THE BIG IDEAS · NUMBER
Column methods, decimals, money, rounding — they all stand on one idea. Here’s how it grows from Year 0 to Year 8, and how to shore it up at home.
🔢If you only ever understand one idea in primary maths, make it this one. Place value — the fact that where a digit sits decides what it's worth — is the idea the entire number system runs on. Column addition, decimals, money, percentages, rounding: all of it is place value wearing different outfits. And when maths goes wrong in Years 3–6, a wobbly place-value foundation is very often the real culprit.
In the number 444, the three fours are all different: 400, 40 and 4. Same digit, different job. That system — each place worth ten times the place to its right — is so efficient that ten symbols can write any number ever needed. But it's genuinely abstract for a five-year-old, because it breaks the rule they just learned: that a numeral means a fixed amount. Suddenly "4" means four somethings, and the something changes with position.
The linchpin is understanding that ten ones become one ten — one thing and ten things at the same time. Teachers call this unitising, and it's why so much early place-value work involves physically bundling: ten sticks bound into one bundle, ten bundles into one hundred-block.
The refreshed curriculum grows place value deliberately, one ring at a time: numbers to 20 in Year 0; tens and ones to 100 in Year 1; hundreds and numbers to 120 in Year 2; numbers to 1000 (and rounding) in Year 3; 10,000 in Year 4; a million — plus tenths and hundredths, place value's extension to decimals — in Year 5; and powers of 10 by Years 7–8. Notice decimals aren't a new topic at all: 0.7 is just the place-value pattern continuing to the right of the ones. Children solid on "each place is ten times its neighbour" find decimals unremarkable; children who memorised columns without the idea hit a wall.
🔍 Why column maths depends on it
The column algorithm for 47 + 38 quietly does this: 7 + 8 = 15, which is one ten and five ones — so five stays and one ten moves left. A child who understands the move owns the method. A child following steps by rote produces answers like 715 — the classic sign the digits have become meaningless symbols.
Ice-block sticks and rubber bands are the classic for a reason. Make bundles of ten, then ask for 34: three bundles and four loose. Then the magic question: "what if we add seven more?"
$1, $10 and $100 (real or pretend) are hundreds, tens and ones in disguise. "Pay me $263 with the fewest notes." Swapping ten $1 coins for a $10 note is renaming.
"Three hundred and seven — that's 3 hundreds, 0 tens, 7 ones." The zero-as-placeholder conversation matters: that 0 isn't nothing, it's holding the tens place open.
"What's ten times bigger than 40? Ten times smaller than 600?" Sliding digits left and right along the place-value scale is exactly the muscle decimals will need.
"That's $28 — call it 30." Rounding (a Year 2–3 skill) is place-value thinking applied, and the supermarket runs free practice sessions daily.
On Kiwi123, place-value mysteries run right through the year shelf — from tens-and-ones cases in Year 1 to powers-of-ten in the senior years — each one twenty questions of exactly this thinking, hidden inside a whodunit. Ten minutes a day on the idea everything else is built on: cheap insurance for the whole of primary maths.
Every Kiwi123 mystery is a whodunit maths activity — read the clues, crack the numbers, catch the culprit. The first ones in every year are free.
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