Fractions of a whole (age 10+)

CONCEPTUAL

Mathematics›Fractions|Ages 10—11|ID: mt_4Km38F4L-6

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers

Mastery Evidence

Explain that 3/4 means 3 ÷ 4 and verify by showing 3/4 × 4 = 3
Solve: '9 people share a 50-pound sack equally — how many pounds each?' and express the answer as 5 5/9
Use a visual model to show that sharing 3 wholes among 4 people gives each person 3/4

Assessment Prompt

“If [child] shares 3 pizzas equally among 4 friends, can they work out what fraction each person gets — and explain why 3 ÷ 4 gives the same answer as 3/4?”

Prerequisites2

Multiplying fractions
hardAges 9—10
Division with remainders (age 10+)
softAges 10—11

Show full prerequisite tree

Multiplying fractions hard
Understanding fraction as division builds on fraction × whole number (inverse reasoning)
- Understanding fractions (age 9+) hard
  a/b as sum of 1/b is prerequisite to understanding a/b as multiple of 1/b
  - Fractions of a whole hard
    Understanding a/b as a parts of size 1/b is prerequisite to understanding a/b as sum of 1/b
    - Fractions of amounts hard
      Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
      - Finding halves and quarters (age 5+) hard
        Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
        
        What Is a Half? hard
        Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        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'
      - What Is a Half? hard
        Working with fractions extends from Y1 understanding of halves
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        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'
      - Division as equal sharing soft
        Finding fractions of quantities uses equal sharing (division)
        
        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'
      - Fraction Notation hard
        Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
    - Fraction Notation hard
      Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
    - Splitting shapes into equal parts (age 7+) hard
      Partition into equal shares is prerequisite to understanding unit fractions
      - Decomposing a shape into more equal shares hard
        Understanding equal shares of different shapes requires concept of more shares = smaller
        
        Halves & Quarters of Shapes hard
        Comparing share sizes requires experience partitioning into halves and quarters
        
        Finding halves and quarters (age 5+) hard
        Partitioning into fourths/quarters extends from Y1 understanding of quarters
        
        What Is a Half? hard
        Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        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)
        
        What Is a Half? hard
        Partitioning shapes into halves extends from Y1 understanding of halves
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        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'
      - Halves & Quarters of Shapes hard
        Extends partitioning from halves/fourths to include thirds
        
        Finding halves and quarters (age 5+) hard
        Partitioning into fourths/quarters extends from Y1 understanding of quarters
        
        What Is a Half? hard
        Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        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'
        
        What Is a Half? hard
        Partitioning shapes into halves extends from Y1 understanding of halves
        
        Division as equal sharing hard
        Finding a half requires equal sharing into 2 groups — a division concept
        
        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'
Division with remainders (age 10+) soft
Division leading to fractions connects to long division skills
- Arrays for multiplication (age 9+) hard
  Long division by 2-digit extends Y5 short division by 1-digit
  - Division as Unknown Factor hard
    Understanding division as unknown-factor supports short division strategy
    - 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'
  - Fluent multiplication and division facts hard
    Fluent ×÷ within 100 is prerequisite to short division of larger numbers
    - 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
- Long multiplication (age 10+) soft
  Checking division with multiplication requires fluent multiplication
  - Long multiplication hard
    Long multiplication 4×2 extends Y5 multiplication up to 4×1 and 2×2
    - Written Multiplication hard
      2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
      - Written Multiplication & Division hard
        Formal short multiplication extends Y3 written multiplication
        
        The three digits of a three-digit number soft
        Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
        
        A Hundred Is Ten Tens hard
        Three-digit place value requires understanding 100 as a unit
        
        A Ten Is Ten Ones hard
        100 as ten tens extends understanding of 10 as ten ones
        
        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)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        The two digits of a two-digit number hard
        Must understand two-digit place value before extending to hundreds
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        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)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        The two digits of a two-digit number hard
        Three-digit PV extends two-digit PV (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)
        
        Writing digits 0-9 hard
        Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
        
        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
        
        Times tables (age 7+) hard
        Written multiplication/division requires known table facts
        
        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
        
        Reading ×, ÷, and = Symbols hard
        Writing multiplication/division statements requires fluency with symbols
        
        Reading +, −, and = symbols soft
        Reading × and ÷ symbols parallels reading + and − symbols
        
        Reading and writing numbers to 20 hard
        Writing number sentences requires reading and writing 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
        
        Addition as combining or putting together two hard
        Reading/writing the + symbol requires understanding what addition means
        
        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
        Reading/writing the − symbol requires understanding what subtraction means
        
        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'
        
        Division as equal sharing hard
        Writing ÷ sentences requires understanding division
        
        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
        Writing × sentences requires understanding multiplication
        
        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'
      - All times tables to 12×12 hard
        Written multiplication requires fluent table facts
        
        Counting in 6s soft
        Counting in 6s/7s/9s supports learning those table facts
        
        Skip Counting (4s, 8s, 50s, 100s) hard
        Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
        
        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
        
        Times tables (age 7+) hard
        All tables to 12×12 extends knowledge of 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
    - Area and the distributive property soft
      Area models for distributive property support understanding long multiplication layout
      - Understanding angles (age 8+) hard
        Must multiply side lengths for area before using area models for distributive property
        
        Area by Tiling hard
        Must see tiling→multiplication connection before computing area via side lengths
        
        Area (age 8+) hard
        Counting unit squares is prerequisite to connecting tiling to multiplication
        
        Understanding Area hard
        Must understand unit squares and area concept before measuring by counting
        
        Measuring length (age 7+) soft
        Length measurement experience supports understanding area as a 2D measurement
        
        Measuring length (age 6+) hard
        Using standard measurement tools extends measuring with non-standard units
        
        Measuring length and height (age 5+) hard
        Measuring with iterated units extends Y1 beginning to measure length
        
        Measuring length soft
        Measuring with units benefits from ability to order and compare lengths
        
        Choosing measurement units soft
        Choosing appropriate tools builds on choosing appropriate units
        
        Capacity and volume hard
        Using standard units for capacity extends from beginning to measure capacity
        
        Measuring length and height (age 5+) hard
        Using standard units for length extends from beginning to measure length
        
        Measuring mass and weight hard
        Using standard units for mass extends from beginning to measure mass

Unlocks3

Dividing by Fractions
softAges 10—11
Decimals and fractions (age 10+)
hardAges 10—11
Dividing fractions (unit fractions)
hardAges 10—11