Decimal place value

PROCEDURAL

Mathematics›Measurement|Ages 10—11|ID: mt_2VpdPjvewx

Convert among different-sized standard measurement units within a given system (e.g. 5 cm to 0.05 m) using decimal notation to up to three decimal places; convert between smaller and larger units of length, mass, volume, and time

Mastery Evidence

Convert 3,250 g to 3.25 kg using decimal notation
Convert 0.45 km to 450 m
Explain the relationship between mm, cm, m, and km using powers of 10

Assessment Prompt

“If [child] needs to convert 5 cm to metres and write the answer as a decimal, can they do it — and also convert 2.45 kg into grams?”

Prerequisites2

Multiplying and dividing (age 10+)
hardAges 10—11
Converting measurement units (age 9+)
hardAges 9—10

Show full prerequisite tree

Multiplying and dividing (age 10+) hard
Converting to 3dp requires ×÷ by 10/100/1000 skills
- Multiplying and dividing hard
  ×÷ by 10/100/1000 to 3dp extends Y5 ×÷ by 10/100/1000
  - Dividing by 10 and 100 hard
    Dividing by 10/100 (Y4 fractions context) is prerequisite to ×÷ by 10/100/1000 with decimals
    - Tenths (age 8+) hard
      Must understand hundredths to identify digit values when dividing by 10/100
      - Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        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)
        
        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
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        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
    - Decimal equivalents of tenths and hundredths hard
      Must know decimal notation to express results of dividing by 10/100
      - Tenths (age 8+) hard
        Must understand hundredths before writing decimal equivalents
        
        Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        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
        
        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)
        
        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
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        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
      - Decimal & Percent Notation hard
        Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
  - Place Value × 10 Pattern hard
    ×10 place-value relationship is prerequisite to ×÷ by powers of 10
    - Place value of each digit hard
      Four-digit place value is prerequisite to understanding ×10 relationship between places
      - The three digits of a three-digit number hard
        Four-digit place value extends three-digit place value
        
        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)
        
        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 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
        
        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
        
        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)
        
        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
- Reading Decimal Places hard
  Understanding digit shifting requires knowing what each decimal place represents
  - Reading and writing numbers (age 10+) hard
    Identifying digit value in 3dp numbers requires reading decimals to thousandths
    - Comparing Decimals hard
      Compare decimals to thousandths extends Y5 decimal comparison
      - Decimal place value (age 8+) hard
        Comparing decimals to 2dp (Y4) is prerequisite to comparing to 3dp
        
        Decimal equivalents of tenths and hundredths hard
        Must understand decimal notation to compare decimals
        
        Tenths (age 8+) hard
        Must understand hundredths before writing decimal equivalents
        
        Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        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
        
        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
        
        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
        
        Fraction Notation hard
        Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        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
        
        Decimal & Percent Notation hard
        Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
      - Tenths (age 9+) soft
        Thousandths understanding supports comparing decimals to 3dp
        
        Decimals for Tenths & Hundredths hard
        Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
        
        Converting tenths to hundredths hard
        10ths as 100ths supports using decimal notation for both
        
        Tenths (age 8+) hard
        Understanding hundredths is prerequisite to working with 10ths and 100ths together
        
        Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        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
        Working with fractions extends from Y1 understanding of halves
        
        Division as equal sharing soft
        Finding fractions of quantities uses equal sharing (division)
        
        Fraction Notation hard
        Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        Rote counting to 100 hard
        Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
        
        Equivalent fractions (age 9+) hard
        Generating equivalent fractions supports converting 10ths to 100ths
        
        Equivalent fractions on a number line hard
        Understanding equivalence conceptually is prerequisite to explaining algebraically
        
        Equivalent fractions hard
        Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
        
        Fractions on a number line soft
        Number line supports seeing equivalent fractions as the same point
        
        Understanding fractions hard
        Extends equivalence of 2/4 and 1/2 to broader equivalent fractions
        
        Fraction Notation hard
        Recognising and showing equivalent fractions requires that vocabulary
        
        Fractions of a whole hard
        Must understand unit fractions to reason about equivalence
        
        Fractions of amounts hard
        Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
        
        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
        
        Fractions on a number line (age 8+) hard
        Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
        
