Practice · Skip-count by the changing place value · Sensim Math

Variant 1 easy

Find the skip-counting rule and determine the number marked by $\bigstar$ .

A row of boxes is connected by arrows, with numbers skip-counted by a fixed rule written in order. From left to right the boxes read $0$ , $2{,}000$ , $4{,}000$ , $6{,}000$ , ☐, ☐, $\bigstar$ , where the last box is $\bigstar$ .

Your answer

Show solution

1 · Understandwhat's really being asked

A chain of 7 boxes skip-counts by a fixed step: 0; 2,000; 4,000; ...; then the $\bigstar$ (the last box). Find the rule and the $\bigstar$ 's value.

Givens

The first boxes are 0, 2,000, and 4,000.
The boxes increase by a fixed skip-count step.
The $\bigstar$ is the 7th (last) box.

Unknowns

The skip-count step and the number at the $\bigstar$

Constraints

Every step in the chain adds the same fixed amount.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Find the constant step from two known neighbors, confirm it with a second pair, then add that step repeatedly to reach the last box.

3 · Execute3 carry out the plan

1Find the step

#5 Look for a Pattern 4.OA.C.5

From 0 to 2,000 the number rises by 2,000, and from 2,000 to 4,000 it rises by 2,000 again. The step is +2,000.

2{,}000 - 0 = 2{,}000

Equal jumps between known boxes reveal the repeating rule.

2Continue the count

#7 Identify Subproblems 4.NBT.A.2

Keep adding 2,000: the next box after 4,000 is 6,000, then 8,000, and so on.

4{,}000 + 2{,}000 = 6{,}000

Each new box is just one more hop of the step.

3Reach the $\bigstar$

#5 Look for a Pattern 4.NBT.A.2

The

\bigstar

is the first box plus 6 steps: 0 + 6 x 2,000 = 12,000.

0 + 6 \times 2{,}000 = 12{,}000

6 equal hops of 2,000 from the start land on the

\bigstar

.

Answer: 12,000

4 · Reviewdoes it hold up?

From the first box to the last there are 6 steps of 2,000, totaling 12,000, and 0 + 12,000 = 12,000, matching the step-by-step result.

Another way: Evaluate finite differences (tool 14): the constant first difference 2,000 confirms a linear pattern, so the nth box is 0 + (n-1) x 2,000.

Standardsmin grade 4

4.OA.C.5 Generate a number or shape pattern following a given rule — Identifying the constant skip-count rule and extending it.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Adding the step across multi-digit numbers to reach the $\bigstar$.

💡Takeaway. This only needs Grade 4 pattern sense: find the equal jump, then keep hopping by it!

Variant 2 easy

Find the skip-counting rule and determine the number marked by $\bigstar$ .

A row of boxes is connected by arrows, with numbers skip-counted by a fixed rule written in order. From left to right the boxes read $12{,}000{,}000$ , $13{,}000{,}000$ , $14{,}000{,}000$ , ☐, ☐, $\bigstar$ , where the last box is $\bigstar$ .

Your answer

Show solution

1 · Understandwhat's really being asked

A chain of 6 boxes skip-counts by a fixed step: 12,000,000; 13,000,000; 14,000,000; ...; then the $\bigstar$ (the last box). Find the rule and the $\bigstar$ 's value.

Givens

The first boxes are 12,000,000, 13,000,000, and 14,000,000.
The boxes increase by a fixed skip-count step.
The $\bigstar$ is the 6th (last) box.

Unknowns

The skip-count step and the number at the $\bigstar$

Constraints

Every step in the chain adds the same fixed amount.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Find the constant step from two known neighbors, confirm it with a second pair, then add that step repeatedly to reach the last box.

3 · Execute3 carry out the plan

1Find the step

#5 Look for a Pattern 4.OA.C.5

From 12,000,000 to 13,000,000 the number rises by 1,000,000, and from 13,000,000 to 14,000,000 it rises by 1,000,000 again. The step is +1,000,000.

