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Giving Change

Maths · Y3 Money
Year 3
Lesson Guide
Explanation
When you pay with more money than something costs, the shop gives the extra back — that's your change. A $3 juice paid with a $5 note: change = 5 − 3 = $2. Change is simply a subtraction: what you PAID minus what it COST. And it's your money — always check you got the right amount!
Your Turn
A $4 sandwich, paid with $10. How much change? Check: 10 − 4 = $6.
Watch Out
Change comes only when you pay MORE than the price. Exact money = no change.
Explanation
Shopkeepers don't subtract — they count UP from the price to the payment. Costs $3.60, paid $5: hop 10c to reach $3.70, hop 30c to reach $4, hop $1 to reach $5. Add the hops: 10c + 30c + $1 = $1.40 change. Counting up through 'nice' numbers is easier than column subtraction with dollars and cents!
Your Turn
Costs $2.75, paid $5. Count up! Check: 25c → $3, then $2 → $5. Change = $2.25.
Watch Out
Count up to the money you HANDED OVER ($5), not to some other number. The hops must add up along the way.
Explanation
Bigger notes, same two hops. Hop one: cents up to the next whole dollar. Hop two: dollars up to the note. Costs $6.50 paid with $10? 50c gets you to $7, then $3 gets you to $10 — change $3.50. Costs $13.20 paid with $20? 80c to $14, then $6 to $20 — change $6.80.
Your Turn
Costs $7.25, paid $10. Two hops! Check: 75c → $8, then $2 → $10. Change = $2.75.
Watch Out
The cents hop: to go from $6.50 to $7 you need 50c — that is 100 − 50. Think "what completes the dollar?"
Explanation
Knowing the change amount is half the job — now build it with real coins, biggest first. Change of $1.40: grab a $1 (40c to go), a 20c (20c to go), another 20c — done, three coins. Same greedy trick as the money puzzles: always the biggest coin that fits. That gives the fewest coins.
Your Turn
Build $2.75 change with the fewest coins. Check: $2 + 50c + 20c + 5c — four coins.
Watch Out
No 25c or 40c coins exist! Build only from 5c, 10c, 20c, 50c, $1, $2.
Explanation
Two quick checks make you change-proof at the shops. Add-back: cost + change must equal what you paid ($3.60 + $1.40 = $5 ✓). Size check: change is always smaller than what you handed over. Master these and try the real-life game — predict the change before the register does. Quiz and exercises await!
Your Turn
You paid $10 for a $8.20 book and got $2.80 change. Add-back check: 8.20 + 2.80 = ? Check: $11 — WRONG change! It should be $1.80.
Watch Out
Machines are usually right, people sometimes are not — the add-back check settles it in seconds.
Step 1: Introduction
Step 1 of 5
You pay too much — money comes back 🧃 juice costs $3 💵 you pay with $5 🪙 change: $2 back change = what you paid − what it cost $5 − $3 = $2 change Change is YOUR money coming back — always check it!
Costs $3.60, paid $5 — count up like a shopkeeper $3.60$3.70$4$5 10c 30c $1 Hop to the next nice number each time: 10c + 30c + $1 = $1.40 change
Bigger notes, same trick Costs $6.50 → paid $10 50c → $7, then $3 → $10. Change = $3.50 Costs $13.20 → paid $20 80c → $14, then $6 → $20. Change = $6.80 Hop 1: cents up to the next whole dollar. Hop 2: dollars up to the note. Add the hops.
Hand back $1.40 in real coins $1 20c 20c $1 + 20c + 20c = $1.40 ✓ Build change biggest-coin-first, without going over. $1.40: take $1 (40c left), take 20c (20c left), take 20c (done!). Fewest coins = happiest pockets.
Is your change right? 🛒 Check 1 — the add-back: cost + change should equal what you paid: $3.60 + $1.40 = $5 ✓ Check 2 — the size check: change must be SMALLER than what you paid (you can't get $7 from $5!) Real-life challenge: next time someone shops, predict the change BEFORE the register shows it! Now practise in the quiz and exercises!
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