The equals sign explained for parents (Australia)

It's a weeknight and your seven-year-old is working through a homework sheet and gets to this one: 4 + 5 = □ + 3. Without a pause they write 9 in the box. It looks like a sensible answer, and plenty of adults would have done the same at first glance. But the right answer is 6, and the reason why is one of the most important ideas in primary maths.

The equals sign is the first maths symbol most children learn to write, and one of the most commonly misunderstood. Many kids quietly decide that = means "now write the answer". That idea works for years on simple sums, then falls over the moment a number sentence looks a little different. Research in maths education has flagged this mix-up for decades, and it shows up in Australian classrooms too.

The good news is that a better meaning is easy to teach at home. This guide explains what the equals sign really means, why children get it wrong, the kinds of number sentences that reveal the problem, how the idea develops across the primary years, and quick games that strengthen it with no worksheets at all.

What the equals sign actually means

The equals sign says that the amount on the left is the same as the amount on the right. That's it. It's a statement of balance, not an instruction to calculate.

So all of these are true:

• 7 = 7
• 3 + 4 = 7
• 7 = 3 + 4
• 3 + 4 = 5 + 2
• 10 − 3 = 2 + 5

Each one is true because both sides name exactly the same amount: seven. The calculation can sit on either side, or on both sides at once.

A helpful phrase for children is "is the same as". Read 3 + 4 = 5 + 2 out loud as "three plus four is the same as five plus two" and the meaning becomes obvious in a way that "three plus four equals..." often doesn't.

The "answer comes next" trap

Most children meet the equals sign in sums like 2 + 3 = 5 or 8 − 1 = 7. The calculation is always on the left, the answer always on the right. After hundreds of these, a pattern forms in the child's head: the symbol is a signal to work something out and write the result.

Teachers sometimes call this an operational view of the equals sign. The fuller meaning, that both sides balance, is called a relational view. Children with only the operational view tend to make very predictable mistakes:

That last example often turns up in older children's working. They're recording steps, a bit like a running commentary, but 9 + 1 doesn't equal 15. Each equals sign in a line has to be true on its own.

None of these mistakes mean a child is "bad at maths". They're a sign that the child has learned a rule that works most of the time. The fix is to widen what the symbol means.

Why this matters more than it looks

It's tempting to treat this as a small technicality. It isn't, for a few reasons.

Missing-number problems depend on it. From around Year 3, children work with number sentences where the unknown could be anywhere: □ + 7 = 15, or 20 − □ = 12. Without the balance idea, these feel like random puzzles.

Algebra is built on it. When letters arrive in high school, solving 2x + 3 = 11 means doing the same thing to both sides to keep them balanced. Children who already see = as a balance point find that step natural. The algebra guide shows how the primary years lay the groundwork.

It supports flexible mental maths. Knowing that 8 + 7 is the same as 10 + 5 lets a child swap a hard sum for an easier one. That's the engine behind strategies like bridging to ten, covered in mental maths strategies.

Fact families make more sense. Seeing 6 + 4 = 10 and 10 = 4 + 6 as the same relationship helps children connect addition and subtraction, which is the heart of fact families.

Teaching the balance idea at home

Use a real balance

If you have kitchen scales with two pans, a coat hanger with two cups hanging off it, or even a seesaw at the park, you have a model of the equals sign. Put 4 blocks and 5 blocks on one side. What could go on the other side to make it level? Ten blocks? Too many. Three blocks plus some more? How many more?

Kids grasp "level" instantly. Once they've felt it with objects, you can say: "The equals sign is like the middle of the seesaw. It tells us both sides weigh the same."

Say "is the same as"

Swap the word "equals" for "is the same as" for a while, especially when reading number sentences aloud. It nudges children to look at both sides rather than rushing to an answer.

