← 2-2 · Skip-count backward to the start · Work Backwards to Recover a Start Value

Skip-count backward to the start · 12 practice problems

4.NBT.A.2

Generated variants — 12

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

Variant 1 answer: 6752

Starting from $\blacksquare$ and skip-counting up by $10$ 4 times, you reach $6792$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 10 4 times lands on 6792. Find the starting number.

Givens

Each skip-count step adds 10.
There are 4 steps.
After 4 steps the number is 6792.

Unknowns

The starting number.

Constraints

Counting up by 10 4 times means adding 10 a total of 4 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 10 by counting back from 6792.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 10 4 times adds 10 4 times, which is 40 in all.

4 \times 10 = 40

4 jumps of 10 stack up to 40.

#11 Work Backwards 4.NBT.A.2

Since 40 was added to reach 6792, the starting number is 40 less than 6792. Counting back: 6792, 6782, 6772, 6762, 6752.

6792 - 40 = 6752

To undo adding 40, you subtract 40, landing on where you began.

Answer: 6752

Review

Check forward: 6752 + 10 = 6762, 6762 + 10 = 6772, 6772 + 10 = 6782, 6782 + 10 = 6792. 4 jumps of 10 from 6752 reach 6792, so the start is right.

Set up the unknown directly: start + 40 = 6792, then subtract 40 from both sides to get start = 6752.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 4 skip-count steps of 10 as a total of 40.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 10s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!

Variant 2 answer: 7300

Starting from $\blacksquare$ and skip-counting up by $100$ 3 times, you reach $7600$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 100 3 times lands on 7600. Find the starting number.

Givens

Each skip-count step adds 100.
There are 3 steps.
After 3 steps the number is 7600.

Unknowns

The starting number.

Constraints

Counting up by 100 3 times means adding 100 a total of 3 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 100 by counting back from 7600.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 100 3 times adds 100 3 times, which is 300 in all.

3 \times 100 = 300

3 jumps of 100 stack up to 300.

#11 Work Backwards 4.NBT.A.2

Since 300 was added to reach 7600, the starting number is 300 less than 7600. Counting back: 7600, 7500, 7400, 7300.

7600 - 300 = 7300

To undo adding 300, you subtract 300, landing on where you began.

Answer: 7300

Review

Check forward: 7300 + 100 = 7400, 7400 + 100 = 7500, 7500 + 100 = 7600. 3 jumps of 100 from 7300 reach 7600, so the start is right.

Set up the unknown directly: start + 300 = 7600, then subtract 300 from both sides to get start = 7300.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 3 skip-count steps of 100 as a total of 300.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 100s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!

Variant 3 answer: 5200

Starting from $\blacksquare$ and skip-counting up by $10$ 3 times, you reach $5230$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 10 3 times lands on 5230. Find the starting number.

Givens

Each skip-count step adds 10.
There are 3 steps.
After 3 steps the number is 5230.

Unknowns

The starting number.

Constraints

Counting up by 10 3 times means adding 10 a total of 3 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 10 by counting back from 5230.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 10 3 times adds 10 3 times, which is 30 in all.

3 \times 10 = 30

3 jumps of 10 stack up to 30.

#11 Work Backwards 4.NBT.A.2

Since 30 was added to reach 5230, the starting number is 30 less than 5230. Counting back: 5230, 5220, 5210, 5200.

5230 - 30 = 5200

To undo adding 30, you subtract 30, landing on where you began.

Answer: 5200

Review

Check forward: 5200 + 10 = 5210, 5210 + 10 = 5220, 5220 + 10 = 5230. 3 jumps of 10 from 5200 reach 5230, so the start is right.

Set up the unknown directly: start + 30 = 5230, then subtract 30 from both sides to get start = 5200.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 3 skip-count steps of 10 as a total of 30.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 10s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!

Variant 4 answer: 8130

Starting from $\blacksquare$ and skip-counting up by $10$ 6 times, you reach $8190$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 10 6 times lands on 8190. Find the starting number.

