Math // Multiplication & Division

Written Multiplication & Division

Write and calculate mathematical statements for multiplication and division using known tables, including two-digit × one-digit, using mental and progressing to formal written methods

Ages
7 to 8
Type
Method
Builds on
3 topics
Leads to
2 topics
Standards
1 code

Quick check

Can the learner work out sums like '23 × 4' or '68 ÷ 4' — either in their head using times table knowledge, or by writing it out step by step?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Calculate 23 × 4 using partitioning (20 × 4 + 3 × 4)
  • Calculate 96 ÷ 8 using known table facts
  • Begin to use a formal written layout for short multiplication

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

3 topics
  • Reading ×, ÷, and = SymbolsRequired

    Multiplication & Division // Ages 6 to 7

    Writing multiplication/division statements requires fluency with symbols

  • Times tables (age 7+)Required

    Multiplication & Division // Ages 7 to 8

    Written multiplication/division requires known table facts

  • The three digits of a three-digit numberHelpful

    Number Representation & Place Value // Ages 7 to 8

    Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)

You are here

Written Multiplication & Division

Ages 7 to 8 // Method

Leads to

2 topics
  • Multi-Step Multiply & DivideRequired

    Multiplication & Division // Ages 7 to 8

    Solving mult/div problems requires computational skills

  • Written MultiplicationRequired

    Multiplication & Division // Ages 8 to 9

    Formal short multiplication extends Y3 written multiplication

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

For children aged 7–8 (UK Year 3, US Grade 3–4) learning to write and calculate two-digit × one-digit multiplication (and matching division) by partitioning via the distributive law. The core engine is splitting a number into tens and ones, multiplying each part, and recombining — e.g. 13×4 = (10×4)+(3×4) = 40+12 = 52. The area model / grid method makes the distributive law visible as the bridge from mental partitioning to the formal written method. Guidance progresses deliberately: mental partitioning → recorded grid → expanded then compact written layout, keeping the link explicit so the written method carries meaning rather than being memorised as steps.

Common misconceptions

  • Place-value error: treating the tens digit as ones (13×4 done as 1×4 + 3×4).
  • Forgetting to combine ALL partial products (computing 10×4 and 3×4 but not adding them).
  • Multiplying digit-by-digit without regard to their place value.
  • Not connecting the grid/area model to the numbers (seeing it as a separate trick).
  • Losing the link between the mental partition and the written record, so the written method becomes meaningless steps.

Useful representations

  • Area model / grid method (distributive law made visible)
  • Partitioning into tens and ones
  • Arrays scaled up to the area model
  • Expanded then compact written layout

Teaching practices

  • Anchor two-digit × one-digit in PARTITIONING and the distributive law: split the tens and ones, multiply each, recombine (13×4 = 10×4 + 3×4 = 40+12 = 52).
  • Use the area model / grid method as the visual of the distributive law — the array grown up — so the formal method later has meaning rather than being a rote procedure.
  • Progress deliberately from mental partitioning → recorded grid → compact written form, keeping the link between them explicit so children can fall back to meaning.
  • Use known table facts as the building blocks (10×4 and 3×4 must be secure) and connect × with ÷ (write the matching division statement).
  • Emphasise place value throughout — the '10' in 13 contributes 10×4=40, not 1×4 — to pre-empt the classic column-multiplication place-value error.

Activities to try

  1. 1

    Splitting a rectangle: area model for 13×4

    Why it works: A two-digit × one-digit product is the sum of the partial products from each place-value part; the '10' in 13 contributes 10×4 = 40 (not 1×4), because you must multiply the whole value of the tens, not just its digit.

    1. Draw or view a rectangle 13 units wide and 4 units tall and cut it with a vertical line at the boundary between the tens and the ones, so it becomes a 10×4 piece and a 3×4 piece.
    2. Work out the product for each piece (10×4 = 40 and 3×4 = 12) and write the number inside each region.
    3. Add the two partial products to find the whole area: 40 + 12 = 52.
    4. Line the grid up next to the expanded written form (40 + 12), saying which partial product matches which region of the grid. Then look at the compact column layout and explain how the 12 from 3×4 becomes 2 ones and a carried ten, which joins the 4 tens from 10×4 to make the 5 tens in 52.
    5. Repeat with 23×4: split into 20×4 = 80 and 3×4 = 12, then combine to 92.
  2. 2

    Moving the split line — the distributive law felt as area

    Why it works: The product is unchanged by how you partition — the distributive law — and partitioning by place value is chosen because it lands on known facts and matches the written numerals.

    1. Starting from a 13×4 rectangle already split at the tens/ones boundary, split the same rectangle (its width of 13) at a different point — for example into a 9×4 piece and a 4×4 piece (note 9 + 4 = 13, so the total width is unchanged) — and compute the two new partial products (36 and 16).
    2. Check that whatever point you split at, the two partial products still add to the same total (52).
    3. Discuss why the split at the tens/ones boundary is the most useful one: it uses known facts (10×4 and 3×4) and lines up with how the number is written.
    4. State the rule in words: splitting the rectangle into parts and adding the parts' areas always gives the whole area.
  3. 3

    Linking multiplication to division with known facts

    Why it works: Division can be reached through known multiplication facts and the same place-value partitioning, so multiplication and division are two views of the same relationship.

    1. Write the division that matches a multiplication fact you have made (e.g. from 10×4 = 40 write 40÷4 = 10).
    2. Solve 96 ÷ 8 by partitioning: split 96 into 80 + 16, divide each by 8 (80÷8 = 10, 16÷8 = 2) and recombine to get 12.
    3. Alternatively, ask 'what times 8 is near 96?' and use the known fact 8×12 = 96.
    4. Check the answer by multiplying back: 8×12 = 80 + 16 = 96.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Ma/KS2/Y3/MD/2

Math // Multiplication & Division

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