Money
Recognise coins/notes; make amounts; give change; decimal (comma) money notation.
Money is a system for measuring value. Coins and notes are physical labels for numbers, and learning money means learning to count, combine, and compare those numbers in the everyday setting of buying and paying.
What it means
A coin or note is worth a fixed amount. In the euro system the coins are 1, 2, 5, 10, 20 and 50 cents plus 1 and 2 euros, and the notes start at 5 euros. One euro is worth 100 cents, so 1 euro = 100 cents, just as one metre is 100 centimetres. Other currencies work the same way with different names: pounds and pence, dollars and cents.
Making an amount means choosing coins whose values add up to a target. Because there are several coins, the same amount can usually be made many ways — 20 cents is one 20c coin, or two 10c, or a 10c and two 5c. This is direct addition practice with a purpose.
Giving change is subtraction. If something costs 30 cents and you pay with a 50c coin, the change is 50 − 30 = 20 cents. A useful trick is to count up from the price to the amount paid: from 30, add 20 to reach 50, so the change is 20.
Decimal (comma) notation writes euros and cents together with a separator. €3,45 means 3 whole euros and 45 cents. The two digits after the comma are the cents — the “tens of cents” and the “single cents” places — which is exactly place value (N1.2) extended one step to the right. Many countries write a comma (3,45), others a point (3.45); both mean the same value.
Worked examples
Make 47 cents with the fewest coins — take the biggest that fits each time:
47c → 20 + 20 = 40, then 5 = 45, then 2 = 47
coins: 20c, 20c, 5c, 2c (4 coins)Give change from €1,00 for a 65c toy, by counting up:
65 → 70 → 80 → 90 → 100
+5 +10 +10 +10 = 35 cents changeRead and add money amounts:
| Item | Price |
|---|---|
| Apple | €0,40 |
| Bread | €1,25 |
| Total | €1,65 |
Line up the commas, add the cents (40 + 25 = 65), then the euros (0 + 1 = 1): €1,65.
The generative-art connection
Coins are countable objects, so money is a natural fit for the dot-multiplier tool (dot-multiplier.nico.art): set a target amount and let each coin become a dot, so an amount you can see is an amount you can count. Making the same total in different ways produces visibly different arrangements of the same size — a picture of “many ways, one value”. The Money Pieces manipulative goes further: it shows each coin beside a proportional area strip, so the child watches value become length. Money is where number becomes something you can arrange, group, and rearrange on screen.
Common misconceptions
- Bigger coin means bigger value. Physically a 2c coin can look larger than a 10c coin. Value is printed, not sized — always read the number.
- More coins means more money. Five 1c coins (5c) are worth less than one 10c coin. Count the values, not the pieces.
- The comma is a gap, not a decoration. In €4,05 the 0 matters: it is 4 euros and 5 cents, not 4 euros and 50 cents. Both cent digits must be written.
What a learner should be able to solve
The benchmark for mastering this concept — the problems a child at this stage is expected to be able to work through.
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A pencil costs `35` cents. Show two different ways to make `35c` using euro coins (the coins are `1, 2, 5, 10, 20, 50` cents and `1, 2` euros). Then say which way uses the fewest coins.
Answer
Many correct answers. E.g. Way A: `20 + 10 + 5 = 35` (3 coins). Way B: `20 + 5 + 5 + 5 = 35` (4 coins), or `10 + 10 + 10 + 5 = 35`. Fewest coins is `20c + 10c + 5c` = 3 coins (take the biggest coin that fits each time).
Art hook Coin-mixer canvas: user drags coin-dots (each labelled with its value) into a tray; the tray sums live. Every valid way to reach 35c gets saved as a row of dots, stacking up a gallery of 'many ways, one value'. Colour each coin value differently so patterns of arrangement pop.
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A sticker costs `28` cents. You pay with a `50c` coin. How much change do you get? Try counting up from `28` to `50`.
Answer
`22` cents. Counting up: `28 → 30` (+2), `30 → 50` (+20), so `2 + 20 = 22`. Check: `50 − 28 = 22`.
Art hook Number-line arc animation: a dot hops from 28 up to 50 in labelled jumps (+2, +20); each hop draws a coloured arc above the line and the change total fills in as the arcs are added.
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Write these amounts using euros-and-comma money notation: (a) `3` euros and `60` cents, (b) `7` euros and `5` cents.
Answer
(a) `€3,60`. (b) `€7,05` — the `0` is needed so it reads 5 cents, not 50 cents.
Art hook A place-value strip that splits at the comma: euros on the left in one colour, the two cent digits on the right in two more colours. Type an amount and watch the digits drop into their correct coloured slots, making the comma a clear boundary.
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You buy an apple for `€0,55` and a banana for `€0,30`. What is the total? Then, if you pay with a `€1` coin, how much change do you get?
Answer
Total `€0,85` (add the cents: `55 + 30 = 85`). Change from `€1,00`: `100 − 85 = 15`, so `€0,15`. Counting up: `85 → 90 → 100` = `5 + 10 = 15`c.
Art hook A two-item shop scene: each price shown as a stack of coin-dots; totalling merges the two stacks and the sum lights up. Then a 'pay €1' bar fills from the total up to 100, and the leftover slice becomes the change coins.
