Long multiplication explained for parents (Australia)

Plenty of parents remember long multiplication as a stack of digits, a row that "starts with a zero" and a final add-up at the bottom — and a vague sense that nobody ever said why. Then a Year 5 sheet comes home with 34 × 26, a grid of boxes your child calls the area model, and a note asking them to show their working. Same maths, different picture.

Long multiplication is a written method for multiplying a number by a two-digit (or bigger) number. You split the second number into its place-value parts, multiply by each part, then add the partial answers together. Everything else — the grid, the columns, the zero in the second row — just keeps those parts tidy.

Below: how classrooms build up to the column method, why that famous zero is there, and how to help without teaching "the old way" over the top of the teacher. It assumes your child already knows what multiplication means; only the written method is new.

Start with what long multiplication actually does

Take 34 × 26. Instead of one giant step, the method breaks the job up:

• 34 × 6 (the ones part of 26) = 204
• 34 × 20 (the tens part of 26) = 680
• 204 + 680 = 884

Long multiplication is partitioning plus adding. If your child already splits numbers into tens and ones for mental maths (partitioning), they already own the main move. The written layout just records it so nothing gets lost.

A quick sense check is worth teaching from day one: 34 × 26 is a bit more than 30 × 25, which is 750, and a bit less than 35 × 30, which is 1050. So 884 sits comfortably in range. (Rounding and the habit of estimating before you calculate do a lot of quiet work here.)

The steps schools usually take on the way

Most Australian classrooms don't jump straight to the compact column method. A common sequence looks like this, though schools vary and your child's teacher may order it differently.

Stage	What it looks like	What it builds
Arrays and equal groups	Rows of dots or counters	Multiplication as rows × columns (arrays, equal groups)
Area model (grid method)	A rectangle cut into place-value boxes	Seeing every partial product
Short multiplication	A number times a single digit, in columns	Carrying (regrouping) in multiplication
Extended (expanded) written method	Each partial product written on its own line	Linking the grid to columns
Compact long multiplication	Two rows plus a total	Speed, once the meaning is solid

If the sheet shows boxes, follow the boxes; if it shows columns, follow the columns. Both reach the same answer.

The area model: why the grid makes sense

The area model treats multiplication as the area of a rectangle. For 34 × 26, draw a rectangle and split one side into 30 and 4, the other into 20 and 6. You get four smaller boxes:

×	30	4
20	600	80
6	180	24

Add the four boxes: 600 + 80 + 180 + 24 = 884.

The grid is longer to write, but it shows where every part of the answer comes from, so errors are easy to spot. When a child says "I got 272", you can point to the grid and ask which box went missing. (Here, the 600 and 80 from the 20 row.)

The same picture returns later for decimals and algebra, so time here isn't wasted.

Short multiplication first: one digit at a time

Before the two-row method, children usually practise multiplying by a single digit in columns. For 23 × 4:

1. Ones: 3 × 4 = 12. Write 2 in the ones column, carry 1 ten.
2. Tens: 2 × 4 = 8 tens, plus the carried 1 = 9 tens.
3. Answer: 92.

If carrying already causes wobbles in addition, the same fix works here: say the value, not just the digit ("one ten", not "a one"). Our guides on column addition and forgetting the carry cover that habit in more detail.

Short multiplication relies on quick recall of times tables. If 7 × 8 still takes a long count, the written method will feel heavy, and that's a facts issue rather than a method issue.

The two-row method and that famous zero

Here's 34 × 26 in the compact layout most parents remember:

The second row starts with a 0 in the ones column. That zero is the step people most often learn without a reason, so it's worth spelling out: you are multiplying by 2 tens, not by 2. Anything times a ten has no ones, so the ones place is empty — and the zero holds that place so the 68 lands in the tens and hundreds where it belongs. (Zero holds the place and place value explain the same idea in other settings.)

Some teachers call it a placeholder; some children say "times twenty" aloud as they write it. A child who can explain the zero rarely forgets it.

Bigger numbers follow the same pattern. For 125 × 12: 125 × 2 = 250, then 125 × 10 = 1250, and 250 + 1250 = 1500. Three-digit by three-digit just adds another row (with two placeholder zeros).

You may also meet the lattice method (a grid with diagonals). If it isn't on your child's sheet, there's no need to introduce it.

What the curriculum expects

Version 9 of the Australian Curriculum: Mathematics builds multiplication gradually. Recall of multiplication facts grows through the middle primary years, and by Year 5 students solve problems that involve multiplying larger numbers by one- and two-digit numbers, choosing efficient strategies and checking that answers are reasonable. In Victoria, the Victorian Curriculum 2.0 is closely based on version 9.

Notice the wording: efficient strategies. The curriculum doesn't insist on one written algorithm, so different schools (and even different classes) may lean on the area model, the extended method or the compact one. Follow your child's class.

