Math // Multiplication & Division

Long multiplication

Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using formal written methods including long multiplication; illustrate with area models

Ages
9 to 10
Type
Method
Builds on
2 topics
Leads to
3 topics
Standards
2 codes

Quick check

Can the learner work out something like '2,346 × 7' or '43 × 28' using the formal column method — setting it out carefully and working through all the steps?

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 2,347 × 6 using formal written layout
  • Calculate 34 × 27 using long multiplication
  • Draw an area model for 45 × 23 and connect to the written method

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

2 topics
  • Written MultiplicationRequired

    Multiplication & Division // Ages 8 to 9

    2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit

  • Area and the distributive propertyHelpful

    Measurement // Ages 8 to 9

    Area models for distributive property support understanding long multiplication layout

You are here

Long multiplication

Ages 9 to 10 // Method

Leads to

3 topics
  • Division with remaindersRequired

    Multiplication & Division // Ages 9 to 10

    Must have formal multiplication method before solving multi-step problems

  • Long multiplication (age 10+)Required

    Multiplication & Division // Ages 10 to 11

    Long multiplication 4×2 extends Y5 multiplication up to 4×1 and 2×2

  • Fractions on a number line (age 9+)Helpful

    Mathematical Thinking // Ages 9 to 10

    Long multiplication with area models connects situations to visual and symbolic representations

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 9–10 year-olds learning formal long multiplication (up to 4-digit × 1-digit and 2-digit × 2-digit), anchor the written algorithm in the area model so the two partial-product rows and the placeholder zero become meaningful place-value facts rather than memorised rules. The central objective: the child sees that the second partial-product row is '×20 (tens)', not '×2', and that the four sub-rectangles of an area model sum to the same total as the two added partial products. Estimation by rounding both factors bounds the answer and catches magnitude slips.

Common misconceptions

  • Omitting the placeholder zero on the second partial product (treating ×20 as ×2).
  • Multiplying only by the ones digit of the two-digit multiplier and forgetting the tens.
  • Carrying errors across several columns, or adding carries into the wrong place.
  • Misaligning partial products when adding them.
  • Not connecting the algorithm to the area model, so errors can't be self-diagnosed.

Useful representations

  • Area/grid model with four sub-rectangles (the home of the partial products)
  • Expanded partial-products layout bridging grid to compact form
  • Compact long-multiplication layout with the placeholder zero
  • Estimation (rounding both factors) to bound the product

Teaching practices

  • Anchor long multiplication in the area model: 2-digit×2-digit as four sub-rectangles, so the two partial-product rows and the shift are seen as ×ones and ×tens.
  • Make the placeholder zero meaningful — the second row is ×20 (tens), not ×2 — rather than a rule to 'put a zero down'.
  • Estimate first by rounding both factors to bound the answer and catch magnitude errors.
  • Progress grid method → expanded partial products → compact long multiplication, keeping the area link visible.
  • Check with the inverse or by comparing to the estimate; watch carrying across multiple columns.

Activities to try

  1. 1

    Bridge the area model to the written method (34 × 27)

    Why it works: The second partial-product row is shifted and carries a placeholder zero because it is ×20 (tens), not ×2; the four area sub-rectangles are exactly the same quantities as the two written partial products broken apart, so the algorithm and the area model are two views of the same calculation.

    1. Estimate first by rounding both factors: 34 × 27 ≈ 30 × 30 = 900, and keep this estimate in view as you work.
    2. Draw an area model for 34 × 27 and partition it into four labelled sub-rectangles: 30×20, 30×7, 4×20, 4×7.
    3. Compute each sub-rectangle: 30×20 = 600, 30×7 = 210, 4×20 = 80, 4×7 = 28.
    4. Alongside, set up the long-multiplication layout and compute the first partial product 34 × 7 = 238 (which is the 30×7 and 4×7 tiles: 210 + 28).
    5. Compute the second partial product 34 × 20 = 680, writing a 0 in the ones place FIRST because this whole row is ×20, i.e. tens (this is the 30×20 and 4×20 tiles: 600 + 80).
  2. 2

    Secure 4-digit × 1-digit short multiplication (2,347 × 6)

    Why it works: Multiplying a multi-digit number by a single digit requires multiplying every digit and correctly handling carries across several columns; estimation bounds the magnitude.

    1. Estimate first: 2,347 × 6 ≈ 2,000 × 6 = 12,000 (or 2,300 × 6 = 13,800 for a tighter bound).
    2. Compute 2,347 × 6 in formal written layout, carrying across each column: 7×6=42 (write 2 carry 4), 4×6=24 plus 4 = 28 (write 8 carry 2), 3×6=18 plus 2 = 20 (write 0 carry 2), 2×6=12 plus 2 = 14.
    3. Read off the answer 14,082 and check it against your estimate.
  3. 3

    Map each written partial product to its area region (45 × 23)

    Why it works: Each written partial product is a sum of two area sub-rectangles, so a child who can map regions to partials understands WHY there are two rows rather than following steps by rote.

    1. Draw an area model for 45 × 23 with four regions: 40×20, 40×3, 5×20, 5×3.
    2. Compute each region: 40×20 = 800, 40×3 = 120, 5×20 = 100, 5×3 = 15.
    3. Add all four regions to get the product: 800 + 120 + 100 + 15 = 1,035.
    4. Now compute 45 × 23 by long multiplication and point to which area regions make up each partial product: 45×3 = 135 (= 120 + 15) and 45×20 = 900 (= 800 + 100).
    5. Confirm the two partial products 135 + 900 = 1,035 equal the sum of the four area regions.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
Common Core State Standards for Mathematics
4.NBT.5
The national curriculum in England: Key stages 1 and 2 framework document
Ma5/2.3d

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