Written Multiplication & Division

PROCEDURAL

Mathematics›Multiplication & Division|Ages 7—8|ID: mt_DyGBW3ZHh3

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

Mastery Evidence

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

Assessment Prompt

“Can [child] 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?”

Curriculum Standards1 alignment

Ma/KS2/Y3/MD/2The national curriculum in England

Calculate multiplication/division statements

write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods

Mathematics · Key Stage 2

Prerequisites3

The three digits of a three-digit number
softAges 7—8
Times tables (age 7+)
hardAges 7—8
Reading ×, ÷, and = Symbols
hardAges 6—7

Show full prerequisite tree

The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- A Hundred Is Ten Tens hard
  Three-digit place value requires understanding 100 as a unit
  - A Ten Is Ten Ones hard
    100 as ten tens extends understanding of 10 as ten ones
    - The teen numbers hard
      Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
      - How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        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'
      - Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals 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'
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Sitting and holding a pencil soft
        Same motor skills for digit formation
  - The two digits of a two-digit number hard
    Must understand two-digit place value before extending to hundreds
    - A Ten Is Ten Ones hard
      Understanding tens and ones place value requires the concept of 10 as a bundle
      - The teen numbers hard
        Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
        
        How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        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'
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals 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'
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Sitting and holding a pencil soft
        Same motor skills for digit formation
    - The teen numbers hard
      General two-digit place value extends from understanding teen number composition
      - How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        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'
      - Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals 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'
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Sitting and holding a pencil soft
        Same motor skills for digit formation
- The two digits of a two-digit number hard
  Three-digit PV extends two-digit PV (tens and ones)
  - A Ten Is Ten Ones hard
    Understanding tens and ones place value requires the concept of 10 as a bundle
    - The teen numbers hard
      Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
      - How Many in Total? hard
        Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
        
        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'
      - Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals 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'
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Sitting and holding a pencil soft
        Same motor skills for digit formation
  - The teen numbers hard
    General two-digit place value extends from understanding teen number composition
    - How Many in Total? hard
      Understanding tens-and-ones composition requires cardinality — knowing numbers represent quantities
      - 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'
    - Reading and writing numbers to 20 hard
      Composing/decomposing teen numbers requires reading and writing those numerals
      - How Many in Total? hard
        Reading/writing numerals 0–20 requires understanding that numerals 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'
      - Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        Sitting and holding a pencil soft
        Same motor skills for digit formation
Times tables (age 7+) hard
Written multiplication/division requires known table facts
- Times tables hard
  3, 4, 8 times tables build on known 2, 5, 10 tables
  - Counting in 2s hard
    Times tables for 2, 5, 10 build on skip counting in 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
  - Multiplication as repeated addition hard
    Recalling times table facts requires understanding multiplication as repeated addition/grouping
    - 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'
- Skip Counting (4s, 8s, 50s, 100s) soft
  Counting in 4s and 8s supports learning those table facts
  - Counting in 2s hard
    Counting in 4s and 8s extends prior skip counting in 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
Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading +, −, and = symbols soft
  Reading × and ÷ symbols parallels reading + and − symbols
  - Reading and writing numbers to 20 hard
    Writing number sentences requires reading and writing numerals
    - How Many in Total? hard
      Reading/writing numerals 0–20 requires understanding that numerals 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'
    - Writing digits 0-9 hard
      Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
      - Sitting and holding a pencil soft
        Same motor skills for digit formation
  - Addition as combining or putting together two hard
    Reading/writing the + symbol requires understanding what addition means
    - 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'
  - Subtraction as taking away or separating hard
    Reading/writing the − symbol requires understanding what subtraction means
    - 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'
- Division as equal sharing hard
  Writing ÷ sentences requires understanding division
  - 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
  Writing × sentences 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'

Unlocks2

Written Multiplication
hardAges 8—9
Multi-Step Multiply & Divide
hardAges 7—8