Write sentences in different shapes

Children only see one layout if that's all we show them. Mix it up:

• 5 + 3 = 8
• 8 = 5 + 3
• 5 + 3 = 4 + 4
• 8 = 8
• 5 + 3 = 3 + 5

Ask "true or false?" about each one. A child who says "8 = 8 is false" has given you useful information, not a wrong answer to correct sharply.

Ask "how do you know?"

When your child finds the missing number, ask them to check both sides. "So 4 + 5 is 9. And 6 + 3 is 9. Same on both sides? Then it's true." This habit of checking is worth more than speed.

True or false: the most useful activity

Teachers lean heavily on true-or-false number sentences because they force children to think about both sides. You can do the same in the car or at dinner. Start easy and build up:

1. 6 = 6 (true)
2. 2 + 2 = 4 (true)
3. 4 = 2 + 2 (true)
4. 3 + 3 = 2 + 4 (true)
5. 5 + 1 = 5 + 2 (false: 6 is not the same as 7)
6. 10 − 2 = 4 + 4 (true)
7. 7 + 6 = 13 + 1 (false)
8. 12 − 5 = 10 − 3 (true)

The best follow-up question is "How could you change it to make it true?" For number 5, a child might change the 2 to a 1, or the first 1 to a 2. Both are great answers.

Missing-number sentences by stage

Once the balance idea is in place, missing-number problems become a natural next step. Here's a rough progression.

Unknown at the end (Prep to Year 1). 3 + 2 = □. This is the familiar layout and a fine place to start.

Unknown in the middle (Years 1 to 2). 3 + □ = 5. Children can count on from 3, or think "what goes with 3 to make 5?" This links closely to number bonds and part-part-whole thinking.

Unknown at the start (Years 1 to 3). □ + 4 = 9 or □ − 3 = 6. Trickier, because you can't simply start counting from the first number. A quick bar model helps: draw a whole of 9 with one part of 4, and the missing start is the other part.

Calculations on both sides (Years 2 to 4). 6 + 5 = □ + 7. The child works out that the left side is 11, then asks what goes with 7 to make 11. The answer is 4.

Larger numbers and other operations (Years 4 to 6). 45 + 28 = 50 + □ (the answer is 23), 6 × □ = 3 × 8 (the answer is 4), or 36 ÷ 4 = □ ÷ 2 (the answer is 18).

A clever shortcut worth noticing

Some children solve 6 + 5 = □ + 7 without adding at all. They notice that 7 is two more than 5, so the box must be two less than 6, which gives 4. That's relational thinking at its best, and it's exactly the flexible reasoning teachers hope to see. If your child does this, ask them to explain it, then celebrate it.

The same idea works with subtraction, but in a slightly different way. In 15 − 9 = 16 − □, the starting number went up by one, so the amount taken away must also go up by one to keep the difference the same. The box is 10. This "same difference" idea is a powerful tool for subtraction.

Related symbols children meet

Once = is solid, children start using its cousins:

• ≠ means "is not equal to": 5 + 1 ≠ 7
• < means "is less than": 4 < 9
• > means "is greater than": 12 > 8

The less-than and greater-than signs belong with comparing numbers. A quick reminder many children like is that the wide open end of the sign always faces the bigger amount.

In upper primary, students also meet number sentences with brackets, such as (3 + 2) × 4 = □. The balance meaning still holds, but they need to know which part to calculate first. The guide to order of operations covers that.

Where the equals sign sits in the curriculum

Equality is threaded through the Algebra strand of the Australian Curriculum: Mathematics (version 9). In the early years, children build number facts and learn to partition and combine numbers, which lays the foundation.

In Year 3, students explain how adding and subtracting undo each other, then put that link to work finding unknown values in number sentences. In Year 4, they find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations. Year 5 extends this to equations involving multiplication and division, and Year 6 to equations involving brackets and combinations of operations.

The Victorian Curriculum 2.0 sequence is much the same, though each school sets its own teaching order, so exact timing can differ.

