Math · Stage 5

Count systematically: arrangements, selections and casework

The Olympiad way to count without missing or double-counting: multiply your choices, decide whether ORDER matters (arrangement vs selection), and when one rule can't do it all — split into cases and add.

✦ Math📘 Stage 5 · S5⏱ ~13 min🧒 Ages 9–10★ Free to start

I can count systematically: arrangements, selections and casework.

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Kavi Counts Without Counting 🦉

"Don't count on your fingers — count with your head," hoots Kavi 🦉. "If I pick a top 3 ways and then shorts 2 ways, that's 3 × 2 = 6 outfits — I never wrote a single one down. The secret is to ask: do I need an order, or just a group? And if it gets messy, I split it into tidy cases and add. That's how you count a hundred things in your head."

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What your child will learn

1The multiplication principle: choices multiplyThere are 3 lunch sets 🍱. With each set you may pick 1 of 2 drinks 🥤. Each set makes its own little group of two drink-choices. Tap each group and count.

2Arrangements: order matters, so multiply the shrinking choicesSeat three children — A, B, C — in a row 🪑. Fill one seat at a time and watch the choices shrink. Tap each card.

3Does ORDER matter? Arrangement or Selection

4Casework: split into cases, count each, then addSometimes one rule can't count it all at once. Count 2-digit numbers built from 1, 2, 3 (repeats allowed) by splitting on the FIRST digit. Tap each card.

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A peek inside

How many ways can 3 children — Ana, Budi and Citra — line up in a row for a photo? 📸

order matters (an arrangement): 1st seat 3 ways × 2nd 2 ways × 3rd 1 way = 3 × 2 × 1

Try this at home: Multiply the choices: 3 shirts and 4 shorts → how many different outfits?

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

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Part of Math · Stage 5 · S5 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.