Generating a pattern from a rule · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Building a pattern from a rule

Mathematics · Multiplication & Division · ages 9-10
Name ______________________   Date ____________

  1. Start at 1 and add 3 each time. What are the first four terms?

    • 1, 4, 7, 10
    • 1, 3, 6, 9
    • 3, 6, 9, 12
    • 1, 4, 8, 12

  2. A pattern rule says 'start at 1, add 3.' What is the number right after 1?

    1?71013
    • 3
    • 4
    • 5

  3. The pattern 'start at 1, add 3' gives 1, 4, 7, 10, 13. True or false: these numbers alternate between odd and even.

    1471013

    Circle one:   True   False

  4. A shape pattern goes circle, square, circle, square, circle. What comes next?

    circlesquarecirclesquarecircle?
    • circle
    • square
    • triangle

  5. Start at 1 and add 3 each time. What is the 5th number in the pattern?

    14710?

    Answer: ______________

  6. Ella says starting at 2 and adding 4 always gives even numbers. Is Ella right?

    Circle one:   True   False

  7. A shape pattern uses 3, 5, 7 sticks for its first three shapes. How many sticks does the 6th shape use?

    Answer: ______________

  8. A pattern goes circle, circle, square, circle, circle, square, circle, circle, and then a missing shape. What is missing?

    circlecirclesquarecirclecirclesquarecirclecircle?
    • circle
    • square
    • triangle

  9. Priya says: 'If I start at 3 and add 4 each time, I'll only get even numbers, just like starting at 2 and adding 4.' Is she right?

    • Yes, because 4 is even
    • Yes, because the step is even
    • No, because the start number is odd

  10. Noah says the rule add 5 starting at 3 gives 3, 8, 12, 17. Is Noah right?

    Circle one:   True   False

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Building a pattern from a rule W1-mt_A-FyLLLLzy-s1

  1. 1, 4, 7, 10 · Adding 3 each time from 1 gives 1, 4, 7, 10.
  2. 4 · Start at 1, then add 3: 1 + 3 = 4.
  3. True · 1 is odd, 4 is even, 7 is odd, 10 is even, 13 is odd. It flips every time.
  4. square · The rule is circle, then square, repeat. After circle comes square.
  5. 13 · Keep adding 3: 1, 4, 7, 10, 13. The fifth number is 13.
  6. True · Ella is right: even plus even is always even, so every term stays even.
  7. 13 · The rule is add 2, so the 6th shape uses 3 + 5 x 2 = 13 sticks.
  8. square · The rule repeats every three shapes: circle, circle, square. The ninth shape completes that group with square.
  9. No, because the start number is odd · Adding an even number never changes whether a number is odd or even. Since 3 is odd, every number in Priya's pattern stays odd.
  10. False · Noah is wrong: 3 + 5 + 5 = 13, not 12, so the terms are 3, 8, 13, 18.
Worksheet · LightMySky