13{,}000{,}000 - 12{,}000{,}000 = 1{,}000{,}000

Equal jumps between known boxes reveal the repeating rule.

2Continue the count

#7 Identify Subproblems 4.NBT.A.2

Keep adding 1,000,000: the next box after 14,000,000 is 15,000,000, then 16,000,000, and so on.

14{,}000{,}000 + 1{,}000{,}000 = 15{,}000{,}000

Each new box is just one more hop of the step.

3Reach the $\bigstar$

#5 Look for a Pattern 4.NBT.A.2

The

\bigstar

is the first box plus 5 steps: 12,000,000 + 5 x 1,000,000 = 17,000,000.

12{,}000{,}000 + 5 \times 1{,}000{,}000 = 17{,}000{,}000

5 equal hops of 1,000,000 from the start land on the

\bigstar

.

Answer: 17,000,000

4 · Reviewdoes it hold up?

From the first box to the last there are 5 steps of 1,000,000, totaling 5,000,000, and 12,000,000 + 5,000,000 = 17,000,000, matching the step-by-step result.

Another way: Evaluate finite differences (tool 14): the constant first difference 1,000,000 confirms a linear pattern, so the nth box is 12,000,000 + (n-1) x 1,000,000.

Standardsmin grade 4

4.OA.C.5 Generate a number or shape pattern following a given rule — Identifying the constant skip-count rule and extending it.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Adding the step across multi-digit numbers to reach the $\bigstar$.

💡Takeaway. This only needs Grade 4 pattern sense: find the equal jump, then keep hopping by it!

Variant 3 easy

Find the skip-counting rule and determine the number marked by $\bigstar$ .

A row of boxes is connected by arrows, with numbers skip-counted by a fixed rule written in order. From left to right the boxes read $90{,}000$ , $94{,}000$ , $98{,}000$ , ☐, ☐, $\bigstar$ , where the last box is $\bigstar$ .

Your answer

Show solution

1 · Understandwhat's really being asked

A chain of 6 boxes skip-counts by a fixed step: 90,000; 94,000; 98,000; ...; then the $\bigstar$ (the last box). Find the rule and the $\bigstar$ 's value.

Givens

The first boxes are 90,000, 94,000, and 98,000.
The boxes increase by a fixed skip-count step.
The $\bigstar$ is the 6th (last) box.

Unknowns

The skip-count step and the number at the $\bigstar$

Constraints

Every step in the chain adds the same fixed amount.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Find the constant step from two known neighbors, confirm it with a second pair, then add that step repeatedly to reach the last box.

3 · Execute3 carry out the plan

1Find the step

#5 Look for a Pattern 4.OA.C.5

From 90,000 to 94,000 the number rises by 4,000, and from 94,000 to 98,000 it rises by 4,000 again. The step is +4,000.

94{,}000 - 90{,}000 = 4{,}000

Equal jumps between known boxes reveal the repeating rule.

2Continue the count

#7 Identify Subproblems 4.NBT.A.2

Keep adding 4,000: the next box after 98,000 is 102,000, then 106,000, and so on.

98{,}000 + 4{,}000 = 102{,}000

Each new box is just one more hop of the step.

3Reach the $\bigstar$

#5 Look for a Pattern 4.NBT.A.2

The

\bigstar

is the first box plus 5 steps: 90,000 + 5 x 4,000 = 110,000.

90{,}000 + 5 \times 4{,}000 = 110{,}000

5 equal hops of 4,000 from the start land on the

\bigstar

.

Answer: 110,000

4 · Reviewdoes it hold up?

From the first box to the last there are 5 steps of 4,000, totaling 20,000, and 90,000 + 20,000 = 110,000, matching the step-by-step result.

Another way: Evaluate finite differences (tool 14): the constant first difference 4,000 confirms a linear pattern, so the nth box is 90,000 + (n-1) x 4,000.

