Describing Rules & Patterns · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Turning a Pattern into a Rule

Learning to Learn · Learning to Learn · ages 8-9
Name ______________________   Date ____________

  1. Look at the pattern: 2, 4, 6, 8. Which sentence describes it as a RULE?

    2468?
    • Add 2 to get the next number
    • The numbers go up
    • 8 is the biggest number here

  2. Seeing a pattern work one time is the same as proving the rule always works.

    Circle one:   True   False

  3. Ravi notices that every word he sees ending in the letter s means more than one thing. Which sentence is his RULE, in his own words?

    • Some words end in s
    • If a word ends in s, it usually means more than one
    • I found this pattern by accident

  4. Sofia writes the numbers 4, 7, 10, 13. She wants to say the rule in her own words. Which sentence tells the rule?

    • Add 3 each time
    • Add 2 each time
    • Double the number each time
    • The numbers go up and down

  5. Four number patterns keep going forever. Which one will NOT have the number 100 in it?

    • 10, 20, 30, 40, ...
    • 25, 50, 75, 100, ...
    • 3, 6, 9, 12, ...
    • 20, 40, 60, 80, ...

  6. Which of these actually proves a rule works, instead of just noticing it?

    • Trying the rule on several new examples
    • Seeing it work one time and stopping there
    • Guessing the rule sounds about right

  7. Maya tried her rule 'add 3' on three numbers and it worked every time. She says that proves the rule always works. Is she right?

    Circle one:   True   False

  8. Nia uses the digits 2, 5, and 8, one time each, to build a growing pattern. When the digits go in order from smallest to biggest, how much does the pattern grow each step?

    Answer: ______________

  9. Jayden rule: the next number is always 3 more. The pattern is 2, 5, 8, 11, 14. He checks the next number in the real list and it is 18, not 17. What should Jayden do?

    • Keep his rule since it worked for the first few numbers
    • Recheck the rule, since it did not hold for a new example
    • Ignore the number 18 and assume the list made a mistake

  10. Look at this pattern: 0, 2, 6, 12, 20, ... The jumps keep changing, but the jumps follow their own rule. What is the next number?

    Answer: ______________

LightMySky · lightmysky.comW1-mt_hbe_kdE_7C-s1

Answer key

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

Turning a Pattern into a Rule W1-mt_hbe_kdE_7C-s1

  1. Add 2 to get the next number · A rule names exactly what happens each time. Here, add 2 every time.
  2. False · One example only shows it worked once. Testing more examples shows whether the rule always holds.
  3. If a word ends in s, it usually means more than one · A rule states what is true every time, not just what you happened to notice.
  4. Add 3 each time · Every new number is 3 more than the one before it, so the rule is add 3 each time.
  5. 3, 6, 9, 12, ... · The pattern that counts by 3s jumps from 99 to 102, so it skips right past 100.
  6. Trying the rule on several new examples · Proving a rule means checking it against cases you have not seen before, not just the first one.
  7. False · A few tries is noticing a pattern. Proving it always works takes more than examples.
  8. 3 · Ordered as 2, 5, 8, each step grows by 3, so that is the rule for the pattern.
  9. Recheck the rule, since it did not hold for a new example · A rule that fails on a new example is not proven yet. Go back and look for a rule that fits all the numbers, instead of ignoring the one that does not fit.
  10. 30 · The jumps are 2, 4, 6, 8, and they grow by 2 each time, so the next jump is 10 and 20 plus 10 is 30.
Worksheet · LightMySky