Math PicnicFree printable practice

Decreasing number patterns worksheets

A shrinking sequence hides a rule just as a growing one does — it takes a fixed amount away each time. These free printable worksheets show a sequence that counts down with one number missing, and ask a child to find the step and fill the gap.

Customize Practice Save as PDF New questions

Kid stuck on one? You don’t just get the sheet.

See it worked step by step →Answer it on screen →
Decreasing number patterns
Decreasing number patterns worksheet — Shrink by a fixed step, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Every sequence subtracts the same amount from one term to the next: 30, 25, 20, 15 steps down by five each time. The child compares neighboring terms to find the step, then applies it to the blank. Naming the constant difference is the reasoning that later becomes a linear rule, met here while the numbers are small enough to check by counting.

Why this sheet works

The blank sits inside the sequence, not at the end, so a child cannot simply keep counting down; they have to work in both directions to be sure the missing term fits its neighbors on each side. Numbers stay friendly and the subtraction stays within reach, so the work is spotting the step rather than the arithmetic.

How this one works

One question from this sheet, worked through a step at a time.

29, ?, 17, 11, 5

29?17115
29?17115
29?17115
29?17115
292317115
  1. Find the rule first, from two numbers you can actually see — never from the gap.
  2. 17 to 11 is − 6. One pair is a guess, though — check it against another.
  3. 11 − 6 = 5, so the rule holds. Two pairs agreeing is what turns a guess into the rule.
  4. Now apply it to the gap: 29 − 6 = 23.
  5. Check it against the number already after the gap: 23 − 6 = 17, which is what is there. The missing number is 23.

Pick another skill