Number Pattern Relationships · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Two Patterns, One Relationship

Mathematics · Algebra · ages 10-11
Name ______________________   Date ____________

  1. Each term in B (add 6 from 0) is what compared with the matching term in A (add 3 from 0)?

    • Three more
    • Twice as big
    • Half as big
    • Six more

  2. Sequence A is 0, 3, 6, 9 and sequence B is 0, 6, 12, 18. What is the 5th term of B?

    Answer: ______________

  3. Pattern A starts at 0 and uses the rule 'add 3'. What are the first four terms?

    036?
    • 0, 3, 6, 9
    • 0, 3, 5, 9
    • 3, 6, 9, 12

  4. When you form an ordered pair from matching terms, the first number always comes from Pattern A.

    Circle one:   True   False

  5. You plot points from Pattern A (x) and Pattern B (y), both starting at 0 with rules 'add 3' and 'add 6'. Where does the point for the 2nd terms (A=3, B=6) go?

    • 3 right, 6 up from the corner
    • 6 right, 3 up from the corner
    • 3 right, 3 up from the corner

  6. Sam says B's rule add 6 is double A's rule add 3, so each B term is double the matching A term. Is Sam right?

    Circle one:   True   False

  7. A continues 0, 3, 6, 9, 12. What is the 6th term of A?

    Answer: ______________

  8. Pattern A starts at 0 with rule 'add 5'. Pattern B starts at 0 with rule 'add 10'. What is the Pattern B term that matches the Pattern A term 20?

    05101520

    Answer: ______________

  9. Ben builds Pattern A with 'add 4' and Pattern B with 'add 8', both from 0. He says the terms will always be in a 1:2 ratio, like 'add 3' and 'add 6'. Is he right?

    • No, because 4 and 8 are not related
    • Yes, because 8 is double 4
    • Yes, but only for the first two terms

  10. Pairs (3, 6), (6, 12), (9, 18), (12, 24) continue. When the first number is 30, what is the second?

    Answer: ______________

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Answer key

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

Two Patterns, One Relationship W1-mt_fxPtngwUfz-s1

  1. Twice as big · 6 is twice 3, so every B term doubles its A partner: 6 vs 3, 12 vs 6, 18 vs 9.
  2. 24 · B adds 6 each time, so its 5th term is 18 + 6 = 24.
  3. 0, 3, 6, 9 · Start at 0 and add 3 each time: 0, 3, 6, 9.
  4. True · The x-value (first number) comes from Pattern A and the y-value comes from Pattern B.
  5. 3 right, 6 up from the corner · The x-coordinate comes from Pattern A (3) and the y-coordinate comes from Pattern B (6).
  6. True · Sam is right: doubling the rule doubles every term from the shared start 0.
  7. 15 · 12 + 3 = 15.
  8. 40 · Pattern B doubles Pattern A. Since the A term is 20, the matching B term is 40.
  9. Yes, because 8 is double 4 · Whenever the second rule doubles the first rule, matching terms stay in a steady 1:2 ratio.
  10. 60 · The second doubles the first: 2 x 30 = 60.
Worksheet · LightMySky