Find the constant skip-count step

4.NBT.A.2 · take · grade 4

Archetype: Generalize a Growing Pattern into a Rule · step in a 12-type progression

The numbers below were made by skip-counting by $\bullet$ , shown on a number line. Find the value of $\bullet$ .

A number line has four evenly spaced tick marks. Reading from left to right, they are labeled $3829$ , $3929$ , $4029$ , $4129$ . The gap between each pair of neighboring numbers is the same, and the numbers were made by skip-counting by that amount.

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Understand

On a number line, four evenly spaced ticks read 3829, 3929, 4029, 4129 from left to right. The numbers were made by skip-counting by the same step each time. Find that step.

Givens

The labeled numbers, left to right, are 3829, 3929, 4029, 4129.
The ticks are evenly spaced, so the gap between neighbors is constant.
The numbers were made by skip-counting by that constant gap.

Unknowns

The size of each skip-count step (the value of the dot).

Constraints

Every neighboring pair differs by the same amount.

Plan

#5 Look for a Pattern · also uses: #1 Draw a Diagram

Equally spaced numbers on a number line are a repeated-structure pattern, so I find the constant difference between two neighboring labels and confirm it repeats.

Execute

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

Subtract a number from the one just after it: 3929 minus 3829 is 100. So one skip is 100.

3929 - 3829 = 100

The change from one tick to the next is exactly one skip, found by subtracting.

#1 Draw a Diagram 2.NBT.A.2

Check the other gaps: 4029 minus 3929 is 100, and 4129 minus 4029 is 100. Every gap is 100, so the skip-count step is 100.

4029 - 3929 = 100,\quad 4129 - 4029 = 100

If each evenly spaced jump is the same 100, the pattern is just counting by hundreds.

Answer: 100

Review

Counting on by 100 from 3829 gives 3929, 4029, 4129, exactly the labels shown, so a step of 100 is correct. Only the hundreds digit changes each time, which matches a jump of 100.

Compare the first and last numbers: 4129 minus 3829 is 300, spread over 3 equal jumps, so each jump is 300 divided by 3, which is 100.

Standards · min grade 4

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Subtracting neighboring four-digit labels to find the constant gap.
2.NBT.A.2 Count within 1000, skip-count by 5s, 10s, and 100s — Recognizing the evenly spaced labels as skip-counting by 100.

💡 Subtract one tick from the next and you've found the skip size, here a clean jump of 100!