AC9MFN05 · FOUNDATION · NUMBER

Adding and Taking Away

ACARA v9 CONTENT DESCRIPTION represent practical situations involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies
Builds on: part-part-whole to 10 (AC9MFN04).

Stories about groups changing

Once a child sees that a number is made of parts, addition and subtraction are the next, natural step. They are not new and separate tricks — they are simply what happens when groups change. Add, and a group grows. Take away, and it shrinks. At Foundation, this is best met not as written sums but as stories acted out with real things: counters, blocks, coins, fingers. The numbers come after the action, to say how many.

Joining Two Groups
Addition is putting two groups together. Count them all, or subitise the small parts — how many altogether?
blue 3green 2
3 and 2 join to make 5.

Joining

Addition is joining. Put a group of four counters beside a group of three, push them together, and ask how many there are now. The answer does not require a formula — a child can count them all, or, once the parts are small and familiar, simply see that four and three is seven. That instant recognition of small amounts, without counting one by one, is subitising, and it makes adding quick.

Taking Away
Subtraction is taking some away from a group. Start with 7, cross out a few — how many are left?
take away 3
3 taken from 7 leaves 4.

Taking away

Subtraction is the opposite motion: taking some away. Start with seven counters, remove three, and count what is left. The same story can be told with anything — birds flying off a fence, biscuits eaten from a plate, coins spent at the tuckshop. The action is always “there were this many, some went, how many remain?”

Count On
Hold the bigger group in your head (5), then count on the rest one by one. A faster strategy than counting from one.
add 3
Counting on from 5… now 5.

Count on, not from one

As children grow more confident, they meet a faster way to add called counting on. Instead of counting a group of five all over again to add two, they hold “five” in their head and count on: six, seven. Starting from the larger group and counting on the smaller one saves effort, and it shows the child that they can trust a number they already know rather than recounting from one every time.

Where children stumble

It helps to know where children commonly stumble, so you can watch for it. A very common one is recounting the whole group every time, even after a child clearly knows how many are in the first part — counting “one, two, three, four” again before going on, rather than starting from four. Another is losing track of which counters have already been taken away during subtraction, so the same one gets removed twice or skipped. Slowing the action down, and saying the running total aloud while pointing, turns a guess into reasoning a child can check.

They Are Linked
The same three numbers make four facts. Adding and taking away are two sides of one picture — this is a fact family.
One story, four facts: 5, 3 and 8.

Four facts, one story

The deepest idea in this unit is that addition and subtraction are linked. If four and three make seven, then seven take away three must leave four. The same three numbers — four, three, seven — make a little family of facts: 4 + 3, 3 + 4, 7 − 4, and 7 − 3. A child who sees this stops treating every sum as a fresh puzzle. Knowing one fact hands them three more for free, because they are all the same story told from different starting points.

The Tuckshop
You have 6 coins for the tuckshop. Spend a few — how many coins are left? A real take-away story.
spend 2
Spend 2, and 4 of the 6 coins are left.

How many now?

None of this needs a worksheet to begin. Sharing snacks, counting toys into and out of a box, or working out how many are left after some are given away all build the same sense. The five visualisations below let a child act these stories out on the screen: join two groups, take some away, count on from the bigger group, see a fact family, and spend coins at the tuckshop. Each one returns to the same simple question — how many now?

Quick self-check
1. You have 4 apples and pick 3 more. How many altogether?
2. There are 8 birds. 3 fly away. How many are left?
3. To work out 6 + 2, the fastest way is to…
4. If 5 + 3 = 8, then 8 − 3 = ?
5. Adding two groups together is called…
Teaching pack: a week of lessons, free to printFive ready-to-teach lessons for this unit: teacher plans, student worksheets, cut-out story mats and counters, a mini-check and every answer. Print it or save as PDF, and the week is prepared.