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Free quantitative reasoning worksheet, grade 8 (ages 13–14, UK Year 9)

10 puzzles on page one, the answers and the rules on page two. Ask your child to say the rule before you check it — that’s the part that sticks.

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Quantitative reasoning worksheet, grade 8 (ages 13–14, UK Year 9)

Name: ____________________

  1. 1.

    If 90 + 176 = 266, then 90 + 173 = ____

    • A261
    • B262
    • C263
    • D265
    • E266

  2. 2.

    53 60 74 95 123 ____

    • A123
    • B130
    • C137
    • D151
    • E158

  3. 3.

    10 × 3 − 11 = ____

    • A19
    • B20
    • C21
    • D30
    • E41

  4. 4.

    47 becomes 197, 72 becomes 297, so 30 becomes ____

    • A120
    • B129
    • C156
    • D197
    • E297

  5. 5.

    3 6 9 15 24 ____

    • A33
    • B38
    • C39
    • D40
    • E48

  6. 6.

    If 180 + 63 = 243, then 182 + 63 = ____

    • A241
    • B243
    • C244
    • D245
    • E246

  7. 7.

    197 becomes 399, 116 becomes 237, so 84 becomes ____

    • A168
    • B173
    • C178
    • D237
    • E399

  8. 8.

    494 becomes 247, 449 becomes 224, so 267 becomes ____

    • A133
    • B134
    • C224
    • D247
    • E534

  9. 9.

    32 38 51 71 98 ____

    • A104
    • B111
    • C125
    • D132
    • E139

  10. 10.

    90 becomes 445, 48 becomes 235, so 22 becomes ____

    • A105
    • B106
    • C110
    • D235
    • E445

Answers, and the rule behind each one

  1. 1. C — 263. Rule: use the pattern, not just the numbers. 173 is 3 less than 176, so the answer is 3 less than 266 — that's 263. You don't have to work it out from scratch.
  2. 2. E — 158. Rule: the gap grows each time. The gap between numbers starts at 7 and grows by 7 every step.
  3. 3. A — 19. Rule: two steps, in order. 10 × 3 is 30. Then 30 − 11 is 19.
  4. 4. B — 129. Rule: multiply by 4, then add 9. 47 times 4 is 188, plus 9 makes 197. 30 times 4 is 120, plus 9 makes 129.
  5. 5. C — 39. Rule: add the two numbers before it. Each number is the two before it added together.
  6. 6. D — 245. Rule: use the pattern, not just the numbers. 182 is 2 more than 180, so the answer is 245 rather than 243.
  7. 7. B — 173. Rule: multiply by 2, then add 5. 197 times 2 is 394, plus 5 makes 399. 84 times 2 is 168, plus 5 makes 173.
  8. 8. A — 133. Rule: halve it, and drop any leftover. Half of 494 is 247, dropping the leftover. Half of 267 is 133 the same way.
  9. 9. D — 132. Rule: the gap grows each time. The gap between numbers starts at 6 and grows by 7 every step.
  10. 10. A — 105. Rule: multiply by 5, then take away 5. 90 times 5 is 450, take away 5 makes 445. 22 times 5 is 110, take away 5 makes 105.