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Patterns in Mathematics

Spotting a rule is not the same as proving it

Three numbers: 5, 8, 11. Add 3 each time and the next number is 14. But is that the only rule that fits?

Both rules give 5, 8, 11 so far.
Step 1 of 4
  1. Both rules give 5, 8, 11 so far.
  2. Rule A adds 3 each time. Next is 14.
  3. Rule B's step is 3, then 3, then 5. Next is 16.
  4. Same three numbers. Two different next numbers.

You cannot know from three numbers alone. Both rules matched the first three numbers perfectly.

Checking further can help. A fourth number, or a reason the rule should hold. Both help you trust a guess.

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This track

  1. 0 Start here
  2. 1 A pattern is a rule
  3. 2 Sequences that add the same amount
  4. 3 Some counts make neat shapes
  5. 4 Odd and even numbers
  6. 5 A growing shape follows a rule too
  7. 6 Spotting a rule is not the same as proving it
  8. 7 The big picture
  9. 8 Track quiz

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