Years 4–6Maths at school

The grid method and long multiplication: a guide for parents

Written by A Dagdelen · Reviewed

Multiplying two two-digit numbers is where many parents meet a method they never learnt: the grid. It is a stepping stone, and it leads straight to the long multiplication you probably do remember.

Illustration: Quizo School

  • Year 4short multiplication by a 1-digit number, in a written layout
  • Year 5long multiplication for two-digit numbers
  • Year 6up to 4 digits by a 2-digit number
  • 12 × 12times tables known by the end of Year 4

What it is and when it appears

  1. The grid method splits numbers into tens and ones. To work out 23 × 14, the child splits 23 into 20 and 3 and 14 into 10 and 4, multiplies each pair in a grid and adds the four answers. It shows why multiplication works: every part of one number is multiplied by every part of the other.
  2. The National Curriculum does not name the grid method. It asks for formal written methods, and the grid is not one of them. Many schools use it as a bridge, so whether and when your child meets it depends on their school.
  3. Short multiplication comes first. In Year 4 children multiply two- and three-digit numbers by a one-digit number "using formal written layout", in columns like addition, carrying as they go.
  4. Long multiplication follows in Years 5 and 6. Year 5 includes long multiplication for two-digit numbers. Year 6 extends it to numbers with up to four digits multiplied by a two-digit number.
  5. Times tables make every method easier. By the end of Year 4 children are expected to know their tables up to 12 × 12, and the Year 4 Multiplication Tables Check tests them. A child who has to count up in fours loses the thread halfway through a long multiplication.

Worked examples: 23 × 14 two ways

The grid method

A grid for 23 × 14, with 20 and 3 across the top and 10 and 4 down the side. The four cells hold 200, 30, 80 and 12. The rows make 230 and 92, and 230 + 92 = 322.×203104200308012= 230= 92230 + 92 = 322
  1. Split 23 into 20 and 3, and 14 into 10 and 4. Write them along the top and down the side of the grid.
  2. Multiply each pair: 20 × 10 = 200, 3 × 10 = 30, 20 × 4 = 80 and 3 × 4 = 12.
  3. Add each row: 200 + 30 = 230 and 80 + 12 = 92.
  4. Add the two rows: 230 + 92 = 322.

Long multiplication

Long multiplication of 23 by 14 under H, T and O headings: a first row of 92 for 23 × 4, with a small carried 1, a second row of 230 for 23 × 10, and the answer 322.HTO23×1492123 × 423023 × 10322
  1. Write 23 above 14, with the ones lined up.
  2. Multiply by the 4 ones: 3 × 4 = 12, write 2 and carry 1; 2 × 4 = 8, plus the 1 makes 9. The first row is 92 (23 × 4).
  3. Multiply by the 1 ten: write 0 in the ones column first, because you are multiplying by 10, then 23 × 1 gives 230 (23 × 10).
  4. Add the two rows: 92 + 230 = 322. They are the same 92 and 230 as in the grid.

How to help at home

“That's not how I learnt it”

If the grid looks long-winded, remember it is the same sum laid out in boxes. Put the grid and the long multiplication side by side and point out that both have a 230 and a 92. Let your child use whichever method their class is working on now.

A 10-minute activity: how many altogether?

Ask how many eggs are in 12 boxes of 6, or how many seats are in 14 rows of 23. Your child estimates, works it out with a grid or the written method, then checks on a calculator. Swap roles: you make a deliberate mistake for them to find.

Keep the tables warm

Two or three minutes of times tables before a multiplication session helps more than a long session on its own.

Estimate before you start

23 × 14 is more than 20 × 14 = 280 and less than 25 × 14 = 350. An answer of 3,220 or 32 shows straight away that something slipped.

Common mistakes

  • Forgetting the zero. In the second row, leaving out the 0 and writing 23 instead of 230. Ask: are we multiplying by 1 or by 10?
  • Multiplying only tens by tens and ones by ones. Working out 20 × 10 and 3 × 4 and stopping at 212. The grid shows the two missing parts.
  • Adding the carry too early. The carried digit is added after the multiplication: 2 × 4 = 8, then 8 + 1 = 9, not (2 + 1) × 4.
  • Losing the place value in the grid. Writing 2 × 1 = 2 instead of 20 × 10 = 200. Saying the full numbers out loud stops this.

Practise and explore on Quizo School

Questions parents ask

Should my child still use the grid in Year 6?

Many children keep it as a check while long multiplication settles. Ask the teacher which method they want your child to use by now.

Is it fine to multiply by the tens first?

Yes. Some schools multiply by the tens first, others by the ones. What matters is the zero in the right place and the two rows added together.

My child knows the method but gets the answer wrong.

Usually it is a times-table fact or a slip in the final addition. Check the small products first.

What is short multiplication?

Multiplying by a one-digit number in a single row, carrying as you go, such as 46 × 3 = 138.

Times tables make multiplication easy

Times tables practice gives your child ten quick questions and a map of the facts they know. It is part of the Family plan. New families get the Family plan free for 14 days, with no card needed.

Start free
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