Standardsmin grade 4

4.OA.C.5 Generate a number or shape pattern following a given rule — Identifying the constant skip-count rule and extending it.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Adding the step across multi-digit numbers to reach the $\bigstar$.

💡Takeaway. This only needs Grade 4 pattern sense: find the equal jump, then keep hopping by it!

Variant 4 medium

Find the skip-counting rule and determine the number marked by $\bigstar$ .

A row of boxes is connected by arrows, with numbers skip-counted by a fixed rule written in order. From left to right the boxes read $1{,}000{,}000$ , $1{,}010{,}000$ , $1{,}020{,}000$ , ☐, ☐, $\bigstar$ , where the last box is $\bigstar$ .

Your answer

Show solution

1 · Understandwhat's really being asked

A chain of 6 boxes skip-counts by a fixed step: 1,000,000; 1,010,000; 1,020,000; ...; then the $\bigstar$ (the last box). Find the rule and the $\bigstar$ 's value.

Givens

The first boxes are 1,000,000, 1,010,000, and 1,020,000.
The boxes increase by a fixed skip-count step.
The $\bigstar$ is the 6th (last) box.

Unknowns

The skip-count step and the number at the $\bigstar$

Constraints

Every step in the chain adds the same fixed amount.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Find the constant step from two known neighbors, confirm it with a second pair, then add that step repeatedly to reach the last box.

3 · Execute3 carry out the plan

1Find the step

#5 Look for a Pattern 4.OA.C.5

From 1,000,000 to 1,010,000 the number rises by 10,000, and from 1,010,000 to 1,020,000 it rises by 10,000 again. The step is +10,000.

1{,}010{,}000 - 1{,}000{,}000 = 10{,}000

Equal jumps between known boxes reveal the repeating rule.

2Continue the count

#7 Identify Subproblems 4.NBT.A.2

Keep adding 10,000: the next box after 1,020,000 is 1,030,000, then 1,040,000, and so on.

1{,}020{,}000 + 10{,}000 = 1{,}030{,}000

Each new box is just one more hop of the step.

3Reach the $\bigstar$

#5 Look for a Pattern 4.NBT.A.2

The

\bigstar

is the first box plus 5 steps: 1,000,000 + 5 x 10,000 = 1,050,000.

1{,}000{,}000 + 5 \times 10{,}000 = 1{,}050{,}000

5 equal hops of 10,000 from the start land on the

\bigstar

.

Answer: 1,050,000

4 · Reviewdoes it hold up?

From the first box to the last there are 5 steps of 10,000, totaling 50,000, and 1,000,000 + 50,000 = 1,050,000, matching the step-by-step result.

Another way: Evaluate finite differences (tool 14): the constant first difference 10,000 confirms a linear pattern, so the nth box is 1,000,000 + (n-1) x 10,000.

Standardsmin grade 4

4.OA.C.5 Generate a number or shape pattern following a given rule — Identifying the constant skip-count rule and extending it.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Adding the step across multi-digit numbers to reach the $\bigstar$.

💡Takeaway. This only needs Grade 4 pattern sense: find the equal jump, then keep hopping by it!

Variant 5 medium

Find the skip-counting rule and determine the number marked by $\bigstar$ .

A row of boxes is connected by arrows, with numbers skip-counted by a fixed rule written in order. From left to right the boxes read $640{,}000$ , $660{,}000$ , ☐, ☐, $\bigstar$ , where the last box is $\bigstar$ .

Your answer

Show solution

1 · Understandwhat's really being asked

A chain of 5 boxes skip-counts by a fixed step: 640,000; 660,000; 680,000; ...; then the $\bigstar$ (the last box). Find the rule and the $\bigstar$ 's value.

Givens

The first boxes are 640,000, 660,000, and 680,000.
The boxes increase by a fixed skip-count step.
The $\bigstar$ is the 5th (last) box.

