Commutative Multiplication

CONCEPTUAL

Mathematics›Multiplication & Division|Ages 6—7|ID: mt_C9ZfT-4cgn

Understand and apply the commutative property of multiplication and recognise that division is not commutative

Mastery Evidence

Explain that 3 × 5 = 5 × 3 and show this with an array rotated
Use commutativity to choose the easier calculation
Demonstrate that 12 ÷ 3 ≠ 3 ÷ 12

Assessment Prompt

“Does [child] know that 4 × 7 gives the same answer as 7 × 4 — so they can choose whichever order is easier to remember from their times tables?”

Curriculum Standards1 alignment

Maths/Y2/MD/3The national curriculum in England

Commutativity of multiplication

Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot.

Mathematics · Key Stage 1

Prerequisites2

Arrays for multiplication
softAges 5—6
Multiplication as repeated addition
hardAges 5—6

Show full prerequisite tree

Arrays for multiplication soft
Arrays help demonstrate commutativity (rotate the array)
- Division as equal sharing hard
  Using arrays for division requires understanding division as grouping
  - Subtraction as taking away or separating hard
    Division as equal sharing/grouping requires understanding subtraction as taking away/separating
    - How Many in Total? hard
      Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
      - One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Multiplication as repeated addition hard
  Using arrays requires understanding what multiplication means
  - Counting in 2s soft
    Skip counting supports understanding equal groups (2s, 5s, 10s)
    - Rote counting to 100 hard
      Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
      - One-to-one counting hard
        One-to-one correspondence requires knowing the number name sequence
  - Addition as combining or putting together two hard
    Multiplication as repeated addition requires understanding addition as combining groups
    - How Many in Total? hard
      Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
      - One-to-one counting hard
        Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
Multiplication as repeated addition hard
Commutativity of multiplication requires understanding multiplication
- Counting in 2s soft
  Skip counting supports understanding equal groups (2s, 5s, 10s)
  - Rote counting to 100 hard
    Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
    - One-to-one counting hard
      One-to-one correspondence requires knowing the number name sequence
- Addition as combining or putting together two hard
  Multiplication as repeated addition requires understanding addition as combining groups
  - How Many in Total? hard
    Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
    - One-to-one counting hard
      Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

Unlocks1

Properties of Operations
hardAges 8—9