        Fractions on a number line hard
        Prior number-line fraction experience feeds into formal unit-fraction placement
        
        Fractions of a whole hard
        Must understand unit fractions before placing them on number line
        
        Equivalent fractions (age 8+) hard
        Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
        
        Equivalent fractions on a number line hard
        Must understand equivalence before generating equivalent fractions
        
        Equivalent fractions hard
        Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
        
        Fractions of a whole hard
        Must understand unit fractions to reason about equivalence
        
        Fractions on a number line (age 8+) hard
        Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
        
        Decimal equivalents of tenths and hundredths hard
        Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
        
        Tenths (age 8+) hard
        Must understand hundredths before writing decimal equivalents
        
        Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        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
        Working with fractions extends from Y1 understanding of halves
        
        Division as equal sharing soft
        Finding fractions of quantities uses equal sharing (division)
        
        Fraction Notation hard
        Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        Rote counting to 100 hard
        Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
        
        Decimal & Percent Notation hard
        Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
        
        Decimal & Percent Notation hard
        Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
    - Place Value × 10 and ÷ 10 soft
      Place-value understanding supports decimal comparison reasoning
      - Tenths (age 9+) soft
        Understanding 1/10 of requires familiarity with thousandths
        
        Decimals for Tenths & Hundredths hard
        Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
        
        Converting tenths to hundredths hard
        10ths as 100ths supports using decimal notation for both
        
        Tenths (age 8+) hard
        Understanding hundredths is prerequisite to working with 10ths and 100ths together
        
        Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        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
        Working with fractions extends from Y1 understanding of halves
        
        Division as equal sharing soft
        Finding fractions of quantities uses equal sharing (division)
        
        Fraction Notation hard
        Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        Rote counting to 100 hard
        Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
        
        Equivalent fractions (age 9+) hard
        Generating equivalent fractions supports converting 10ths to 100ths
        
        Equivalent fractions on a number line hard
        Understanding equivalence conceptually is prerequisite to explaining algebraically
        
        Equivalent fractions hard
        Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
        
        Fractions on a number line soft
        Number line supports seeing equivalent fractions as the same point
        
        Understanding fractions hard
        Extends equivalence of 2/4 and 1/2 to broader equivalent fractions
        
        Fraction Notation hard
        Recognising and showing equivalent fractions requires that vocabulary
        
        Fractions of a whole hard
        Must understand unit fractions to reason about equivalence
        
        Fractions of amounts hard
        Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
        
        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
        
        Fractions on a number line (age 8+) hard
        Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
        
        Fractions on a number line hard
        Prior number-line fraction experience feeds into formal unit-fraction placement
        
        Fractions of a whole hard
        Must understand unit fractions before placing them on number line
        
        Equivalent fractions (age 8+) hard
        Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
        
        Equivalent fractions on a number line hard
        Must understand equivalence before generating equivalent fractions
        
        Equivalent fractions hard
        Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
        
        Fractions of a whole hard
        Must understand unit fractions to reason about equivalence
        
        Fractions on a number line (age 8+) hard
        Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
        
        Decimal equivalents of tenths and hundredths hard
        Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
        
        Tenths (age 8+) hard
        Must understand hundredths before writing decimal equivalents
        
        Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        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
        Working with fractions extends from Y1 understanding of halves
        
        Division as equal sharing soft
        Finding fractions of quantities uses equal sharing (division)
        
        Fraction Notation hard
        Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        Rote counting to 100 hard
        Skip counting in 2s, 5s, 10s requires fluent rote counting by ones first
        
        Decimal & Percent Notation hard
        Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
        
        Decimal & Percent Notation hard
        Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
      - Place Value × 10 Pattern hard
        ×10 both directions extends Y5 ×10 relationship
        
        Place value of each digit hard
        Four-digit place value is prerequisite to understanding ×10 relationship between places
        
        The three digits of a three-digit number hard
        Four-digit place value extends three-digit place value
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        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'
        
        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
        
        Reading and writing numbers to 20 hard
        Composing/decomposing teen numbers requires reading and writing those numerals
        
        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
        
        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)
    - Tenths (age 9+) hard
      Reading/writing decimals to thousandths requires understanding thousandths place
      - Decimals for Tenths & Hundredths hard
        Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
        
