Fluent addition and subtraction

PROCEDURAL

Mathematics›Addition & Subtraction|Ages 6—7|ID: mt_3e_PQxwC12

Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

Mastery Evidence

Rapidly recall 7 + 8 = 15 and 15 − 8 = 7
Use 6 + 4 = 10 to derive 60 + 40 = 100
Derive 35 + 5 = 40 from knowledge that 5 + 5 = 10

Assessment Prompt

“Can [child] quickly recall facts like '9 + 7 = 16' and '16 − 7 = 9', and use those to help work out bigger sums like '90 + 70'?”

Curriculum Standards1 alignment

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

Recall addition and subtraction facts

Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100.

Mathematics · Key Stage 1

Prerequisites2

Addition and subtraction within 20
hardAges 6—7
The two digits of a two-digit number
softAges 6—7

Show full prerequisite tree

Addition and subtraction within 20 hard
Fluent recall of facts to 20 builds from strategic calculation within 20
- 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'
The two digits of a two-digit number soft
Deriving facts to 100 benefits from place value understanding
- 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

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