Givens

Each skip-count step adds 10.
There are 6 steps.
After 6 steps the number is 8190.

Unknowns

The starting number.

Constraints

Counting up by 10 6 times means adding 10 a total of 6 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 10 by counting back from 8190.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 10 6 times adds 10 6 times, which is 60 in all.

6 \times 10 = 60

6 jumps of 10 stack up to 60.

#11 Work Backwards 4.NBT.A.2

Since 60 was added to reach 8190, the starting number is 60 less than 8190. Counting back: 8190, 8180, 8170, 8160, 8150, 8140, 8130.

8190 - 60 = 8130

To undo adding 60, you subtract 60, landing on where you began.

Answer: 8130

Review

Check forward: 8130 + 10 = 8140, 8140 + 10 = 8150, 8150 + 10 = 8160, 8160 + 10 = 8170, 8170 + 10 = 8180, 8180 + 10 = 8190. 6 jumps of 10 from 8130 reach 8190, so the start is right.

Set up the unknown directly: start + 60 = 8190, then subtract 60 from both sides to get start = 8130.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 6 skip-count steps of 10 as a total of 60.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 10s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!

Variant 5 answer: 7800

Starting from $\blacksquare$ and skip-counting up by $100$ 6 times, you reach $8400$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 100 6 times lands on 8400. Find the starting number.

Givens

Each skip-count step adds 100.
There are 6 steps.
After 6 steps the number is 8400.

Unknowns

The starting number.

Constraints

Counting up by 100 6 times means adding 100 a total of 6 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 100 by counting back from 8400.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 100 6 times adds 100 6 times, which is 600 in all.

6 \times 100 = 600

6 jumps of 100 stack up to 600.

#11 Work Backwards 4.NBT.A.2

Since 600 was added to reach 8400, the starting number is 600 less than 8400. Counting back: 8400, 8300, 8200, 8100, 8000, 7900, 7800.

8400 - 600 = 7800

To undo adding 600, you subtract 600, landing on where you began.

Answer: 7800

Review

Check forward: 7800 + 100 = 7900, 7900 + 100 = 8000, 8000 + 100 = 8100, 8100 + 100 = 8200, 8200 + 100 = 8300, 8300 + 100 = 8400. 6 jumps of 100 from 7800 reach 8400, so the start is right.

Set up the unknown directly: start + 600 = 8400, then subtract 600 from both sides to get start = 7800.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 6 skip-count steps of 100 as a total of 600.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 100s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!

Variant 6 answer: 6000

Starting from $\blacksquare$ and skip-counting up by $100$ 5 times, you reach $6500$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 100 5 times lands on 6500. Find the starting number.

Givens

Each skip-count step adds 100.
There are 5 steps.
After 5 steps the number is 6500.

Unknowns

The starting number.

Constraints

Counting up by 100 5 times means adding 100 a total of 5 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 100 by counting back from 6500.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 100 5 times adds 100 5 times, which is 500 in all.

5 \times 100 = 500

5 jumps of 100 stack up to 500.

#11 Work Backwards 4.NBT.A.2

Since 500 was added to reach 6500, the starting number is 500 less than 6500. Counting back: 6500, 6400, 6300, 6200, 6100, 6000.

6500 - 500 = 6000

To undo adding 500, you subtract 500, landing on where you began.

Answer: 6000

Review

Check forward: 6000 + 100 = 6100, 6100 + 100 = 6200, 6200 + 100 = 6300, 6300 + 100 = 6400, 6400 + 100 = 6500. 5 jumps of 100 from 6000 reach 6500, so the start is right.

Set up the unknown directly: start + 500 = 6500, then subtract 500 from both sides to get start = 6000.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 5 skip-count steps of 100 as a total of 500.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 100s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!

Variant 7 answer: 5110

Starting from $\blacksquare$ and skip-counting up by $100$ 2 times, you reach $5310$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 100 2 times lands on 5310. Find the starting number.

