Problem
Find the constant skip-count step
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.
Base-ten numbers
Your answer
Watch out Only the hundreds digit goes up by one, but each jump is a whole hundred, not one.
How to solve
Strategy Look for a Pattern — 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.
1STEP 1
Find the gap between two neighbors
Subtract two neighbors: 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.
4.NBT.A.2Look For A PatternOne skip-count step equals the difference between two neighboring labels, 3929 minus 3829.
Why?
Skip-counting builds the line by adding the same step to reach each next tick, so 3929 is 3829 with exactly one step added on.
Why?
Skip-counting by a fixed size is just adding that same amount over and over, so every hop from one tick to the next adds one identical step.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Because 3929 is 3829 plus one step, taking 3829 away from 3929 gives that step back.
Why?
Subtraction is the reverse of addition, so it undoes the added step and leaves the step by itself.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
2STEP 2
Confirm the step repeats
The other gaps match: 4029 minus 3929 and 4129 minus 4029 are both 100, so the step is 100.
4029 - 3929 = 100, 4129 - 4029 = 100
If each evenly spaced jump is the same 100, the pattern is just counting by hundreds.
2.NBT.A.2Draw A DiagramAnswer
100
3929 - 3829 = 100
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.
Takeaway
Subtract one tick from the next and you've found the skip size, here a clean jump of 100!
- Find the gap between two neighbors
- Confirm the step repeats
Where next?
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