Extending Table Patterns

Mastery Evidence

Notice that all multiples of 4 are even and use this to check answers
Derive 8 × 7 from 8 × 5 + 8 × 2 by spotting the pattern
Describe a rule for a growing pattern (e.g. 'add 50 each time') and use it to predict the next terms

Assessment Prompt

“When [child] is learning their times tables, do they use known facts to figure out ones they're not sure of — for example, using 5 × 6 = 30 to work out that 6 × 6 = 36?”

Prerequisites3

Generalising Patterns
hardAges 6—7
Skip Counting (4s, 8s, 50s, 100s)
softAges 7—8
Times tables (age 7+)
softAges 7—8

Show full prerequisite tree

Generalising Patterns hard
Age 7-8 repeated reasoning builds on age 6-7
- 10 More or 10 Less soft
  Mentally finding 10 more/less uses generalised repeated reasoning about place value
  - One More Each Time soft
    10 more/less generalises the concept of one more/one less to tens
    - How Many in Total? hard
      Understanding 'one more/one less' requires understanding that each number represents a quantity (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'
  - The two digits of a two-digit number hard
    Mentally finding 10 more/less requires understanding that the tens digit changes
    - 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
- Addition and subtraction within 20 soft
  Deriving facts within 20 from known facts (near doubles, make ten) exercises generalising from patterns
  - Number bonds to 9 hard
    Making-ten strategy requires knowing bonds to 10
    - Numbers up to 10 into pairs hard
      Making 10 is a specific application of decomposing numbers into pairs
      - Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        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'
  - Fluent adding and subtracting within 10 hard
    Strategies for within-20 calculation build on fluent within-10 knowledge
    - Number bonds to 9 hard
      Fluency within 10 requires knowing number bonds to 10
      - Numbers up to 10 into pairs hard
        Making 10 is a specific application of decomposing numbers into pairs
        
        Addition as combining or putting together two hard
        Decomposing numbers into pairs requires understanding addition as combining
        
        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'
    - Fluent adding and subtracting within 5 hard
      Fluency within 10 extends from fluency within 5
      - Addition as combining or putting together two hard
        Fluency with addition within 5 requires understanding addition as combining
        
        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
        Fluency with subtraction within 5 requires understanding subtraction as taking away
        
        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'
- Finding efficient methods hard
  Age 6-7 generalising from repeated reasoning builds on age 5-6 noticing repeated patterns
  - Counting in 2s soft
    Skip counting exercises recognising repeating calculation patterns
    - 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
  - One More Each Time soft
    The +1 pattern in counting is the earliest repeated reasoning
    - How Many in Total? hard
      Understanding 'one more/one less' requires understanding that each number represents a quantity (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
Skip counting patterns exercise generalising from repetition
- 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+) soft
Multiplication table patterns exercise repeated reasoning
- 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

Unlocks1

Times tables (age 8+)
hardAges 8—9