Equivalent fractions (age 9+)
CONCEPTUALExplain why a fraction a/b is equivalent to (n×a)/(n×b) using visual models; use this principle to recognise and generate equivalent fractions, including tenths and hundredths
Mastery Evidence
- Use a fraction strip to show 2/3 = 4/6 = 6/9
- Explain that multiplying numerator and denominator by the same number gives an equivalent fraction because the size of the whole is unchanged
- Generate three fractions equivalent to 3/5 and verify with diagrams
Assessment Prompt
“If [child] needs to make 2/3 look different without changing its value, can they multiply the top and bottom by the same number and explain why the fraction stays the same?”
Prerequisites2
- Equivalent fractions on a number linehardAges 8—9
- Equivalent fractions (age 8+)hardAges 8—9
Show full prerequisite tree
- 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
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Division as equal sharing 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
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- 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
- 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
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Division as equal sharing 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
- 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
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Division as equal sharing hard
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
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Division as equal sharing hard
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'
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- 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'
- 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
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Division as equal sharing hard
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
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- 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
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- 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
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- 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'
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- 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'
- 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
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Division as equal sharing hard
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
- 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
- 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
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Division as equal sharing 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
- 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
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Division as equal sharing hard
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
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- 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'
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- 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'
- 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
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- Division as equal sharing hard
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
- 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
- Fractions of amounts hard
Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding
- Finding halves and quarters (age 5+) hard
Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- One-to-one counting hard
Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'
- 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
- Fraction Notation hard
Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary
- Splitting shapes into equal parts (age 7+) hard
Partition into equal shares is prerequisite to understanding unit fractions
- Decomposing a shape into more equal shares hard
Understanding equal shares of different shapes requires concept of more shares = smaller
- Halves & Quarters of Shapes hard
Comparing share sizes requires experience partitioning into halves and quarters
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- 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)
- Finding halves and quarters (age 5+) hard
Partitioning into fourths/quarters extends from Y1 understanding of quarters
- What Is a Half? hard
Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4
- Division as equal sharing hard
Finding a half requires equal sharing into 2 groups — a division concept
- Subtraction as taking away or separating hard
Division as equal sharing/grouping requires understanding subtraction as taking away/separating
- How Many in Total? hard
Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)
- 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'
Unlocks6
- Simplifying FractionshardAges 10—11
- Reasoning with EquivalencessoftAges 9—10
- Converting tenths to hundredthshardAges 9—10
- Comparing fractions (age 9+)hardAges 9—10
- Adding fractions (different denominators)hardAges 9—10
- Multiplication as scalingsoftAges 10—11