Order of Operations & Number Sentences

A typical OC opening question: 83 − ▲ = 29 + 26. It's your Year 3 balance idea, now standard OC fare. Kill the side you can compute (29 + 26 = 55), then the puzzle shrinks to 83 − ▲ = 55 — the gap between 67 and 49 is 18. Check by rebuilding: 83 − 28 = 55 ✓. Notice the wrong options are built from numbers you can SEE (17, 32, 49, and 67+49=116) — the test bets you'll grab a visible number instead of thinking.

When operations mix, order matters: brackets first, then multiply and divide, then add and subtract. So 20 − 3 × 4 is 20 − 12 = 8, never 17 × 4. Equal-rank operations run left to right: 20 ÷ 4 × 5 = 25. OC rarely asks this rule nakedly — it hides inside 'I buy 5 buildings at 106 points each and one farm…' stories where you must build the right expression yourself.

An OC-style structure question: a tree where each circle equals its two children added. 96 splits into 37 and P; 37 splits into 25 and Q; P splits into 52 and R. Find Q × R. Attack the tree wherever TWO of three numbers are known: Q = 37 − 25 = 12. P = 96 − 37 = 59. R = 59 − 52 = 7. Answer: 12 × 7 = 84. The skill is choosing your entry point — start where the puzzle is already solvable, and each answer unlocks the next.

Magic-shape puzzles look like trial and error — but there's a beautiful shortcut. OC style: place 1–5 in a cross so both lines add to 9; what's the middle number? The trick: all five numbers total 1+2+3+4+5 = 15, but the two lines total 9 + 9 = 18. Why the difference? The MIDDLE number is counted in both lines — twice! So it contributes the extra: 18 − 15 = 3. The middle is 3. Count-twice reasoning beats an hour of guessing.

The final OC skill here: turning a story into your own number sentence. OC style: 800 points, buy 4 buildings at 115 each and a farm, 90 left — farm cost? Write it: 800 − 4×115 − farm = 90. Solve in order: buildings cost 460, leaving 340; the farm took 340 − 90 = 250. Check the story balances: 800 − 460 − 250 = 90 ✓. Story → sentence → order of operations → check. Quiz and exercises await — five options each, like the real test!