        Converting tenths to hundredths hard
        10ths as 100ths supports using decimal notation for both
        
        Tenths (age 8+) hard
        Understanding hundredths is prerequisite to working with 10ths and 100ths together
        
        Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        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
        
        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
        
        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
        
        Fraction Notation hard
        Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        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
        
        Equivalent fractions (age 9+) hard
        Generating equivalent fractions supports converting 10ths to 100ths
        
        Equivalent fractions on a number line hard
        Understanding equivalence conceptually is prerequisite to explaining algebraically
        
        Equivalent fractions hard
        Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
        
        Fractions on a number line soft
        Number line supports seeing equivalent fractions as the same point
        
        Fractions of amounts hard
        Placing fractions on number line requires knowing what fractions are
        
        Tenths soft
        Counting in tenths supports placing fractions on a number line
        
        Understanding fractions hard
        Extends equivalence of 2/4 and 1/2 to broader equivalent fractions
        
        Reading +, −, and = symbols soft
        Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
        
        Fractions of amounts hard
        Writing fractions and recognising equivalence requires knowing what the fractions mean
        
        Fraction Notation hard
        Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
        
        Fraction Notation hard
        Recognising and showing equivalent fractions requires that vocabulary
        
        Fractions of a whole hard
        Must understand unit fractions to reason about equivalence
        
        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
        Working with fractions extends from Y1 understanding of halves
        
        Division as equal sharing soft
        Finding fractions of quantities uses equal sharing (division)
        
        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
        Extends partitioning from halves/fourths to include thirds
        
        Fractions on a number line (age 8+) hard
        Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
        
        Fractions on a number line hard
        Prior number-line fraction experience feeds into formal unit-fraction placement
        
        Fractions of amounts hard
        Placing fractions on number line requires knowing what fractions are
        
        Tenths soft
        Counting in tenths supports placing fractions on a number line
        
        Fractions of a whole hard
        Must understand unit fractions before placing them on number line
        
        Fractions of amounts hard
        Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
        
        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
        
        Equivalent fractions (age 8+) hard
        Generating equivalent fractions with visual models is prerequisite to algebraic explanation of equivalence
        
        Equivalent fractions on a number line hard
        Must understand equivalence before generating equivalent fractions
        
        Equivalent fractions hard
        Diagram-based equivalent fractions is prerequisite to formal equivalence understanding
        
        Fractions on a number line soft
        Number line supports seeing equivalent fractions as the same point
        
        Understanding fractions hard
        Extends equivalence of 2/4 and 1/2 to broader equivalent fractions
        
        Fraction Notation hard
        Recognising and showing equivalent fractions requires that vocabulary
        
        Fractions of a whole hard
        Must understand unit fractions to reason about equivalence
        
        Fractions of amounts hard
        Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
        
        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
        
        Fractions on a number line (age 8+) hard
        Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
        
        Fractions on a number line hard
        Prior number-line fraction experience feeds into formal unit-fraction placement
        
        Fractions of a whole hard
        Must understand unit fractions before placing them on number line
        
        Decimal equivalents of tenths and hundredths hard
        Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
        
        Tenths (age 8+) hard
        Must understand hundredths before writing decimal equivalents
        
        Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        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
        
        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
        
        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
        
        Fraction Notation hard
        Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        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
        
        Decimal & Percent Notation hard
        Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
        
        Decimal & Percent Notation hard
        Using decimal notation for fractions requires decimal, tenths, and hundredths vocabulary
Converting measurement units (age 9+) hard
Y6 unit conversion with decimals extends Y5 metric conversion
- Converting measurement units hard
  Y4 unit conversion is prerequisite to systematic metric conversions with tables
  - Calculating with measurements hard
    Measuring in standard units is prerequisite to converting between units
    - Comparing and ordering measurements hard
      Extends comparing/ordering measures to adding/subtracting them
      - Choosing measurement units hard
        Comparing and ordering measurements with symbols requires being able to measure in standard units
        
        Capacity and volume hard
        Using standard units for capacity extends from beginning to measure capacity
        
        Comparing Capacity hard
        Measuring capacity with units requires first being able to compare capacities
        
        Measurable Attributes of Objects hard
        Comparing capacity requires understanding capacity as a measurable attribute
        
