Fluent adding and subtracting within 100

PROCEDURAL

Mathematics›Addition & Subtraction|Ages 7—8|ID: mt_cChv2j_-Da

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction

Mastery Evidence

Add two-digit numbers within 100 efficiently (e.g. 46 + 37 using place-value partitioning)
Subtract two-digit numbers within 100 fluently (e.g. 83 − 25)
Choose between strategies (decomposing, compensating, using known facts) based on the numbers involved

Assessment Prompt

“Can [child] reliably add or subtract two-digit numbers like '68 + 27' or '91 − 45', choosing the best strategy for each problem?”

Curriculum Standards1 alignment

2.NBT.5Common Core State Standards for Mathematics

Fluently add and subtract within 100

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Number and Operations in Base Ten

Prerequisites2

Adding within 100
hardAges 6—7
Fluent adding and subtracting within 20
hardAges 7—8

Show full prerequisite tree

Adding within 100 hard
Fluency within 100 builds on strategy-based adding within 100
- Addition and subtraction within 20 hard
  Adding within 100 extends within-20 strategies to larger numbers
  - 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 hard
  Adding within 100 using PV requires understanding 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
Fluent adding and subtracting within 20 hard
Fluency within 100 requires fluent single-digit facts
- 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'

Unlocks9

Numbers on a number line
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Halves and quarters (age 7+)
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Addition and subtraction word problems
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Addition and subtraction within 1000
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Mental addition and subtraction (age 7+)
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Adding and subtracting (age 7+)
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Adding numbers
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Two-Step Word Problems
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Addition and subtraction strategies (age 7+)
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