Unknowns

The skip-count step and the number at the $\bigstar$

Constraints

Every step in the chain adds the same fixed amount.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Find the constant step from two known neighbors, confirm it with a second pair, then add that step repeatedly to reach the last box.

3 · Execute3 carry out the plan

1Find the step

#5 Look for a Pattern 4.OA.C.5

From 640,000 to 660,000 the number rises by 20,000, and from 660,000 to 680,000 it rises by 20,000 again. The step is +20,000.

660{,}000 - 640{,}000 = 20{,}000

Equal jumps between known boxes reveal the repeating rule.

2Continue the count

#7 Identify Subproblems 4.NBT.A.2

Keep adding 20,000: the next box after 680,000 is 700,000, then 720,000, and so on.

680{,}000 + 20{,}000 = 700{,}000

Each new box is just one more hop of the step.

3Reach the $\bigstar$

#5 Look for a Pattern 4.NBT.A.2

The

\bigstar

is the first box plus 4 steps: 640,000 + 4 x 20,000 = 720,000.

640{,}000 + 4 \times 20{,}000 = 720{,}000

4 equal hops of 20,000 from the start land on the

\bigstar

.

Answer: 720,000

4 · Reviewdoes it hold up?

From the first box to the last there are 4 steps of 20,000, totaling 80,000, and 640,000 + 80,000 = 720,000, matching the step-by-step result.

Another way: Evaluate finite differences (tool 14): the constant first difference 20,000 confirms a linear pattern, so the nth box is 640,000 + (n-1) x 20,000.

Standardsmin grade 4

4.OA.C.5 Generate a number or shape pattern following a given rule — Identifying the constant skip-count rule and extending it.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Adding the step across multi-digit numbers to reach the $\bigstar$.

💡Takeaway. This only needs Grade 4 pattern sense: find the equal jump, then keep hopping by it!

Variant 6 medium

Find the skip-counting rule and determine the number marked by $\bigstar$ .

A row of boxes is connected by arrows, with numbers skip-counted by a fixed rule written in order. From left to right the boxes read $200{,}000$ , $205{,}000$ , $210{,}000$ , ☐, $\bigstar$ , where the last box is $\bigstar$ .

Your answer

Show solution

1 · Understandwhat's really being asked

A chain of 5 boxes skip-counts by a fixed step: 200,000; 205,000; 210,000; ...; then the $\bigstar$ (the last box). Find the rule and the $\bigstar$ 's value.

Givens

The first boxes are 200,000, 205,000, and 210,000.
The boxes increase by a fixed skip-count step.
The $\bigstar$ is the 5th (last) box.

Unknowns

The skip-count step and the number at the $\bigstar$

Constraints

Every step in the chain adds the same fixed amount.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Find the constant step from two known neighbors, confirm it with a second pair, then add that step repeatedly to reach the last box.

3 · Execute3 carry out the plan

1Find the step

#5 Look for a Pattern 4.OA.C.5

From 200,000 to 205,000 the number rises by 5,000, and from 205,000 to 210,000 it rises by 5,000 again. The step is +5,000.

205{,}000 - 200{,}000 = 5{,}000

Equal jumps between known boxes reveal the repeating rule.

2Continue the count

#7 Identify Subproblems 4.NBT.A.2

Keep adding 5,000: the next box after 210,000 is 215,000, then 220,000, and so on.

210{,}000 + 5{,}000 = 215{,}000

Each new box is just one more hop of the step.

3Reach the $\bigstar$

#5 Look for a Pattern 4.NBT.A.2

The

\bigstar

is the first box plus 4 steps: 200,000 + 4 x 5,000 = 220,000.

200{,}000 + 4 \times 5{,}000 = 220{,}000

4 equal hops of 5,000 from the start land on the

\bigstar

.

Answer: 220,000

4 · Reviewdoes it hold up?

From the first box to the last there are 4 steps of 5,000, totaling 20,000, and 200,000 + 20,000 = 220,000, matching the step-by-step result.