Givens

Each skip-count step adds 100.
There are 2 steps.
After 2 steps the number is 5310.

Unknowns

The starting number.

Constraints

Counting up by 100 2 times means adding 100 a total of 2 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 100 by counting back from 5310.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 100 2 times adds 100 2 times, which is 200 in all.

2 \times 100 = 200

2 jumps of 100 stack up to 200.

#11 Work Backwards 4.NBT.A.2

Since 200 was added to reach 5310, the starting number is 200 less than 5310. Counting back: 5310, 5210, 5110.

5310 - 200 = 5110

To undo adding 200, you subtract 200, landing on where you began.

Answer: 5110

Review

Check forward: 5110 + 100 = 5210, 5210 + 100 = 5310. 2 jumps of 100 from 5110 reach 5310, so the start is right.

Set up the unknown directly: start + 200 = 5310, then subtract 200 from both sides to get start = 5110.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 2 skip-count steps of 100 as a total of 200.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 100s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!

Variant 8 answer: 4217

Starting from $\blacksquare$ and skip-counting up by $10$ 5 times, you reach $4267$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 10 5 times lands on 4267. Find the starting number.

Givens

Each skip-count step adds 10.
There are 5 steps.
After 5 steps the number is 4267.

Unknowns

The starting number.

Constraints

Counting up by 10 5 times means adding 10 a total of 5 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 10 by counting back from 4267.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 10 5 times adds 10 5 times, which is 50 in all.

5 \times 10 = 50

5 jumps of 10 stack up to 50.

#11 Work Backwards 4.NBT.A.2

Since 50 was added to reach 4267, the starting number is 50 less than 4267. Counting back: 4267, 4257, 4247, 4237, 4227, 4217.

4267 - 50 = 4217

To undo adding 50, you subtract 50, landing on where you began.

Answer: 4217

Review

Check forward: 4217 + 10 = 4227, 4227 + 10 = 4237, 4237 + 10 = 4247, 4247 + 10 = 4257, 4257 + 10 = 4267. 5 jumps of 10 from 4217 reach 4267, so the start is right.

Set up the unknown directly: start + 50 = 4267, then subtract 50 from both sides to get start = 4217.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 5 skip-count steps of 10 as a total of 50.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 10s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!

Variant 9 answer: 2308

Starting from $\blacksquare$ and skip-counting up by $10$ 4 times, you reach $2348$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 10 4 times lands on 2348. Find the starting number.

Givens

Each skip-count step adds 10.
There are 4 steps.
After 4 steps the number is 2348.

Unknowns

The starting number.

Constraints

Counting up by 10 4 times means adding 10 a total of 4 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 10 by counting back from 2348.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 10 4 times adds 10 4 times, which is 40 in all.

4 \times 10 = 40

4 jumps of 10 stack up to 40.

#11 Work Backwards 4.NBT.A.2

Since 40 was added to reach 2348, the starting number is 40 less than 2348. Counting back: 2348, 2338, 2328, 2318, 2308.

2348 - 40 = 2308

To undo adding 40, you subtract 40, landing on where you began.

Answer: 2308

Review

Check forward: 2308 + 10 = 2318, 2318 + 10 = 2328, 2328 + 10 = 2338, 2338 + 10 = 2348. 4 jumps of 10 from 2308 reach 2348, so the start is right.

Set up the unknown directly: start + 40 = 2348, then subtract 40 from both sides to get start = 2308.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 4 skip-count steps of 10 as a total of 40.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 10s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!

Variant 10 answer: 9011

Starting from $\blacksquare$ and skip-counting up by $10$ 7 times, you reach $9081$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 10 7 times lands on 9081. Find the starting number.

Givens

Each skip-count step adds 10.
There are 7 steps.
After 7 steps the number is 9081.

Unknowns

The starting number.

Constraints

Counting up by 10 7 times means adding 10 a total of 7 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 10 by counting back from 9081.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 10 7 times adds 10 7 times, which is 70 in all.

