Math · Stage 3
Magic squares and number arrays
Every line of a magic square adds to the same total — so one known line-total unlocks any missing entry.
✦ Math📘 Stage 3 · S3⏱ ~11 min🧒 Ages 7–8★ Free to start
I can complete a magic square and number array.
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Kavi's Magic Grid 🔳
Kavi finds a 3×3 grid glowing on the floor ✨. "Every row, every column, even the slanting lines all add to the same number — that's the magic total!" hoots Kavi. "If a line reads 2, ▢, 6 and the magic total is 15, I don't guess — I know 2 + 6 = 8, so the missing cell is 15 − 8 = 7!"
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What your child will learn
1One line, one fixed totalIn a magic square every line adds to the same magic total. Here the total is 15. If you can already see part of a line — say two cells adding to 8 — the number bond shows the rest: 15 is the whole, 8 is the part you see.
2The centre is the total shared three waysA classic magic square uses 1 to 9, and 1 + 2 + … + 9 = 45. Spread fairly over 3 lines, each line is 45 ÷ 3 = 15. Tap Hop +5 → and watch the landings: 5, 10, 15 — three equal fives.
3Know the bonds of 15, crack it fastEvery missing cell is a bond of 15 in disguise. If two cells add to 14, the last is 1; if they add to 6, the last is 9. The faster you know the bonds of the magic total, the faster the whole square falls into place.
4Number arrays grow by a fixed stepA number array is a line of numbers that climb by the same step each time. Here the step is 3: 3, 6, 9, 12, 15. Spot the step, and you can fill any gap or say the next term.
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A peek inside
The magic total is 15. A row reads 2, ▢, 6. What is the missing number?
see 2 and 6 → 2 + 6 = 8 · 15 − 8 = 7 · check: 2 + 7 + 6 = 15 ✓
Try this at home: Magic total is 15. A row shows 4, 3, __ . The missing number is __
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 3 · S3 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.