        Measuring length and height (age 5+) hard
        Using standard units for length extends from beginning to measure length
        
        Comparing Lengths & Heights hard
        Measuring length with units requires first being able to compare lengths directly
        
        Measurable Attributes of Objects hard
        Comparing lengths/heights requires first identifying length as a measurable attribute
        
        Measuring mass and weight hard
        Using standard units for mass extends from beginning to measure mass
        
        Measuring mass and weight (age 4+) hard
        Measuring mass with units requires first being able to compare masses directly
        
        Measurable Attributes of Objects hard
        Comparing mass/weight requires first identifying mass as a measurable attribute
      - Comparing and ordering numbers soft
        Using >, <, = for measurements parallels using them for numbers
        
        The two digits of a two-digit number hard
        Comparing two-digit numbers 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
        
        Two written numerals between 1 and 10 soft
        Comparing two-digit numbers extends from comparing single-digit written numerals
        
        Comparing groups: more or fewer soft
        Comparing written numerals is the symbolic form of comparing quantities — conceptual comparison helps but isn't strictly required
        
        Counting objects to 20 soft
        Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20
        
        How Many in Total? hard
        Answering 'how many?' requires the cardinality principle
        
        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'
        
        One-to-one counting hard
        Counting objects to answer 'how many?' requires one-to-one correspondence
    - Choosing measurement units hard
      Extends Y2 standard unit measurement to include mm and to add/subtract measures
      - Capacity and volume hard
        Using standard units for capacity extends from beginning to measure capacity
        
        Comparing Capacity hard
        Measuring capacity with units requires first being able to compare capacities
        
        Measurable Attributes of Objects hard
        Comparing capacity requires understanding capacity as a measurable attribute
      - Measuring length and height (age 5+) hard
        Using standard units for length extends from beginning to measure length
        
        Comparing Lengths & Heights hard
        Measuring length with units requires first being able to compare lengths directly
        
        Measurable Attributes of Objects hard
        Comparing lengths/heights requires first identifying length as a measurable attribute
      - Measuring mass and weight hard
        Using standard units for mass extends from beginning to measure mass
        
        Measuring mass and weight (age 4+) hard
        Measuring mass with units requires first being able to compare masses directly
        
        Measurable Attributes of Objects hard
        Comparing mass/weight requires first identifying mass as a measurable attribute
  - Time Units and Calendar Facts hard
    Knowing seconds/minute, days/month etc. is prerequisite to unit conversion problems
    - Number of minutes in an hour hard
      Extends knowing minutes in an hour to seconds in a minute and days in months
      - Telling time to the minute hard
        Knowing 60 min = 1 hour and 24 hours = 1 day extends from measuring time in hours/minutes/seconds
        
        Comparing durations hard
        Measuring time in units requires understanding time comparison language first
- Multiplying and dividing soft
  ×÷ by 10/100/1000 supports metric unit conversions
  - Dividing by 10 and 100 hard
    Dividing by 10/100 (Y4 fractions context) is prerequisite to ×÷ by 10/100/1000 with decimals
    - Tenths (age 8+) hard
      Must understand hundredths to identify digit values when dividing by 10/100
      - Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        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)
        
        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
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        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
    - Decimal equivalents of tenths and hundredths hard
      Must know decimal notation to express results of dividing by 10/100
      - Tenths (age 8+) hard
        Must understand hundredths before writing decimal equivalents
        
        Tenths hard
        Count in tenths is prerequisite to extending to hundredths
        
        Fractions of amounts hard
        Tenths extend fraction understanding from halves, thirds, quarters
        
        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
        
        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)
        
        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
        
        Counting in 2s soft
        Skip counting supports counting in tenths
        
        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
      - Decimal & Percent Notation hard
        Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
  - Place Value × 10 Pattern hard
    ×10 place-value relationship is prerequisite to ×÷ by powers of 10
    - Place value of each digit hard
      Four-digit place value is prerequisite to understanding ×10 relationship between places
      - The three digits of a three-digit number hard
        Four-digit place value extends three-digit place value
        
        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)
        
        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 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
        
        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
        
        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)
        
        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

Unlocks2

Measurement Conversions
hardAges 10—11
Unit Conversions
hardAges 11—12