ACARA v9 CONTENT DESCRIPTION “find unknown values in numerical equations involving addition and subtraction, and recognise and explain the equivalence of number sentences using the relationship between the two sides of the equals sign”
The equals sign is often read as "makes" or "the answer is", but its real meaning is that the two sides have the same value. A number sentence is like a balance scale: 5 plus 3 on one side balances 4 plus 4 on the other because both make eight. This view, equals as balance rather than a signal to compute, is the key idea of the unit. It lets a child judge whether a sentence is true, find a missing number that keeps the balance, and later handle sentences with operations on both sides — all by asking one question: are the two sides really the same?
Equals means balance
The equals sign means the two sides have the same value, like a balanced scale.
Does 5 + 3 balance 4 + 4? Equals means both sides are the same.
Finding the missing number
When a number sentence has a box for an unknown, the task is to find the value that keeps both sides equal. In 12 equals 3 times a box, the box must be 4, because 3 times 4 makes the twelve on the other side. The equals sign anchors the search: whatever the box is, the two sides must match. This is the same balance idea put to work — not computing left to right, but finding the number that makes the scale level. Solving for an unknown this way is the foundation of all the equation work that algebra builds later.
Find the missing number
An unknown box is filled so that both sides of the equals stay equal.
What number in the box makes both sides equal?
An operation on each side
Number sentences are not always a sum on the left and an answer on the right; an operation can sit on both sides. In 4 plus 5 equals a box plus 6, both sides are additions, and the box must make them match: the left is 9, so the box is 3. The trick is to work out the side you fully know first, then find what the unknown side needs. Sentences like this break the habit of reading the equals sign as "work it out", because here it genuinely means "the same as", with real expressions on both sides.
Operations on both sides
A number sentence can have an operation on each side and still balance.
Both sides have an operation. What fills the box so the sides stay equal?
Changing both sides together
Because a number sentence is a balance, there is a powerful rule for changing it: whatever you do to one side, do to the other, and it stays balanced. Add three to both sides of a true sentence and it is still true; the scale stays level. Add to only one side and the balance is lost. This rule, doing the same to both sides, is exactly how equations are solved in later years, and seeing it on a balance now — both pans rising together — builds the intuition before any formal method. Equality is preserved by treating the two sides alike.
Keep it balanced
Doing the same thing to both sides keeps a number sentence equal.
The scale balances: 6 equals 6. What happens if you add to one side only? To both?
True or false sentences
Once equals means balance, any number sentence can be judged true or false by checking whether its two sides are really equal. 7 plus 5 equals 6 plus 6 is true, because both make twelve; 4 times 3 equals 5 plus 6 is false, because twelve is not eleven. Deciding the truth of a sentence is a direct test of the balance idea, and it trains a child to evaluate both sides rather than assume the sentence must be correct. This habit of checking, rather than trusting the equals sign, is what makes equivalence a tool for reasoning, not just a rule.
True or false?
A number sentence is true only when both sides are really equal.
Is this number sentence true or false: 7 + 5 = 6 + 6?
Solving by keeping balance
Pulling the unit together, solving a number sentence means finding the value in the box that keeps both sides equal, whatever shape the sentence takes. A box plus four equals ten needs six; three times a box equals fifteen needs five. Each is solved by asking what the unknown must be for the balance to hold, not by reading left to right. With the equals sign understood as balance, missing numbers found, operations handled on both sides, the same-to-both-sides rule, and true-or-false checking, a child has a genuine understanding of equivalence — the idea that underlies every equation in the mathematics to come.
Find every box
Each number sentence needs the one value in the box that keeps it balanced.
Each sentence has one box that makes it balance. Reveal each missing value.
Quick self-check
1. The number sentence 5 + 3 = 4 + 4 is true because...
2. In 12 = 3 x __, the box must be...
3. To find the box in 4 + 5 = __ + 6, first work out...
4. If a number sentence balances, doing the same thing to both sides...