ACARA v9 CONTENT DESCRIPTION “add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers, and using a variety of mental strategies”
Adding and subtracting in your head is not a feat of memory; it is place value put to work. Because a number like 47 is just 40 and 7, it can be taken apart, added in pieces and put back together — and the same freedom lets numbers be rounded, reordered or regrouped to make a calculation easy. This unit gathers the mental strategies the curriculum names: partitioning by place, rounding and adjusting, jumping by place, regrouping, and rearranging to make tens. None is the one right way; together they give a child choices, and choosing well is what makes mental arithmetic quick and confident.
Partition to add
Split each number into tens and ones, add each place, then combine.
Partition both numbers by place value: split 47 and 36 into tens and ones.
Partition by place value
The most basic mental strategy is to split both numbers into tens and ones, add each place separately, then combine. For 47 + 36, the tens give 70, the ones give 13, and together they make 83. Partitioning works because place value guarantees that tens only combine with tens and ones with ones, so a single two-digit sum becomes two small, manageable ones. It is the strategy nearly every other one builds on, and it makes the structure of the number visible — a child who partitions is reasoning about the number, not just pushing digits around.
Round and adjust
Round a number to a friendly ten, add, then adjust by what you added.
Make 39 friendly: round it up to 40 and remember to adjust.
Round, then adjust
When a number is close to a ten, it is often quicker to round it up, add the friendly number, then adjust by what was added. To work out 47 + 39, add 40 to get 87, then take back the extra 1 for 86. This compensating strategy turns an awkward number into an easy one and corrects for the change at the end, and it is exactly how many adults add in their heads without noticing. It rests on a simple idea: changing a number by a known amount changes the answer by the same amount, so you can always undo it.
Jump by place
Count on from the first number: add the tens, then the ones.
Start at 56. Jump on by the tens of 27 first, then the ones.
Jump by place on a line
Another way to add is to keep one number whole and count on from it by place, jumping the tens first and then the ones. Starting at 56 and adding 27 means jumping +20 to 76, then +7 to 83. Jumping by place keeps a single running total in mind rather than juggling two numbers, which many children find easier, and the number line makes the movement concrete. It is the same partition idea — splitting 27 into 20 and 7 — but applied to only one of the numbers, which is sometimes the lighter mental load.
Regroup to subtract
When the ones run short, open a ten into ten ones, then subtract.
There are not enough ones to take 8 from 3. Regroup: open one ten.
Regroup when ones run short
Subtraction sometimes asks for more ones than there are, and the answer is to regroup: open one ten into ten ones. For 63 − 28, there are not enough ones to take 8 from 3, so 63 is regrouped as 50 and 13; then 13 − 8 = 5 and 50 − 20 = 30, giving 35. Regrouping is the subtraction counterpart of carrying, and it depends entirely on the idea that a ten and ten ones are the same amount wearing different clothes. Understanding why the ten can be opened is what stops regrouping from being a mysterious rule.
Pick a strategy
A good mental mathematician chooses the strategy that suits the numbers.
Different sums suit different strategies. Which fits 47 + 39 best?
Choosing the right strategy
Having several strategies is only useful if a child can pick a good one, and the choice depends on the numbers. A number near a ten, like 39, invites rounding and adjusting; a subtraction where the ones run short calls for regrouping; a pair of round tens needs nothing fancy at all. Part of becoming fluent is glancing at a calculation and seeing which strategy will be lightest, rather than grinding every problem the same way. There is often more than one valid route, but a flexible mathematician reaches for the one that suits the numbers in front of them.
Rearrange to make tens
Order does not matter in addition, so reorder to make easy tens first.
Adding can be done in any order. Spot a pair here that makes a friendly 10.
Rearrange to make tens
Addition can be done in any order, and that freedom is itself a strategy: reorder the numbers to make easy tens first. In 8 + 5 + 2, pairing the 8 and the 2 makes 10, leaving a simple 10 + 5. Looking for pairs that bond to a ten before adding the rest is a habit that speeds up longer sums and reduces mistakes. This rearranging rests on the same property that lets us partition and regroup — that numbers can be split and recombined freely — and it completes a Year 3 toolkit of mental strategies that the times-tables work of the next Algebra unit will extend to multiplication.