distance of 5,050 from 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=505{,}050 - 5{,}000 = 50
On the number line 5,050 sits to the right of 5,000.

4Compare the gaps

#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<40050 < 200 < 400
The smallest gap wins.
Answer: 5,050
4 · Reviewdoes it hold up?

5,050 differs from 5,000 by only 50, less than the other gaps (200, 400), so 5,050 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 5,000.
💡Takeaway. This only needs Grade 4 comparing: measure each number's gap from the target and pick the smallest gap!
Variant 9 hard answer: 10,100

Which of the following numbers is closest to 10,00010{,}000? Write it.

8,80010,50010,1008{,}800 \qquad 10{,}500 \qquad 10{,}100

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=1,20010{,}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=50010{,}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=10010{,}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<1,200100 < 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 answer: 20,200

Which of the following numbers is closest to 20,00020{,}000? Write it.

19,50020,80020,20019{,}500 \qquad 20{,}800 \qquad 20{,}200

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=50020{,}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=80020{,}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=20020{,}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<800200 < 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!