Generalising from repeated reasoning · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Finding the Rule Behind the Facts

Mathematics · Mathematical Thinking · ages 8-9
Name ______________________   Date ____________

  1. Mo knows 8×5=40 and 8×2=16. What is 8×7?

    • 42
    • 46
    • 56

  2. If 3×4=12, what is 3×40?

    3×4=123×40=?
    • 120
    • 1200
    • 42

  3. In the fraction 4/8, the numerator (4) is half of the denominator (8), so 4/8 equals 1/2.

    Circle one:   True   False

  4. Zara knows 7×5=35 and 7×3=21. Use these to find 7×8.

    Answer: ______________

  5. If 6×3=18, what is 6×300?

    6×3=186×300=?
    • 180
    • 1800
    • 306

  6. Which fraction is NOT equal to 1/2?

    • 3/6
    • 4/9
    • 5/10

  7. Priya says 9×7 = 9×5 + 9×2 = 45 + 16 = 61. What went wrong?

    • She multiplied 9×2 correctly but added wrong
    • She should have used 9×2=18, giving 45+18=63
    • 61 is correct, there is no mistake

  8. Since 4×5=20 and 5000 is 1000 times bigger than 5, what is 4×5000?

    4×5=204×5000=?
    • 200
    • 2000
    • 20000
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Answer key

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

Finding the Rule Behind the Facts W1-mt_aivrWs6jrS-s1

  1. 56 · 40 + 16 = 56. Both parts must be multiplied by 8 before adding.
  2. 120 · One extra zero in (4 becomes 40) means one extra zero out: 12 becomes 120.
  3. True · 4 is half of 8, so the rule holds and 4/8 is the same amount as 1/2.
  4. 56 · 5 and 3 add up to 8, so 35+21=56 gives 7×8.
  5. 1800 · 300 is 100 times bigger than 3, so the answer is also 100 times bigger: 18×100=1800.
  6. 4/9 · Half of 9 is 4.5, not 4, so 4/9 breaks the rule and is not equal to 1/2.
  7. She should have used 9×2=18, giving 45+18=63 · 9×2 is 18, not 16. Fixing that: 45+18=63, the true value of 9×7.
  8. 20000 · If one number gets 1000 times bigger, the answer does too: 20 becomes 20,000.
Worksheet · LightMySky