7 \times 10 = 70

7 jumps of 10 stack up to 70.

#11 Work Backwards 4.NBT.A.2

Since 70 was added to reach 9081, the starting number is 70 less than 9081. Counting back: 9081, 9071, 9061, 9051, 9041, 9031, 9021, 9011.

9081 - 70 = 9011

To undo adding 70, you subtract 70, landing on where you began.

Answer: 9011

Review

Check forward: 9011 + 10 = 9021, 9021 + 10 = 9031, 9031 + 10 = 9041, 9041 + 10 = 9051, 9051 + 10 = 9061, 9061 + 10 = 9071, 9071 + 10 = 9081. 7 jumps of 10 from 9011 reach 9081, so the start is right.

Set up the unknown directly: start + 70 = 9081, then subtract 70 from both sides to get start = 9011.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 7 skip-count steps of 10 as a total of 70.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 10s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!

Variant 11 answer: 3365

Starting from $\blacksquare$ and skip-counting up by $10$ 5 times, you reach $3415$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 10 5 times lands on 3415. Find the starting number.

Givens

Each skip-count step adds 10.
There are 5 steps.
After 5 steps the number is 3415.

Unknowns

The starting number.

Constraints

Counting up by 10 5 times means adding 10 a total of 5 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 10 by counting back from 3415.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 10 5 times adds 10 5 times, which is 50 in all.

5 \times 10 = 50

5 jumps of 10 stack up to 50.

#11 Work Backwards 4.NBT.A.2

Since 50 was added to reach 3415, the starting number is 50 less than 3415. Counting back: 3415, 3405, 3395, 3385, 3375, 3365.

3415 - 50 = 3365

To undo adding 50, you subtract 50, landing on where you began.

Answer: 3365

Review

Check forward: 3365 + 10 = 3375, 3375 + 10 = 3385, 3385 + 10 = 3395, 3395 + 10 = 3405, 3405 + 10 = 3415. 5 jumps of 10 from 3365 reach 3415, so the start is right.

Set up the unknown directly: start + 50 = 3415, then subtract 50 from both sides to get start = 3365.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 5 skip-count steps of 10 as a total of 50.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 10s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!

Variant 12 answer: 4470

Starting from $\blacksquare$ and skip-counting up by $100$ 4 times, you reach $4870$ . Find the number $\blacksquare$ .

Show solution

Understand

Starting from an unknown number and skip-counting up by 100 4 times lands on 4870. Find the starting number.

Givens

Each skip-count step adds 100.
There are 4 steps.
After 4 steps the number is 4870.

Unknowns

The starting number.

Constraints

Counting up by 100 4 times means adding 100 a total of 4 times.

Plan

#11 Work Backwards · also uses: #5 Look for a Pattern

The end result is given and we want the start, which is the classic signal to work backwards: undo each step of 100 by counting back from 4870.

Execute

#5 Look for a Pattern 2.NBT.A.2

Going up by 100 4 times adds 100 4 times, which is 400 in all.

4 \times 100 = 400

4 jumps of 100 stack up to 400.

#11 Work Backwards 4.NBT.A.2

Since 400 was added to reach 4870, the starting number is 400 less than 4870. Counting back: 4870, 4770, 4670, 4570, 4470.

4870 - 400 = 4470

To undo adding 400, you subtract 400, landing on where you began.

Answer: 4470

Review

Check forward: 4470 + 100 = 4570, 4570 + 100 = 4670, 4670 + 100 = 4770, 4770 + 100 = 4870. 4 jumps of 100 from 4470 reach 4870, so the start is right.

Set up the unknown directly: start + 400 = 4870, then subtract 400 from both sides to get start = 4470.

Standards · min grade 4

2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing 4 skip-count steps of 100 as a total of 400.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Counting back by 100s through four-digit numbers to reach the start.

💡 When you know where you ended up, just hop backwards the same number of steps to find where you started!