Fluent adding and subtracting within 20

PROCEDURAL

Mathematics›Addition & Subtraction|Ages 7—8|ID: mt__t4afSyZRm

Fluently add and subtract within 20 using mental strategies; know from memory all sums of two one-digit numbers

Mastery Evidence

Answer any single-digit addition fact within 3 seconds
Recall subtraction facts within 20 from memory (e.g. 15 − 8 = 7)
Use known addition facts to derive related subtraction facts rapidly

Assessment Prompt

“Can [child] instantly recall all the single-digit addition facts — like '7 + 8 = 15' — without needing to count or think for more than a second?”

Curriculum Standards1 alignment

2.OA.2Common Core State Standards for Mathematics

Fluently add and subtract within 20

Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

Operations and Algebraic Thinking

Prerequisites2

Addition and subtraction within 20
hardAges 6—7
Fluent adding and subtracting within 10
hardAges 6—7

Show full prerequisite tree

Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting 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'
Fluent adding and subtracting within 10 hard
Fluency within 20 builds on fluency within 10
- 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'

Unlocks1

Fluent adding and subtracting within 100
hardAges 7—8