Fluent multiplication and division facts

PROCEDURAL

Mathematics›Multiplication & Division|Ages 8—9|ID: mt_WX30dzi4dt

Fluently multiply and divide within 100 using strategies such as the relationship between multiplication and division

Mastery Evidence

Answer any single-digit multiplication fact within 3 seconds
Answer any related division fact within 3 seconds
Use known facts to derive unknown facts (e.g. 9 × 7 from 10 × 7 − 7)

Assessment Prompt

“Can [child] answer any times table fact up to 10 × 10 quickly — and also give the related division facts, like '63 ÷ 9 = 7' from knowing '9 × 7 = 63'?”

Curriculum Standards1 alignment

3.OA.7Common Core State Standards for Mathematics

Fluently multiply and divide within 100

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Prerequisites3

Division as Unknown Factor
softAges 8—9
Times tables
hardAges 6—7
Times tables (age 7+)
hardAges 7—8

Show full prerequisite tree

Division as Unknown Factor soft
Using mult/div relationship as strategy supports fluency
- What Multiplication Means hard
  Connecting division to multiplication requires understanding products
  - Arrays for multiplication (age 7+) hard
    Extends array-based repeated addition to formal multiplication interpretation
    - Arrays for multiplication hard
      Rectangular arrays with repeated addition extends array representation from Y2
      - Division as equal sharing hard
        Using arrays for division requires understanding division as grouping
        
        Subtraction as taking away or separating hard
        Division as equal sharing/grouping requires understanding subtraction as taking away/separating
        
        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'
      - Multiplication as repeated addition hard
        Using arrays requires understanding what multiplication means
        
        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'
    - Multiplication as repeated addition hard
      Expressing array totals as sums of equal addends requires understanding multiplication as repeated addition
      - 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'
  - Multiplication as repeated addition hard
    Interpreting products formalises repeated addition/equal groups from Y1
    - 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'
- What Division Means hard
  Seeing division as unknown-factor requires understanding division first
  - Division as equal sharing hard
    Interpreting quotients formalises equal sharing/grouping from Y1
    - Subtraction as taking away or separating hard
      Division as equal sharing/grouping requires understanding subtraction as taking away/separating
      - 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'
Times tables hard
Fluency within 100 builds on knowing 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'
Times tables (age 7+) hard
Fluency within 100 builds on knowing 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

Unlocks3

Multiplying by Tens
hardAges 8—9
Arrays for multiplication (age 9+)
hardAges 9—10
Patterns in Times Tables
hardAges 8—9