Math · Stage 5
Inclusion-exclusion counting
Two groups that overlap are easy to over-count. Add them, then take the overlap back — and the leftovers are the ones in neither group.
✦ Math📘 Stage 5 · S5⏱ ~12 min🧒 Ages 9–10★ Free to start
I can count with the inclusion-exclusion rule.
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Kavi Counts Twice 🙌
At Kavi's party 🎉 Kavi called, “Hands up if you like cake 🍰!” — 12 hands. “Hands up for ice cream 🍨!” — 9 hands. “That's 21 treat-lovers!” But 4 friends had raised both hands — Kavi counted them twice. “So I take the 4 back: 12 + 9 − 4 = 17 like at least one. That little take-back is the inclusion-exclusion trick!”
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What your child will learn
1Two groups make THREE regionsWhen two groups overlap there are really three kinds of friend: cake only, ice cream only, and the ones who like both. Drop each friend in the right box →
2Add them, and 'both' is counted twiceHere are the party counts. If you just add the two groups you get 12 + 9 = 21 — but the 4 'both' friends are hiding inside the cake bar and the ice-cream bar.
3The inclusion-exclusion ruleTap each card. One way double-counts the overlap; the other fixes it. The rule works for any two overlapping groups.
4And the ones in neither groupSay the whole class has 25 children and 17 like at least one treat. Everyone else likes neither — they are the leftovers from the total.
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A peek inside
In a class of 28, 16 play football ⚽ and 13 play chess ♟️. 7 play both. How many play at least one?
add the two groups, then subtract the overlap once: 16 + 13 − 7
Try this at home: At least one: 15 like tea 🍵, 11 like coffee ☕, 6 like both → __
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 5 · S5 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.