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Worksheets›Grade 4›Factors, primes & patterns›Number patterns from a rule

Number Patterns from a Rule Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

Grade 4CCSS 4.OA.C.5Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Adding a one-digit number

  1. 1.Start at 7. Add 2 each time.
  2. 2.Start at 6. Add 8 each time.
  3. 3.Start at 1. Add 3 each time.
  4. 4.Start at 19. Add 5 each time.
  5. 5.Start at 0. Add 4 each time.
  6. 6.Start at 3. Add 9 each time.
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

A pattern rule says where to start and what to do each time. Write the start number first, then apply the rule to it to get the second number, apply it again to get the third, and so on. Always apply the rule to the number just before, not to the start.

EasyStart at 11. Add 4 each time.Adding a one-digit numberMediumStart at 91. Add 25 each time.Adding or subtracting larger numbersHardStart at 28. Add 45 each time.Multiplying, and adding two-digit numbers

How to solve it: a worked example

Use the rule to write the first five numbers of the pattern.

  1. StartStart at 0. Add 7 each time.
  2. Add 7 to each number to get the next0 + 7 = 77 + 7 = 1414 + 7 = 2121 + 7 = 28
  3. Answer0, 7, 14, 21, 28

Common mistakes to watch for

  • Applying the rule to the start number every time, as in 3, 7, 7, 7.
  • Counting the start as the result of the first step, so the pattern is one number short.
  • When multiplying, adding the factor instead, as in 2, 5, 8 for ‘multiply by 3’.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

Related worksheets

Factor pairsPrime and composite numbersMulti-digit multiplicationLong division with remaindersAdding & subtracting like fractions

FAQ

What should students notice besides the next number?

Features the rule doesn't state outright, such as "add 6 starting from 3 always gives odd numbers" or "multiply by 3 makes the numbers grow faster and faster".

Is the starting number part of the first five numbers?

Yes. The pattern starts with the given number, then applies the rule four times. Applying it five times is a common slip.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix number patterns from a rule with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.