Volume as additive
PROCEDURALRecognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms
Mastery Evidence
- Decompose an L-shaped solid into two cuboids and calculate total volume
- Solve a real-world problem requiring the volume of a composite figure (e.g. a step-shaped structure)
- Explain why splitting a composite solid into rectangular prisms allows calculation of total volume
Assessment Prompt
“If an L-shaped swimming pool is made of two rectangular sections, can [child] find the volume of each section separately and add them to get the total volume of the pool?”
Prerequisites2
- Addition and subtraction strategies (age 10+)softAges 10—11
- Estimating answers (age 10+)hardAges 10—11
Show full prerequisite tree
- Addition and subtraction strategies (age 10+) soft
Adding volumes of sub-figures uses decimal addition
- Reading and writing numbers (age 10+) hard
Adding/subtracting decimals requires reading and comparing 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
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 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
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 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
- 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
- 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
- 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)
- 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
- 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
- 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
- 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
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
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
- 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
- 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
- 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
- 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
- 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
- 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
- Addition as combining or putting together two hard
Reading/writing the + symbol requires understanding what addition means
- Subtraction as taking away or separating hard
Reading/writing the − symbol requires understanding what subtraction means
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
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
- 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
- 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
- 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'
- 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 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)
- 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)
- Fluent addition and subtraction (age 9+) hard
Decimal addition/subtraction builds on fluent whole-number columnar algorithm
- 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)
- 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 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)
- 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)
- Adding and subtracting (age 7+) hard
Four-digit columnar methods extend three-digit columnar methods
- Fluent adding and subtracting within 100 hard
Columnar methods require fluent within-100 addition/subtraction
- Addition and subtraction within 20 hard
Adding within 100 extends within-20 strategies to larger numbers
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- Addition as combining or putting together two hard
Fluency with addition within 5 requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Fluency with subtraction within 5 requires understanding subtraction as taking away
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- The two digits of a two-digit number hard
Adding within 100 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)
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- Addition as combining or putting together two hard
Fluency with addition within 5 requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Fluency with subtraction within 5 requires understanding subtraction as taking away
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Addition as combining or putting together two hard
Fluency with addition within 5 requires understanding addition as combining
- 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
Fluency with subtraction within 5 requires understanding subtraction as taking away
- 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'
- Addition and subtraction within 1000 hard
Formal columnar methods build on conceptual understanding of composing/decomposing
- The three digits of a three-digit number hard
Three-digit operations require three-digit place-value understanding
- 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)
- Fluent adding and subtracting within 100 hard
Adding/subtracting within 1000 extends within-100 skills
- Addition and subtraction within 20 hard
Adding within 100 extends within-20 strategies to larger numbers
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Fluency with addition within 5 requires understanding addition as combining
- Subtraction as taking away or separating hard
Fluency with subtraction within 5 requires understanding subtraction as taking away
- The two digits of a two-digit number hard
Adding within 100 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
- 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)
- Addition and subtraction within 20 hard
Fluency within 20 requires prior strategy-based adding/subtracting within 20
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- Fluent adding and subtracting within 10 hard
Strategies for within-20 calculation build on fluent within-10 knowledge
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Fluency with addition within 5 requires understanding addition as combining
- Subtraction as taking away or separating hard
Fluency with subtraction within 5 requires understanding subtraction as taking away
- Numbers up to 10 into pairs hard
Making 10 is a specific application of decomposing numbers into pairs
- Addition as combining or putting together two hard
Decomposing numbers into pairs requires understanding addition as combining
- Addition as combining or putting together two hard
Fluency with addition within 5 requires understanding addition as combining
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- Subtraction as taking away or separating hard
Fluency with subtraction within 5 requires understanding subtraction as taking away
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- Measuring length (age 10+) hard
Measuring by counting cubes requires understanding unit cube concept
- Area (age 8+) hard
Counting unit squares for area supports extending to counting unit cubes for volume
- Measuring length (age 7+) soft
Length measurement experience supports understanding area as a 2D measurement
- Measuring length (age 6+) hard
Using standard measurement tools extends measuring with non-standard units
- Measuring length and height (age 5+) hard
Measuring with iterated units extends Y1 beginning to measure length
- 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
- Comparing Lengths & Heights hard
Ordering 3 objects by length and indirect comparison extends direct length comparison
- Measurable Attributes of Objects hard
Comparing lengths/heights requires first identifying length as a measurable attribute
- 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
- Written Multiplication hard
2/3-digit × 1-digit written method is prerequisite to 4-digit × 1-digit and 2-digit × 2-digit
- Written Multiplication & Division hard
Formal short multiplication extends Y3 written multiplication
- The three digits of a three-digit number soft
Two-digit × one-digit uses place-value partitioning (e.g. 23 × 4 = 20 × 4 + 3 × 4)
- 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)
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Reading ×, ÷, and = Symbols hard
Writing multiplication/division statements requires fluency with symbols
- Reading and writing numbers to 20 hard
Writing number sentences requires reading and writing numerals
- How Many in Total? hard
Reading/writing numerals 0–20 requires understanding that numerals represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Writing digits 0-9 hard
Writing numerals requires the motor skill of forming digits 0-9 (taught in English handwriting)
- 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'
- 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'
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Skip Counting (4s, 8s, 50s, 100s) hard
Counting in 6s/7s/9s/25s/1000s extends counting in 4s/8s/50s/100s
- Multiplication as repeated addition hard
Recalling times table facts requires understanding multiplication as repeated addition/grouping
- Addition as combining or putting together two hard
Multiplication as repeated addition requires understanding addition as combining groups
- How Many in Total? hard
Understanding addition as combining groups requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Area and the distributive property soft
Area models for distributive property support understanding long multiplication layout
- Understanding angles (age 8+) hard
Must multiply side lengths for area before using area models for distributive property
- Area by Tiling hard
Must see tiling→multiplication connection before computing area via side lengths
- Measuring length (age 7+) soft
Length measurement experience supports understanding area as a 2D measurement
- Measuring length (age 6+) hard
Using standard measurement tools extends measuring with non-standard units
- Measuring length and height (age 5+) hard
Measuring with iterated units extends Y1 beginning to measure length
- Capacity and volume hard
Using standard units for capacity extends from beginning to measure capacity
- Measuring length and height (age 5+) hard
Using standard units for length extends from beginning to measure length
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