Another way: Evaluate finite differences (tool 14): the constant first difference 5,000 confirms a linear pattern, so the nth box is 200,000 + (n-1) x 5,000.

Standardsmin grade 4

4.OA.C.5 Generate a number or shape pattern following a given rule — Identifying the constant skip-count rule and extending it.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Adding the step across multi-digit numbers to reach the $\bigstar$.

💡Takeaway. This only needs Grade 4 pattern sense: find the equal jump, then keep hopping by it!

Variant 7 medium

Find the skip-counting rule and determine the number marked by $\bigstar$ .

A row of boxes is connected by arrows, with numbers skip-counted by a fixed rule written in order. From left to right the boxes read $8{,}500{,}000$ , $8{,}550{,}000$ , ☐, $\bigstar$ , where the last box is $\bigstar$ .

Your answer

Show solution

1 · Understandwhat's really being asked

A chain of 4 boxes skip-counts by a fixed step: 8,500,000; 8,550,000; 8,600,000; ...; then the $\bigstar$ (the last box). Find the rule and the $\bigstar$ 's value.

Givens

The first boxes are 8,500,000, 8,550,000, and 8,600,000.
The boxes increase by a fixed skip-count step.
The $\bigstar$ is the 4th (last) box.

Unknowns

The skip-count step and the number at the $\bigstar$

Constraints

Every step in the chain adds the same fixed amount.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Find the constant step from two known neighbors, confirm it with a second pair, then add that step repeatedly to reach the last box.

3 · Execute3 carry out the plan

1Find the step

#5 Look for a Pattern 4.OA.C.5

From 8,500,000 to 8,550,000 the number rises by 50,000, and from 8,550,000 to 8,600,000 it rises by 50,000 again. The step is +50,000.

8{,}550{,}000 - 8{,}500{,}000 = 50{,}000

Equal jumps between known boxes reveal the repeating rule.

2Continue the count

#7 Identify Subproblems 4.NBT.A.2

Keep adding 50,000: the next box after 8,600,000 is 8,650,000, then 8,700,000, and so on.

8{,}600{,}000 + 50{,}000 = 8{,}650{,}000

Each new box is just one more hop of the step.

3Reach the $\bigstar$

#5 Look for a Pattern 4.NBT.A.2

The

\bigstar

is the first box plus 3 steps: 8,500,000 + 3 x 50,000 = 8,650,000.

8{,}500{,}000 + 3 \times 50{,}000 = 8{,}650{,}000

3 equal hops of 50,000 from the start land on the

\bigstar

.

Answer: 8,650,000

4 · Reviewdoes it hold up?

From the first box to the last there are 3 steps of 50,000, totaling 150,000, and 8,500,000 + 150,000 = 8,650,000, matching the step-by-step result.

Another way: Evaluate finite differences (tool 14): the constant first difference 50,000 confirms a linear pattern, so the nth box is 8,500,000 + (n-1) x 50,000.

Standardsmin grade 4

4.OA.C.5 Generate a number or shape pattern following a given rule — Identifying the constant skip-count rule and extending it.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Adding the step across multi-digit numbers to reach the $\bigstar$.

💡Takeaway. This only needs Grade 4 pattern sense: find the equal jump, then keep hopping by it!

Variant 8 hard

Find the skip-counting rule and determine the number marked by $\bigstar$ .

A row of boxes is connected by arrows, with numbers skip-counted by a fixed rule written in order. From left to right the boxes read $4{,}270{,}000$ , $4{,}273{,}000$ , $4{,}276{,}000$ , ☐, ☐, $\bigstar$ , where the last box is $\bigstar$ .

Your answer

Show solution

1 · Understandwhat's really being asked

A chain of 6 boxes skip-counts by a fixed step: 4,270,000; 4,273,000; 4,276,000; ...; then the $\bigstar$ (the last box). Find the rule and the $\bigstar$ 's value.

