Kavi, the KAVI owl, waving on a book
HomeAcademyAIWho it's forPricingFAQLabsContactGet Started
Math · Stage 6

Apply counting principles: arrangements, combinations and paths

To count choices, multiply the steps. To arrange a row, multiply down to 1. To choose a team, divide out the repeats. And to count grid paths, add your way across.

✦ Math📘 Stage 6 · S6⏱ ~13 min🧒 Ages 10–12★ Free to start
I can apply counting principles: arrangements, combinations and paths.
Start the free lesson →⬇ Printable PDF
Kavi the owl for Math
📖

Kavi's Big Count 🔢

Kavi has 3 hats 🎩 and 2 scarves 🧣. “How many different looks?” Instead of trying them all on, Kavi multiplies: every hat can go with every scarf, so 3 × 2 = 6 looks. “When I can count the choices step by step, I never have to guess — and never miss one. That's the counting magic ✨: multiply to combine, arrange a row down to 1, divide out the repeats to choose, and add my way across a grid.”

🎓

What your child will learn

1First ask: does the ORDER matter?Before you count, decide which kind of problem it is. If swapping two things makes a different result, order matters — that's an arrangement. If swapping changes nothing, order doesn't matter — that's a combination. Drop each one in the right box →
2Multiply the choices at each stepKavi has 3 shirts 👕 and 2 hats 🧢. Tap each card — one way is slow and risky, the other always works.
3Arranging a whole rowTo line up n different things, the first spot has n choices, the next n−1, then n−2 … down to 1. Multiply them all. Watch how quickly the count climbs:
4Choose a team, and count the pathsWhen order does NOT matter, the ordered count double-counts. And a grid of right/up moves is secretly a choosing problem. Tap each card.
🔍

A peek inside

You have 3 T-shirts 👕 and 4 pairs of shorts 🩳. How many different outfits can you make?
multiply the choices at each step: 3 × 4

Try this at home: Outfits: 2 hats 🧢 and 5 scarves 🧣 → how many hat-and-scarf looks?

Ready to play and learn?

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

Start the free lesson →⬇ Download PDF

Part of Math · Stage 6 · S6 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.