Non-routine problem solving (Grade 3)
What the Grade 3 paper rewards
Grade 3 non-routine problems rarely need a formula. They test whether you can find a rule, keep track of information, and check your answer against the story. Typical tasks involve repeating patterns, balance puzzles, simple counting with two categories, and "work backwards" number machines.
Core moves
- Find the rule, then test it twice. A pattern is only a guess until it predicts two terms you already know.
- Work backwards. If a machine doubles a number and adds 3 to get 17, undo the last step first: 17 − 3 = 14, then 14 ÷ 2 = 7.
- Use parity as a quick check. Even + even = even; odd + odd = even. If your answer has the wrong parity, recompute.
- Draw a table for "how many ways" questions so you do not count the same case twice.
Worked example
The sequence is 3, 7, 15, 31, ___. Differences: 4, 8, 16 - each difference doubles. That suggests the rule "double and add 1": 3×2+1=7, 7×2+1=15, 15×2+1=31. Applying it once more gives 31×2+1=63. Check: the next difference would be 32, and 31+32=63, so the two descriptions agree. Answer: 63.
Traps
- Continuing only the first difference (4, 8, 12) instead of checking whether the differences themselves follow a rule.
- Answering a number that fits the first three terms but fails the fourth.
- Mixing up "how many more" with "how many in all".
- Ignoring units in a story: 7 marbles, not 7 boxes.