Place value and number senseGrades 2–5
Number patterns worksheets with rules
Each row shows a number sequence with gaps and a Rule box. Students find the rule and fill the blanks. Choose adding or subtracting, multiplying, skip counting or a mix, and set one to four blanks per row.
- Fresh problems every time
- Answer key on its own page
- Print or PDF, Letter or A4
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On this page
Rule-finding, not just counting on
A number pattern is a list that follows a rule. Spotting the rule is the real skill: once a student can say "this goes up by 8 each time," they can extend the pattern in either direction and predict terms far down the line. That habit is the foundation of algebra, where a sequence becomes a function.
This page is about the thinking side. Every row prints seven numbers (six for multiplying patterns), hides some of them, and ends with a Rule box. The student has to work out the rule and write it, not just fill the gaps. The first number in each row is always shown, so there is a place to start.
Setting up the sheet
- Pattern type. Add or subtract a number produces steps of 2 to 15 that go up, and about one row in three goes down. Multiply (growing) uses doubling, tripling or multiplying by 10 and starts from a small number. Skip counting uses the counting-by steps, and Mixed blends them with extra weight on adding and subtracting.
- Skip count by. Shown for the skip counting and Mixed types only. Leave it on Mixed for variety.
- Missing numbers in each row. Anywhere from 1 to 4. One blank is almost a gift, because the neighbors reveal the step. Four blanks in a seven-term row force the student to find the rule from just three numbers.
- Number of problems. From 6 to 20 rows.
A good path is one blank with add-or-subtract patterns, then two blanks, then bring in multiplying. Mixed sheets with three or four blanks are a challenge for students who are comfortable.
Worked example: a row with two gaps
Suppose a row reads: 4, 12, 20, __, 36, __, 52.
- Compare the neighbors that are both shown: 12 and 20 differ by 8, and 4 to 12 also differs by 8.
- Check one more pair that is far apart. From 20 to 36 there is one hidden term between, so the gap is 16, which is two steps of 8. The rule is +8.
- Fill the first gap: 20 + 8 = 28.
- Fill the second gap: 36 + 8 = 44.
- Verify the end: 44 + 8 = 52, which matches the last number.
The completed row is 4, 12, 20, 28, 36, 44, 52 with the rule +8.
A shrinking row follows the same logic. For 61, 54, __, 40, 33, __, 19, the numbers drop by 7, so the rule is −7. The gaps are 47 and 26, and 26 − 7 = 19 confirms it.
For a growing row such as 3, 6, 12, __, 48, 96, the numbers do not differ by a constant amount, since 6 − 3 = 3 but 12 − 6 = 6. Dividing instead shows 6 ÷ 3 = 2 and 12 ÷ 6 = 2, so the rule is ×2, and the gap is 24.
Answer key pitfalls
- Right numbers, empty rule. A student fills in the blanks but leaves the Rule box blank. Ask for it every time. Writing "+8" or "×2" is the real objective.
- Wrong sign on the rule. In a shrinking row, writing +7 shows the student noticed the size but not the direction. The key prints a minus sign.
- Using only one pair. In 4, 12, __, 28 the step could be mistaken from a single gap. Comparing two separate pairs catches the error.
- Treating multiply like add. If the differences grow, switch to dividing consecutive terms.
Extending the idea
Rows with a growing step make a good conversation about why some patterns speed up. For younger students who just need to count by a given number, the separate skip counting worksheets are simpler and shorter on rule-writing. Pattern work also gives a gentle lead into algebra: try the one-step equations worksheet once students describe rules fluently. The multiplication chart is useful for checking multiply rules.