Math · Stage 3
List arrangements and combinations systematically by casework
Split the problem into neat cases, count each case, then add — so you catch every arrangement and never double up.
✦ Math📘 Stage 3 · S3⏱ ~10 min🧒 Ages 7–8★ Free to start
I can list arrangements and combinations systematically by casework.
📖
Kavi's Number Cards 🔢
Kavi has three cards — 1, 2, 3 — and wants every 2-digit number, each card used once. "If I guess, I'll miss one or write it twice!" hoots Kavi. So Kavi works in cases: first card 1 → 12, 13 · first card 2 → 21, 23 · first card 3 → 31, 32. "Three cases, 2 each — that's 6, every one found!"
🎓
What your child will learn
1Split the work into casesTo find every 2-digit number from the cards 1, 2, 3 (each used once), group them by the first digit. That is casework: each case is a tidy little box. Drop each number into its case →
2Count each case, then addOnce the cases are sorted, count how many are in each — then add the cases together. Every bar is one case.
3Casework beats guessingThe same six numbers, found two ways. Tap each list to see what happens when you are tidy — and when you are not.
4When order does NOT matterSometimes the order does not count — like choosing 2 flavours from vanilla, choc, mango. Then V-C is the same as C-V. Use casework again, but skip repeats: start with V (V-C, V-M), then C (C-M), then M (nothing new).
🔍
A peek inside
How many 2-digit numbers can you make from cards 1, 2, 3, each used once? Use casework by first digit.
first 1 → 12,13 · first 2 → 21,23 · first 3 → 31,32 → 2+2+2
Try this at home: Casework by first digit — 2-digit numbers from cards 5, 6, 7: first 5 → 56, 57 · first 6 → 65, 67 · first 7 → __, __ · total ways = __
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.