Year by year: a rough picture

Year 3: multiplication as equal groups and arrays; facts for twos, threes, fives and tens; doubling and halving as a mental tool. No long multiplication yet. Year map: Year 3 maths.

Year 4: facts up to 10 × 10 become more automatic; two-digit by one-digit using partitioning, the area model or short multiplication. Year map: Year 4 maths.

Year 5: two-digit by two-digit (and three-digit by one- or two-digit), often with the area model leading into a written method; estimating to check. Year map: Year 5 maths.

Year 6: more fluent written methods, larger numbers inside word problems, and early links to multiplying decimals (decimals). Year map: Year 6 maths.

These are typical patterns, not deadlines.

Helping at home without "the way I learnt it"

The biggest kindness is to ask before you show. "How did your teacher do it?" saves a tug-of-war between two methods. If you only know the compact column, that's fine — match it to the grid by pointing out that each row of the column is two boxes of the grid added together.

Questions that keep your child thinking (rather than copying):

• "What's a rough answer before we start?"
• "Which part of 26 are we multiplying by right now — the 6 or the 20?"
• "Why is there a zero at the start of this row?"
• "Does our answer match the estimate?"
• "Could you check it with the grid?"

Ten minutes and one or two careful problems beat a rushed page. If it turns into tears, stop and come back later (homework without tears has gentle scripts).

Quick games that build the skills underneath

1. Estimate showdown — read a multiplication from a shopping catalogue (12 packs of 24 rolls) and everyone guesses. Closest estimate wins; then work it out properly.
2. Grid art — draw the area model on grid paper with real squares for a small case like 13 × 12. Counting the boxes proves the partial products.
3. Tens-times race — call out 34 × 10, 34 × 20, 34 × 30. Children notice the pattern (and the zero) without a lecture.
4. Spot the slip — write a worked example with one deliberate mistake (a missing zero, a forgotten carry). Your child plays teacher and finds it.
5. Factor flip — try 25 × 16 as 25 × 4 × 4. It links to factors and multiples and shows there's more than one route.

Slips we see often (and how to steer them)

Leaving out the placeholder zero. The answer comes out about ten times too small. Ask, "Are we multiplying by 2 or by 20?"

Lining digits up on the left. Columns drift and the add-up goes wrong. Squared paper, or ruling place-value columns, fixes most of this.

Adding the carry too early. In 47 × 3, multiply 4 × 3 first, then add the carried 2 (12 + 2 = 14 tens, so 141). Saying each step aloud helps.

Forgetting to add the rows. Some children stop at the partial products. A boxed "now add" step at the bottom of the layout helps.

No estimate, no alarm bell. An answer of 8840 for 34 × 26 should feel wrong. Encourage a quick estimate every time.

Patchy tables. If most errors are single facts, practise those separately (times tables without tears) and keep the written method for later.

How it connects to long division

Long multiplication and long division are partners: division's "multiply, then subtract" steps use the same place-value thinking, and multiplying back is a handy way to check a division.

If it keeps being a struggle

If, after relaxed practice over several weeks, your child still can't explain any part of the method, or gets anxious whenever multiplication appears, have a quiet chat with the teacher and bring a recent example. Ask which method the class is using and what you can practise at home.

For a wider view, when to worry about maths, maths anxiety in children and Is my child behind in maths? are worth a read next. Nothing here is a diagnosis; ongoing worries are for the school or a qualified professional.

FAQ

What is long multiplication in simple words?

A written way to multiply by a two-digit (or bigger) number: multiply by each place-value part separately, then add the answers.

Why is there a zero in the second row?

Because you're multiplying by tens. The zero holds the ones place so the rest of the answer sits in the right columns.

Is the area model the same as long multiplication?

It's the same maths shown as a grid. The column method is a shorter way to record the same partial products.

When do Australian kids learn long multiplication?

Usually around Years 5–6, after short multiplication by one digit. Schools vary, so check with the class teacher.

Should I teach the method I learnt at school?

Ask how the class does it first. If you show your own method, link it back to theirs so your child isn't juggling two systems.

My child knows the steps but gets wrong answers. Why?

Often it's a single times-table fact or a column that drifted. Check the estimate, then look for the box or row that went astray.

Where to from here

This week, pick one problem from homework and solve it twice: once with the grid and once in columns, then compare the rows. When your child can point to where the 680 lives in both, the method has started to make sense.

For a broader picture of how your child's maths is tracking, try Ziado's free check: roughly 10 minutes, adaptive, one-off, with partial results only and no account or card required (the full placement opens after signup). It's not a long multiplication test, NAPLAN practice or medical advice. To see what ongoing practice looks like, browse Ziado maths — Individual and Family plans both open with a 14-day free trial, and the pricing page sets out the details.