Math // Multiplication & Division

Written Multiplication

Multiply two-digit and three-digit numbers by a one-digit number using formal written layout

Ages
8 to 9
Type
Method
Builds on
2 topics
Leads to
2 topics
Standards
1 code

Quick check

Can the learner work out '347 × 6' by setting it out formally in a column — multiplying each digit separately and carrying where needed?

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.
  • Set out and solve 47 × 6 using short multiplication
  • Set out and solve 234 × 5 using short multiplication with carrying
  • Check the answer using estimation (e.g. 234 × 5 ≈ 200 × 5 = 1000)

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

You are here

Written Multiplication

Ages 8 to 9 // Method

Leads to

2 topics
  • Multiply & Add ProblemsRequired

    Multiplication & Division // Ages 8 to 9

    Problems require formal written multiplication skills

  • Long multiplicationRequired

    Multiplication & Division // Ages 9 to 10

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

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 ages 8–9, build formal short (columnar) multiplication of 2- and 3-digit numbers by a 1-digit number ON TOP of the area/grid model so that 'carrying' is understood as regrouping place value, not a ritual. Estimate first to bound the answer, work partial products in columns with the carry recorded, then connect the compact answer back to the sum of the area sub-products. Core examples: 47×6=282 and 234×5=1170.

Common misconceptions

  • Treating carrying as a meaningless ritual and misplacing or forgetting the carried digit.
  • Multiplying only the ones and 'adding' the tens digit rather than multiplying it (place-value error): 47×6 giving 42+... wrong.
  • Aligning digits incorrectly or dropping a place, producing answers off by a factor of 10.
  • Not connecting the compact method to the area model, so errors can't be self-diagnosed.
  • Skipping estimation, so a wildly wrong magnitude goes unnoticed.

Useful representations

  • Area/grid model (partition each factor by place value) — the conceptual home of short multiplication
  • Place-value columns with counters — makes carrying = regrouping visible
  • The compact columnar layout with the carry digit recorded
  • Estimation on a number line / rounding — to bound the answer

Teaching practices

  • Build the algorithm from the area/grid method: 47×6 as 40×6 + 7×6 laid out as two sub-rectangles, THEN compress to the columnar form so 'carrying' is understood as regrouping, not a rule.
  • Require an estimate before calculating (rounding a factor) to set an expected magnitude and catch place-value slips.
  • Make the meaning of the carried digit explicit — it is regrouped tens/hundreds, written and then added in — not a mysterious little number.
  • Use place-value counters/columns alongside the written digits during the transition so each written step maps to a concrete regrouping.
  • Practise with numbers that force carrying in different columns, and check answers against the estimate and via the inverse.

Activities to try

  1. 1

    Method bridge: area model beside the columns

    Why it works: The carried digits are the area model regrouped and folded into columns — multiply the digit first, THEN add the carry, keeping one digit per column.

    1. Estimate first by rounding a factor, e.g. for 234×5 use ≈200×5=1000 (or ≈50×6=300 for 47×6), and write the estimate down before calculating.
    2. Draw an area/grid model splitting a factor by place value: for 234×5 make three sub-rectangles 200×5, 30×5 and 4×5; for 47×6 make 40×6 and 7×6.
    3. Set out the same calculation in a short-multiplication column layout right next to the area model.
    4. Work each partial product in the columns in lockstep with the matching sub-rectangle. For 234×5: 5×4=20 → write 0 in the ones and regroup 2 tens; 5×3=15, +2=17 → write 7 in the tens, regroup 1 hundred; 5×2=10, +1=11 → write 1 in the hundreds and 1 in the thousands, giving 1170.
    5. Say aloud what each carried digit means, e.g. 'the little 2 is 2 regrouped tens'.
  2. 2

    Make the carry visible with place-value counters

    Why it works: Carrying is the physical act of regrouping ten of one unit into one of the next place; the written carry records that move.

    1. Under the column headings, lay out the first factor with place-value counters as many times as the one-digit multiplier says (e.g. 6 groups of 47 for 47×6), so the counters show the whole product.
    2. As you compute each partial product, physically move a regrouped ten (or hundred) one column to the left to represent the carried digit.
    3. Match each counter move to the little digit you write above the next column.
    4. Narrate: 'ten ones regroup into one ten, so the ten moves left.'
  3. 3

    Annotated worked example as a reference anchor

    Why it works: Every column in the compact method has a home in the area model, and every carry names a specific regrouped place value.

    1. Study a worked 234×5 with the area model above and the matching short-multiplication below.
    2. For each column, read (or reveal) the explanation of the partial product and what its carry stands for, e.g. 'this is 2 regrouped tens' (from 5×4=20) and 'this is 1 regrouped hundred' (from 5×3=15, +2=17).
    3. Match each area sub-rectangle to the column it feeds into.

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/Y4/MD/4

Math // Multiplication & Division

More in Multiplication & Division

All 57 topics