Givens

The first boxes are 4,270,000, 4,273,000, and 4,276,000.
The boxes increase by a fixed skip-count step.
The $\bigstar$ is the 6th (last) box.

Unknowns

The skip-count step and the number at the $\bigstar$

Constraints

Every step in the chain adds the same fixed amount.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Find the constant step from two known neighbors, confirm it with a second pair, then add that step repeatedly to reach the last box.

3 · Execute3 carry out the plan

1Find the step

#5 Look for a Pattern 4.OA.C.5

From 4,270,000 to 4,273,000 the number rises by 3,000, and from 4,273,000 to 4,276,000 it rises by 3,000 again. The step is +3,000.

4{,}273{,}000 - 4{,}270{,}000 = 3{,}000

Equal jumps between known boxes reveal the repeating rule.

2Continue the count

#7 Identify Subproblems 4.NBT.A.2

Keep adding 3,000: the next box after 4,276,000 is 4,279,000, then 4,282,000, and so on.

4{,}276{,}000 + 3{,}000 = 4{,}279{,}000

Each new box is just one more hop of the step.

3Reach the $\bigstar$

#5 Look for a Pattern 4.NBT.A.2

The

\bigstar

is the first box plus 5 steps: 4,270,000 + 5 x 3,000 = 4,285,000.

4{,}270{,}000 + 5 \times 3{,}000 = 4{,}285{,}000

5 equal hops of 3,000 from the start land on the

\bigstar

.

Answer: 4,285,000

4 · Reviewdoes it hold up?

From the first box to the last there are 5 steps of 3,000, totaling 15,000, and 4,270,000 + 15,000 = 4,285,000, matching the step-by-step result.

Another way: Evaluate finite differences (tool 14): the constant first difference 3,000 confirms a linear pattern, so the nth box is 4,270,000 + (n-1) x 3,000.

Standardsmin grade 4

4.OA.C.5 Generate a number or shape pattern following a given rule — Identifying the constant skip-count rule and extending it.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Adding the step across multi-digit numbers to reach the $\bigstar$.

💡Takeaway. This only needs Grade 4 pattern sense: find the equal jump, then keep hopping by it!

Variant 9 hard

Find the skip-counting rule and determine the number marked by $\bigstar$ .

A row of boxes is connected by arrows, with numbers skip-counted by a fixed rule written in order. From left to right the boxes read $3{,}400{,}000$ , $3{,}500{,}000$ , $3{,}600{,}000$ , ☐, ☐, $\bigstar$ , where the last box is $\bigstar$ .

Your answer

Show solution

1 · Understandwhat's really being asked

A chain of 6 boxes skip-counts by a fixed step: 3,400,000; 3,500,000; 3,600,000; ...; then the $\bigstar$ (the last box). Find the rule and the $\bigstar$ 's value.

Givens

The first boxes are 3,400,000, 3,500,000, and 3,600,000.
The boxes increase by a fixed skip-count step.
The $\bigstar$ is the 6th (last) box.

Unknowns

The skip-count step and the number at the $\bigstar$

Constraints

Every step in the chain adds the same fixed amount.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Find the constant step from two known neighbors, confirm it with a second pair, then add that step repeatedly to reach the last box.

3 · Execute3 carry out the plan

1Find the step

#5 Look for a Pattern 4.OA.C.5

From 3,400,000 to 3,500,000 the number rises by 100,000, and from 3,500,000 to 3,600,000 it rises by 100,000 again. The step is +100,000.

3{,}500{,}000 - 3{,}400{,}000 = 100{,}000

Equal jumps between known boxes reveal the repeating rule.

2Continue the count

#7 Identify Subproblems 4.NBT.A.2

Keep adding 100,000: the next box after 3,600,000 is 3,700,000, then 3,800,000, and so on.

3{,}600{,}000 + 100{,}000 = 3{,}700{,}000

Each new box is just one more hop of the step.

