ACARA v9 CONTENT DESCRIPTION “partition one- and two-digit numbers in different ways using physical and virtual materials, including partitioning two-digit numbers into tens and ones”
A number is not a single solid lump — it can be taken apart and put back together, and it stays the same number all the while. This idea, called partitioning, is one of the most powerful in early mathematics. A child who sees that seven is made of three and four, or five and two, has stopped treating numbers as fixed labels and started treating them as quantities that can be composed and decomposed at will.
Break a Number Apart
Seven can be split in many ways and it is still seven. Move the divider and watch the two parts change while the total stays the same.
3 and 4 make 7.
One number, many splits
The first thing to feel is that one number holds many splits. Seven counters can be pushed into a group of three and a group of four; slide one across and it becomes two and five. The parts change, but the whole does not. Playing with these splits builds a deep flexibility — the child learns that 7 is not just “after 6” but a quantity with an inner structure they can rearrange.
Tens and Ones
The most useful way to split a two-digit number is into tens and ones. Reveal how 47 comes apart.
Tap to split 47.
The split that matters most
For two-digit numbers, one split matters most of all: into tens and ones. Forty-seven is four tens and seven ones. This is not just one option among many — it is the way our whole number system is built, and it is what makes the digits mean what they mean. The 4 in 47 is not four; it is four tens. Seeing the bars of ten and the loose ones side by side is what turns a written numeral into a real quantity in a child’s mind.
Many Ways, Same Number
Thirty-six does not have only one split. It is 30 and 6, but also 20 and 16, or 10 and 26. Step through — the total never changes.
30 + 6 = 36
Regrouping keeps the total
But tens and ones is not the only way to break a two-digit number, and exploring others builds real number sense. Thirty-six is thirty and six, but it is equally twenty and sixteen, or ten and twenty-six. Each regrouping keeps the total at thirty-six. This flexibility is exactly what children will lean on later when they add and subtract — trading a ten for ten ones, or the reverse, is the heart of regrouping.
Build It from Parts
Now go the other way: choose tens and ones to build a number. Make 53.
0 — keep adjusting to reach 53.
Taking apart, putting together
Partitioning works in both directions. Taking a number apart is one skill; building one from its parts is the other, and they reinforce each other. Choosing five tens and three ones to make fifty-three is the same understanding seen from the other side. A child who can move fluently between the whole and its parts has the foundation for all the calculation that follows.
Counting with Ten-Coins
Splitting into tens and ones is how we count quickly with ten-counters and single counters. Step through each amount.
24 is 2 tens and 4 ones.
Counting in tens is faster
This is also intensely practical. Counting a pile of counters is far faster in groups of ten than one at a time, and handling ten-counters and single counters is exactly the tens-and-ones split made physical. So partitioning is not an abstract exercise — it is how we count money, how we read prices, and how we manage quantities quickly in real life. A child who can see forty-seven as four tens and seven ones can count out that many counters in seconds, not minutes.
Always still itself
The five visualisations below let a child explore partitioning from every side: slide a divider to split seven, break 47 into tens and ones, regroup 36 in several ways, build 53 from chosen parts, and count amounts with ten-counters. Each one returns to the same intuition — a number can be taken apart many ways and is always still itself.
Quick self-check
1. If you split 7 into 3 and some more, the other part is...