Square and cube numbers

CONCEPTUAL

Mathematics›Multiplication & Division|Ages 9—10|ID: mt_gxCIASSezX

Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)

Mastery Evidence

Identify 49 as 7² and explain that 7 × 7 = 49
Calculate 4³ = 64 and explain it means 4 × 4 × 4
List the first ten square numbers

Assessment Prompt

“Does [child] know that '5²' means 5 × 5 = 25 and '3³' means 3 × 3 × 3 = 27 — and can they work out other squared and cubed numbers?”

Prerequisites1

All times tables to 12×12
hardAges 8—9

Show full prerequisite tree

All times tables to 12×12 hard
Tables fluency to 12×12 is prerequisite to recognising square numbers
- Counting in 6s soft
  Counting in 6s/7s/9s supports learning those table facts
  - Skip Counting (4s, 8s, 50s, 100s) hard
    Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
    - 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
- Times tables (age 7+) hard
  All tables to 12×12 extends knowledge of 3/4/8 tables
  - 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

Unlocks2

Factors, multiples, and primes (age 9+)
hardAges 9—10
Precise Maths Vocabulary
softAges 9—10