Multiplication and Division Word Problems

PROCEDURAL

Mathematics›Multiplication & Division|Ages 8—9|ID: mt_Zdv-b-iW5K

Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities

Mastery Evidence

Solve an equal-groups word problem using multiplication
Solve a measurement division problem (e.g. 'How many 4-cm pieces from a 28-cm ribbon?')
Solve an array/area word problem using multiplication

Assessment Prompt

“If you tell [child] 'there are 7 boxes with 9 pencils in each — how many pencils?', can they recognise it as a multiplication problem and solve it correctly?”

Curriculum Standards1 alignment

3.OA.3Common Core State Standards for Mathematics

Solve multiplication and division word problems

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Prerequisites2

What Multiplication Means
hardAges 8—9
What Division Means
hardAges 8—9

Show full prerequisite tree

What Multiplication Means hard
Word problems require understanding what products mean
- 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
Word problems require understanding what quotients mean
- 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'

Unlocks1

Multiplicative Comparison
hardAges 9—10