ACARA v9 CONTENT DESCRIPTION “add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator”
Adding and subtracting larger numbers is not a new trick; it is place value put to work. Split each number into hundreds, tens and ones, deal with each column on its own, then put the pieces back together. The reason this is allowed is that a three-digit number is already a sum of its places, so 354 is just 300 and 50 and 4. Add like to like — ones to ones, tens to tens — and the only thing to watch is what happens when a column overflows or runs short. Doing this without a calculator is the point: the machine hides the structure, and the structure is exactly what Year 3 is learning.
Partition and add
Break both numbers into their places, add each column, then put them back together.
Split 354 and 283 into hundreds, tens and ones, then add one column at a time.
Add the columns, then look for ten
When you add column by column, each column produces a small sum, and the question is only whether that sum has reached ten. Ones that reach ten bundle into a ten; tens that reach ten bundle into a hundred. Adding 354 and 283, the tens give 5 and 8 which is 13 — thirteen tens is one hundred and three tens, so a hundred moves up a column. Nothing about the digits is mysterious once you see that every column plays by the same rule the ones do: ten of me makes one of the next place up.
The regroup bundle
When ten ones gather, they bundle into a single ten. This is the carry.
7 ones, not yet a ten. Keep adding ones until ten of them bundle up.
Regrouping is just bundling
The word carry sounds like a rule to memorise, but it is the bundling children have done since Year 1, now happening one place higher. Ten ones gather and become a single ten; the ten goes up to the tens column and the leftover ones stay behind. Seeing 13 ones become 1 ten and 3 ones removes the magic from the little carried 1. Subtraction does the reverse: when the top digit is too small to give, a larger place is unbundled back into ten of the smaller, so a ten reopens into ten ones. Carrying and borrowing are one idea — bundling — read in two directions.
Partition and subtract
When the top digit is too small, regroup a larger place down so it can lend.
To do 523 − 167, the ones run short, so open up a ten into ten ones first, then subtract.
Subtraction can borrow from next door
To take 167 from 523, the ones ask for 7 from 3 and come up short, so the tens lend: one ten becomes ten ones, leaving the ones column with thirteen to work from. The same can happen in the tens. The top number has not changed in value — it has only been rearranged into a more useful shape, exactly as 523 can be seen as 4 hundreds, 11 tens and 13 ones when it needs to be. This is why regrouping is honest rather than a trick: it is the same quantity, repacked so the subtraction can go through.
Rearrange to make it easy
A number near a round one is a gift: add the round number, then adjust.
199 is close to a round number. Add the round number, then take back the difference.
Rearrange before you reach for the rule
The descriptor asks children to rearrange numbers to assist calculation, and the best example is a number sitting just below a round one. To add 199, add 200 and hand one back; to add 98, add 100 and return two. This compensation strategy keeps the work in the head and avoids regrouping altogether, and it teaches a habit worth more than any single sum: look at the numbers before you start, because a friendlier path is often hiding in plain sight. Good calculators choose a method to fit the numbers rather than grinding every problem the same way.
Count up the line
Subtraction is the gap between two numbers. Jump up from the smaller to the larger.
Jump up from 167 towards 523 in friendly hops. The total distance is the answer.
Subtraction is the distance between
There is a second way to see 523 minus 167 that many children find easier: not as taking away, but as the gap between the two numbers. Stand on 167 and jump up the line in friendly hops — to the next ten, the next hundred, then on to 523 — and the jumps you make add up to the answer. This count-up method turns a borrow-heavy subtraction into a short addition, and it quietly proves that subtraction and addition are the same relationship seen from two ends. It is also exactly how shopkeepers once counted out change.
Which column regroups?
Before calculating, predict where the carry or borrow will happen.
In 167 + 58, which column forces a regroup?
Predict the regroup
A strong calculator looks before leaping: which column, if any, will cross ten? Checking the ones first tells you whether a carry or a borrow is coming, and that prediction makes the whole calculation calmer, because nothing surprises you partway through. Some problems need no regrouping at all, and spotting those saves effort. With partitioning, regrouping, rearranging and counting up all in hand, three-digit addition and subtraction stop being a procedure to fear and become a set of choices — and the multiplication and division of Year 3 builds on this same place-value thinking next.