Math · Stage 4
Count arrangements and paths systematically (casework, Pascal)
Two big counting moves: MULTIPLY choices that happen in a row, and ADD up separate cases — then count grid paths the Pascal way.
✦ Math📘 Stage 4 · S4⏱ ~12 min🧒 Ages 8–9★ Free to start
I can count arrangements and paths systematically (casework, Pascal).
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Kavi Counts Without Listing 🧮
"Too many to list one by one?" hoots Kavi. "Then count smart! When choices happen in a row, I multiply. When they split into separate cases, I add. And for paths across a grid, I let Pascal do the adding for me ✨."
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What your child will learn
1Choices in a row → MULTIPLYKavi has 3 shirts and 2 hats. Each shirt can go with each hat, so every new shirt adds 2 more looks. That is why we multiply: 3 × 2 = 6 different looks.
2Separate cases → ADD them upSome counts split into separate cases that can't both happen. Count each case, then add. How many ways to climb 3 steps using 1-steps and 2-steps? Split by the first move. Tap each card.
3Grid paths → each corner ADDS the two before itTo count shortest RIGHT/UP paths across a street grid, write at each crossing the number of ways to reach it. You can only arrive from the left or from below, so each crossing is the sum of those two — exactly like Pascal's triangle. Tap ◀ less / more ▶.
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A peek inside
An ice-cream has 4 flavours and 2 cone types — one of each. How many different ice-creams?
choices in a row → multiply: 4 × 2
Try this at home: Choices in a row — MULTIPLY: 3 drinks × 2 snacks = __ combos
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 4 · S4 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.