3Reach the $\bigstar$

#5 Look for a Pattern 4.NBT.A.2

The

\bigstar

is the first box plus 5 steps: 3,400,000 + 5 x 100,000 = 3,900,000.

3{,}400{,}000 + 5 \times 100{,}000 = 3{,}900{,}000

5 equal hops of 100,000 from the start land on the

\bigstar

.

Answer: 3,900,000

4 · Reviewdoes it hold up?

From the first box to the last there are 5 steps of 100,000, totaling 500,000, and 3,400,000 + 500,000 = 3,900,000, matching the step-by-step result.

Another way: Evaluate finite differences (tool 14): the constant first difference 100,000 confirms a linear pattern, so the nth box is 3,400,000 + (n-1) x 100,000.

Standardsmin grade 4

4.OA.C.5 Generate a number or shape pattern following a given rule — Identifying the constant skip-count rule and extending it.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Adding the step across multi-digit numbers to reach the $\bigstar$.

💡Takeaway. This only needs Grade 4 pattern sense: find the equal jump, then keep hopping by it!

Variant 10 hard

Find the skip-counting rule and determine the number marked by $\bigstar$ .

A row of boxes is connected by arrows, with numbers skip-counted by a fixed rule written in order. From left to right the boxes read $4{,}270{,}000$ , $4{,}273{,}000$ , $4{,}276{,}000$ , $4{,}279{,}000$ , ☐, ☐, $\bigstar$ , where the last box is $\bigstar$ .

Your answer

Show solution

1 · Understandwhat's really being asked

A chain of 7 boxes skip-counts by a fixed step: 4,270,000; 4,273,000; 4,276,000; ...; then the $\bigstar$ (the last box). Find the rule and the $\bigstar$ 's value.

Givens

The first boxes are 4,270,000, 4,273,000, and 4,276,000.
The boxes increase by a fixed skip-count step.
The $\bigstar$ is the 7th (last) box.

Unknowns

The skip-count step and the number at the $\bigstar$

Constraints

Every step in the chain adds the same fixed amount.

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #7 Identify Subproblems

Find the constant step from two known neighbors, confirm it with a second pair, then add that step repeatedly to reach the last box.

3 · Execute3 carry out the plan

1Find the step

#5 Look for a Pattern 4.OA.C.5

From 4,270,000 to 4,273,000 the number rises by 3,000, and from 4,273,000 to 4,276,000 it rises by 3,000 again. The step is +3,000.

4{,}273{,}000 - 4{,}270{,}000 = 3{,}000

Equal jumps between known boxes reveal the repeating rule.

2Continue the count

#7 Identify Subproblems 4.NBT.A.2

Keep adding 3,000: the next box after 4,276,000 is 4,279,000, then 4,282,000, and so on.

4{,}276{,}000 + 3{,}000 = 4{,}279{,}000

Each new box is just one more hop of the step.

3Reach the $\bigstar$

#5 Look for a Pattern 4.NBT.A.2

The

\bigstar

is the first box plus 6 steps: 4,270,000 + 6 x 3,000 = 4,288,000.

4{,}270{,}000 + 6 \times 3{,}000 = 4{,}288{,}000

6 equal hops of 3,000 from the start land on the

\bigstar

.

Answer: 4,288,000

4 · Reviewdoes it hold up?

From the first box to the last there are 6 steps of 3,000, totaling 18,000, and 4,270,000 + 18,000 = 4,288,000, matching the step-by-step result.

Another way: Evaluate finite differences (tool 14): the constant first difference 3,000 confirms a linear pattern, so the nth box is 4,270,000 + (n-1) x 3,000.

Standardsmin grade 4

4.OA.C.5 Generate a number or shape pattern following a given rule — Identifying the constant skip-count rule and extending it.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Adding the step across multi-digit numbers to reach the $\bigstar$.

💡Takeaway. This only needs Grade 4 pattern sense: find the equal jump, then keep hopping by it!

Skip-count by the changing place value · 10 practice problems

Generated variants — 10

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Where next?