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Math · Stage 6

Assumption, units & before-after problems

Real puzzles hide two unknowns at once. Pretend they are all one kind and fix the gap, turn a ratio into equal units, or spot the part that never changes — three Olympiad moves for before-and-after problems.

✦ Math📘 Stage 6 · S6⏱ ~14 min🧒 Ages 10–12★ Free to start
I can solve multi-variable assumption, units and before-after problems with ratio change.
Start the free lesson →⬇ Printable PDF
Kavi the owl for Math
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Kavi's Farm Puzzle 🐔🐇

Kavi peeked over the fence 🔭 and counted 8 heads and 22 legs in the pen. “If they were all chickens that's only 16 legs — too few!” Kavi grinned. “Let me pretend they're all chickens, then swap some for rabbits until the legs match. Three extra pairs of legs → 3 rabbits and 5 chickens. This pretend-then-fix trick cracks heaps of two-unknown puzzles!”

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What your child will learn

1Pretend first, then fix the gapA pen holds chickens 🐔 and rabbits 🐇 — 7 heads, 20 legs. Two unknowns at once! The trick: pretend they are all one kind, then swap. Tap each card →
2A ratio is just equal unitsBen and Mia share 48 stickers in the ratio 1 : 3. Draw the shares as units — Ben is 1 unit tall, Mia is 3 units tall.
3Before and after: find what stays the sameApples 🍎 and oranges 🍊 start at 3 : 2. Then 10 oranges are added — the apples do not change. Now it is 3 : 4. Tap to see the anchor →
4Which part never changes?Every before-after puzzle gets easy once you spot the part that stays the same. Sort each story by what is unchanged →
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A peek inside

A farm has chickens 🐔 and rabbits 🐇. There are 9 heads and 26 legs. How many rabbits?
pretend all 9 are chickens → 9 × 2 = 18 legs; 26 − 18 = 8 extra; each rabbit adds 2 legs → 8 ÷ 2

Try this at home: Assumption: tricycles (3 wheels) 🛺 and bicycles (2 wheels) 🚲 — 7 cycles, 17 wheels. How many tricycles?

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.