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🧩 5th grade math · Patterns & Algebra

Two patterns on a graph

Make two lists from two rules, then pair the matching terms. Look for how each pair is related.

Worked example

Rule A: start at 0 and add 4. Rule B: start at 0 and add 16. Which list shows the first four pairs (a number from A, then the matching number from B)?
Answer: (0, 0), (4, 16), (8, 32), (12, 48)
A is 0, 4, 8, 12 and B is 0, 16, 32, 48. Pair them in order: (0, 0), (4, 16), (8, 32), (12, 48).

For grown-ups: Two numerical patterns; ordered pairs on a graph. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 5.OA.B.3
What this practises, for teachers

Practices two numerical patterns; ordered pairs on a graph (5.OA.B.3). A printable sheet with its answer key, worked answers on the page, no accounts.

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For your class

🖨️ Printable sheet and key

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More printables, with answer keys, for this grade:

Try three

  1. Rule A: start at 0 and add 5. Rule B: start at 0 and add 10. Which list shows the first four pairs (a number from A, then the matching number from B)?
    Show the answer and how
    Answer: (0, 0), (5, 10), (10, 20), (15, 30)
    A is 0, 5, 10, 15 and B is 0, 10, 20, 30. Pair them in order: (0, 0), (5, 10), (10, 20), (15, 30).
  2. Rule A: start at 0 and add 5. Rule B: start at 5 and add 5. Each number in B is how much more than the matching number in A?
    Show the answer and how
    Answer: 5
    Pair up the terms: 0 and 5; 5 and 10; 10 and 15; 15 and 20. B is always 5 more: 5. Answer: 5.
  3. Rule A: start at 0 and add 5. Rule B: start at 0 and add 15. Which list shows the first four pairs (a number from A, then the matching number from B)?
    Show the answer and how
    Answer: (0, 0), (5, 15), (10, 30), (15, 45)
    A is 0, 5, 10, 15 and B is 0, 15, 30, 45. Pair them in order: (0, 0), (5, 15), (10, 30), (15, 45).

Before and after

Learn first: Order of operations (5th)

Name: ____________________Date: ____________Score: ____ / 12

Two patterns on a graph (5th grade)

  1. Rule A: start at 0 and add 2. Rule B: start at 0 and add 8. Which list shows the first four pairs (a number from A, then the matching number from B)?
  2. Rule A: start at 0 and add 2. Rule B: start at 0 and add 4. Which list shows the first four pairs (a number from A, then the matching number from B)?
  3. Rule A: start at 0 and add 2. Rule B: start at 0 and add 6. Which list shows the first four pairs (a number from A, then the matching number from B)?
  4. Rule A: start at 0 and add 6. Rule B: start at 0 and add 18. Which list shows the first four pairs (a number from A, then the matching number from B)?
  5. Rule A: start at 0 and add 6. Rule B: start at 0 and add 18. Which list shows the first four pairs (a number from A, then the matching number from B)?
  6. Rule A: start at 0 and add 2. Rule B: start at 0 and add 6. Which list shows the first four pairs (a number from A, then the matching number from B)?
  7. Rule A: start at 0 and add 3. Rule B: start at 8 and add 3. Each number in B is how much more than the matching number in A?
  8. Rule A: start at 0 and add 6. Rule B: start at 0 and add 18. Each number in B is how many times the matching number in A? (Look at the pairs: 6 and 18; 12 and 36; 18 and 54.)
  9. Rule A: start at 0 and add 2. Rule B: start at 5 and add 2. Each number in B is how much more than the matching number in A?
  10. Rule A: start at 0 and add 2. Rule B: start at 2 and add 2. Each number in B is how much more than the matching number in A?
  11. Rule A: start at 0 and add 2. Rule B: start at 0 and add 6. Which list shows the first four pairs (a number from A, then the matching number from B)?
  12. Rule A: start at 0 and add 3. Rule B: start at 5 and add 3. Each number in B is how much more than the matching number in A?

Answer key

  1. (0, 0), (2, 8), (4, 16), (6, 24)
  2. (0, 0), (2, 4), (4, 8), (6, 12)
  3. (0, 0), (2, 6), (4, 12), (6, 18)
  4. (0, 0), (6, 18), (12, 36), (18, 54)
  5. (0, 0), (6, 18), (12, 36), (18, 54)
  6. (0, 0), (2, 6), (4, 12), (6, 18)
  7. 8
  8. 3
  9. 5
  10. 2
  11. (0, 0), (2, 6), (4, 12), (6, 18)
  12. 5

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