Skip-count by the changing place value

4.NBT.A.24.OA.C.5 · adapt · grade 4

Archetype: Place-Value Regrouping · step in a 7-type progression

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 $\bigstar$ .

Show solution

Understand

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

Givens

The first three boxes are 4,270,000, 4,273,000, and 4,276,000.
The boxes increase by a fixed skip-count step.
The star is the sixth (last) box, two boxes after the second blank.

Unknowns

The skip-count step and the number at the star

Constraints

Every step in the chain adds the same fixed amount.

Plan

#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 sixth box.

Execute

#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 (the thousands place changes).

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

Equal jumps between known boxes reveal the repeating rule.

#7 Identify Subproblems 4.NBT.A.2

Continue adding 3,000: the 4th box is 4,276,000 + 3,000 = 4,279,000 and the 5th box is 4,279,000 + 3,000 = 4,282,000.

4{,}276{,}000 + 3{,}000 = 4{,}279{,}000,\quad 4{,}279{,}000 + 3{,}000 = 4{,}282{,}000

Each new box is just one more hop of 3,000.

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

The 6th box is 4,282,000 + 3,000 = 4,285,000. (Equivalently, the star is the first box plus five steps: 4,270,000 + 5 × 3,000 = 4,285,000.)

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

Five equal hops of 3,000 from the start land on the star.

Answer: 4,285,000

Review

From the first box to the sixth 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.

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)×3,000; at n = 6 this is 4,285,000.

Standards · min grade 4

4.OA.C.5 Generate a number or shape pattern following a given rule — Identifying the constant +3,000 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 star.

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