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Ravi says: 'I have `six` coins so I must have more money than Mia, who has only `two` coins.' Is Ravi always right? Give an example that shows what you mean.
Answer
No — count values, not coins. Example: Ravi's six `1c` coins are `6c`, but Mia's two `2 euro` coins are `€4,00`. More coins does not mean more money; you add the printed values.
Art hook Side-by-side scales: two pans each hold coin-dots. The pan sizes are set by total value, not by how many dots — so a pan with two big-value dots can outweigh a pan crowded with tiny ones. Toggling coins tips the balance in real time.
Training exercises
Practice problems, easier first, that build toward the bar above. Each doubles as a seed for an interactive artwork.
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Name each euro coin's value: how many cents is a `5c` coin worth? A `20c` coin? A `50c` coin?
Answer
`5` cents, `20` cents, and `50` cents. The number printed on the coin is its value.
Art hook A colour wheel of coins: place each coin value as a dot around a circle, sized by value. Tapping a dot labels its worth — a gentle 'meet the coins' warm-up.
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Which is worth more: one `10c` coin, or three `2c` coins? How do you know?
Answer
The `10c` coin. Three `2c` coins are `2 + 2 + 2 = 6` cents, and `10 > 6`. Count the values, not the number of coins.
Art hook Two trays of dots side by side; each tray's height grows with its total value. The 10c tray visibly rises above the three-dot 6c tray, showing 'fewer coins, more value'.
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Count this handful: one `20c`, one `10c`, and one `5c` coin. How much is it altogether?
Answer
`20 + 10 + 5 = 35` cents.
Art hook Drop three coin-dots into a jar; a running total counter ticks up as each lands, turning a pile into a number.
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Make `40` cents using only `10c` coins. How many coins do you need?
Answer
Four `10c` coins, because `10 + 10 + 10 + 10 = 40` (or `4 × 10 = 40`).
Art hook Skip-count-by-ten number line: dots land at 10, 20, 30, 40, each a 10c coin. Great as a bridge to times-tables — the same jump repeated.
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A rubber costs `18` cents. You pay with a `20c` coin. How much change do you get?
Answer
`2` cents. `20 − 18 = 2` (count up: `18 → 20` is `+2`).
Art hook A tiny arc from 18 to 20 on a number line — the smallest possible change hop, colour-coded to match the 2c coin.
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Show two different ways to make `20` cents with euro coins.
Answer
Many answers, e.g. one `20c`; or two `10c`; or `10c + 5c + 5c`; or four `5c`. Each adds to 20.
Art hook A 'ways to make 20' grid where each row is a different coin combo laid out as dots. New valid combos append as new rows, growing a quilt of equal-value patterns.
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Write `€2,15` in words: how many euros and how many cents is that?
Answer
`2` euros and `15` cents. The digits after the comma are the cents.
Art hook Comma-splitter widget: the amount slides apart at the comma into a euros block and a cents block, each in its own colour, making the notation readable at a glance.
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Spot the mistake. Sam writes '`4` euros and `5` cents' as `€4,5`. What did Sam get wrong, and what is the correct way to write it?
Answer
Cents always use two digits, so `5` cents must be written `05`. The correct amount is `€4,05`. Written as `€4,50` it would mean 50 cents, and `€4,5` is not a proper money amount.
Art hook A two-slot cents display that flashes a warning when only one cent digit is entered; a leading 0 slides in to fill the empty slot, showing why both digits matter.
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A drink costs `€1,20` and a biscuit costs `€0,50`. What do they cost together?
Answer
`€1,70`. Add the cents: `20 + 50 = 70`; add the euros: `1 + 0 = 1`; total `€1,70`.
Art hook Two price-stacks of coin-dots merge into one taller stack; the combined total appears with the comma placed automatically between euros and cents.
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Make `67` cents with the fewest coins you can. Which coins do you use?
Answer
`50 + 10 + 5 + 2 = 67` — four coins. Take the biggest coin that fits each time: 50, then 10, then 5, then 2.
Art hook A 'greedy coin' animation: at each step the largest fitting coin-dot drops in and the remaining amount counts down, visualising the fewest-coins strategy.
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A toy costs `73` cents. You pay with a `1 euro` coin. How much change do you get? Then show that change with the fewest coins.
Answer
Change is `100 − 73 = 27` cents. Counting up: `73 → 80 → 90 → 100` = `7 + 10 + 10 = 27`. Fewest coins: `20 + 5 + 2 = 27` (3 coins).
Art hook Two linked panels: left panel counts UP from 73 to 100 with arcs to find 27c; right panel then rebuilds that 27c as the fewest coin-dots — change, both as a hop and as a handful.
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You have three `20c` coins and one `50c` coin. Can you pay for something that costs exactly `€1,00`? Explain.
Answer
No. `€1,00` is `100` cents. Check the totals you can make: `50`, `50 + 20 = 70`, `50 + 20 + 20 = 90`, `50 + 20 + 20 + 20 = 110`, and using only the 20c coins `20`, `40`, `60`. None of these equals `100`, so you cannot make exactly `€1,00` with these coins.
Art hook A subset-explorer: toggle each coin-dot on/off and a live total shows which sums are reachable. Highlight in green any combo that hits a chosen target, in grey those that miss — a visual 'what can I make?' puzzle.