Equality skills from Prep to Year 6

Prep: comparing groups of objects as "the same" or "more"; making two towers the same height. See Prep maths.

Year 1: writing simple addition sentences; starting to see that 4 + 1 and 3 + 2 make the same total. See Year 1 maths.

Year 2: true-or-false sentences; missing numbers in different positions; using addition facts to 20. See Year 2 maths.

Year 3: unknown values in addition and subtraction sentences, using the link between the two operations. See Year 3 maths.

Year 4: solving equations with calculations on both sides; using properties such as order not mattering in addition. See Year 4 maths.

Year 5: unknowns in multiplication and division equations. See Year 5 maths.

Year 6: equations with brackets and mixed operations, preparing for algebra. See Year 6 maths.

Quick games for home

1. Make it level. Use a homemade coat-hanger balance and paper cups. Drop counters, pasta or coins into each cup and challenge your child to make it balance with different combinations.
2. Same total, different sums. Pick a number such as 10. Take turns saying a sum that makes it: 6 + 4, 12 − 2, 5 + 5. Then write two of them with an equals sign between.
3. True or false? Say a number sentence out loud. Your child gives a thumbs up for true, thumbs down for false, then fixes the false ones.
4. Mystery box. Write a sentence with a box anywhere in it. Your child solves it, then writes one for you. Kids love trying to stump a parent.
5. Domino balance. Lay two dominoes side by side. Do they show the same total? If not, which domino could you swap in to balance them?
6. Fix my working. Write 7 + 3 = 10 + 4 = 14 deliberately. Can your child spot why it's not true and write it correctly as two separate lines?

A few minutes is plenty. If maths homework regularly ends in tears, homework without tears has calmer approaches, and maths anxiety in children may help if worry is getting in the way.

Common mix-ups and how to respond

Writing the total of the left side in the box. Point to both sides and ask, "Is 9 + 3 the same as 9?" Let the child find the mismatch.

Adding every number in the sentence. Cover the right side, work out the left, then uncover and ask what's needed to match.

Saying 8 = 8 is wrong. Try "Is eight the same as eight?" Most children agree straight away once the words change.

Running equals signs together. Show that each equals sign is a promise that both sides match. Writing steps on separate lines keeps every promise true.

Getting confused when the answer is on the left. Practise reading sentences from right to left. 10 = 7 + 3 is just as true backwards.

When to look more closely

Most children shift their understanding with a little exposure and conversation. If your child is in Year 4 or above and still consistently treats = as "write the answer", struggles with any missing-number layout, or gets anxious whenever a sentence looks unfamiliar, it's worth mentioning to the class teacher. They can tell you how your child is going with number sentences in class.

For bigger-picture worries, read is my child behind in maths? or the guide on when to worry about maths. An online guide can't assess your child, so for persistent difficulties, have a chat with the teacher or another qualified education professional.

FAQ

What does the equals sign mean for kids?

It means both sides of a number sentence have the same value. A simple way to say it is "is the same as". So 2 + 5 = 7 reads "two plus five is the same as seven".

Why does my child write the wrong number in 4 + 5 = □ + 3?

They're likely reading = as "the answer goes here" and writing 9. The left side does make 9, but the right side needs to make 9 as well, so the box must be 6.

Is 7 = 3 + 4 correct?

Yes. The equals sign works in both directions, so the calculation can be on the left, the right or both sides.

When do Australian children learn to find missing numbers?

Under version 9 of the Australian Curriculum, finding unknown values in addition and subtraction sentences is named in Year 3, with multiplication and division in Year 5 and brackets with mixed operations in Year 6. Many children meet simpler missing-number sentences earlier.

Try this tonight

Write 5 + 2 = □ + 4 on a scrap of paper and ask your child to fill in the box. Whatever they write, ask them to read both sides aloud using "is the same as". If they spot the mismatch and fix it, you've just watched the balance idea click.

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