Measurement Conversions
PROCEDURALSolve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts
Mastery Evidence
- Solve: 'A recipe uses 0.75 kg of flour. How many grams are needed for 3 batches?'
- Compare 2.5 litres and 2,450 ml by converting to the same unit
- Solve a multi-step problem involving time, distance, and unit conversion
Assessment Prompt
“If [child] is filling a fish tank that holds 60 litres and the tap fills it at 3.5 litres per minute, can they work out how long it will take to fill the tank?”
Prerequisites2
- Decimal place valuehardAges 10—11
- Fractions on a number linehardAges 9—10
Show full prerequisite tree
- Dividing by 10 and 100 hard
Dividing by 10/100 (Y4 fractions context) is prerequisite to ×÷ by 10/100/1000 with decimals
- 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
- 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)
- 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
- Decimal equivalents of tenths and hundredths hard
Must know decimal notation to express results of dividing by 10/100
- 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
- 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
- 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)
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- 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
- 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)
- 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)
- 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
- 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
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- Decimals for Tenths & Hundredths hard
Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
- Tenths (age 8+) hard
Understanding hundredths is prerequisite to working with 10ths and 100ths together
- 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 (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- 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
- Decimal equivalents of tenths and hundredths hard
Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
- 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
- Decimals for Tenths & Hundredths hard
Decimal notation for 10ths/100ths is prerequisite to extending to thousandths
- Tenths (age 8+) hard
Understanding hundredths is prerequisite to working with 10ths and 100ths together
- 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 (age 8+) hard
Equivalent fractions as the same point on a number line directly uses the fraction number-line representation
- 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
- Decimal equivalents of tenths and hundredths hard
Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
- 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 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
- The teen numbers hard
Understanding 10 as a bundle builds on understanding teen numbers as 'a ten and some ones'
- 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
General two-digit place value extends from understanding teen number composition
- 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
- 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
- Tenths (age 8+) hard
Understanding hundredths is prerequisite to working with 10ths and 100ths together
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- 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 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
- 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 (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
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- 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 (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
- 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)
- 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)
- 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
- 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'
- 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 (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
- Dividing by 10 and 100 hard
Dividing by 10/100 (Y4 fractions context) is prerequisite to ×÷ by 10/100/1000 with decimals
- 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
- 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)
- 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
- Decimal equivalents of tenths and hundredths hard
Must know decimal notation to express results of dividing by 10/100
- 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
- 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
- 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)
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- 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
- 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)
- 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)
- Estimating and comparing money hard
Y4 estimate/compare/calculate measures is prerequisite to word problems with fractions/decimals
- 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'
- Reading and writing numbers to 20 hard
Recognising coin values requires reading numerals (1, 2, 5, 10, 20, 50)
- 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)
- 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'
- Reading and writing numbers to 20 hard
Recognising coin values requires reading numerals (1, 2, 5, 10, 20, 50)
- 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)
- Calculating with measurements hard
Standard unit measurement is prerequisite to estimating and calculating measures
- 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 (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
- 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)
- 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)
- 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
- 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'
- 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 (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
- Tenths (age 8+) hard
Understanding hundredths is prerequisite to working with 10ths and 100ths together
- 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)
- 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'
- 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
- 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
- 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
- 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
- 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)
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- 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
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- 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)
- 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'
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- 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
- 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
- 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)
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- 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
- 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)
- 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
- 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
- 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
- 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
- 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
- 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
- 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)
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- 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
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- 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
- 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
- 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)
- 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
- 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
- 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
- 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
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Reading +, −, and = symbols soft
Writing fraction sentences (1/2 of 6 = 3) requires understanding the = sign
- 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)
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- 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)
- 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)
- Fractions of amounts hard
Writing fractions and recognising equivalence requires knowing what the fractions mean
- 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
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Fraction Notation hard
Writing fractions and recognising equivalence requires 'equivalent fraction' vocabulary
- 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
- 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
- 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)
- 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
- 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
- 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
- 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
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- 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
- 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
- Decimal equivalents of tenths and hundredths hard
Y4 decimal equivalents of 10ths/100ths is prerequisite to formal decimal notation for fractions
- 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)
- 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'
- 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
- 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 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 (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
- 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)
- 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)
- 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
- 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'
- 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 (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
- Dividing by 10 and 100 hard
Dividing by 10/100 (Y4 fractions context) is prerequisite to ×÷ by 10/100/1000 with decimals
- 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
- 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)
- 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
- Decimal equivalents of tenths and hundredths hard
Must know decimal notation to express results of dividing by 10/100
- 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
- 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
- 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)
- Fraction Notation hard
Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator
- Decimal & Percent Notation hard
Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary
- 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
- 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)
- 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)
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