Number - Fractions (including Decimals)
KS2MA-Y4-D004
Equivalent fractions using multiples and factors, hundredths as fractions and decimals, fractions greater than one, tenths and hundredths as decimal place value, rounding decimals, and comparing decimals.
National Curriculum context
In Year 4, the fractions domain expands significantly to include decimals for the first time. Pupils learn that the decimal system extends the place value system to the right of the decimal point — tenths (one tenth = 0.1) and hundredths (one hundredth = 0.01). The non-statutory guidance explains that pupils connect tenths to place value and decimal measures, and understand that decimal notation is an alternative to fraction notation for parts of a whole. Pupils learn to find equivalent fractions systematically by multiplying numerator and denominator by the same number, and to add and subtract fractions and mixed numbers with the same denominator. This domain bridges the fraction understanding of Year 3 with the percentages and fraction operations of Year 5.
3
Concepts
2
Clusters
2
Prerequisites
3
With difficulty levels
Lesson Clusters
Understand hundredths and extend decimal place value
introduction CuratedHundredths and decimal place value and the decimal equivalents of common fractions are co-taught (C010 and C012 mutually co-teach) and together establish the decimal number system.
Generate and use equivalent fractions
practice CuratedGenerating equivalent fractions using multiples and factors is a distinct procedural skill that builds on Year 3 fraction understanding and underpins all fraction arithmetic to come.
Teaching Suggestions (1)
Study units and activities that deliver concepts in this domain.
Fractions and Decimals: Equivalence and Tenths/Hundredths
Mathematics Pattern SeekingPedagogical rationale
Y4 is where fractions and decimals first connect explicitly. Children must understand that 0.1, 1/10, and one-tenth are three representations of the same quantity. Fraction walls and place value charts displayed side by side make this equivalence visible. The concept of equivalent fractions is also new and requires concrete proof through fraction tiles — children need to see that 2/4 and 1/2 cover exactly the same length before they trust the abstract equivalence.
Prerequisites
Concepts from other domains that pupils should know before this domain.
Concepts (3)
Hundredths and decimal place value
Keystone knowledge AI DirectMA-Y4-C010
A hundredth is one of one hundred equal parts of a whole (1/100 = 0.01). The second decimal place (hundredths) extends the decimal place value system established with tenths in Year 3. Mastery means pupils understand that 0.01 = 1/100, can count up and down in hundredths, understand that 10 hundredths = 1 tenth, and can identify the value of any digit in a decimal number with two decimal places.
Teaching guidance
Use a 10 × 10 grid (like a hundred square but representing one whole): each small square is 1/100 = 0.01, each row/column of 10 squares is 1/10 = 0.1. Hundredths number lines (0 to 1 marked in 0.01 steps) provide pictorial support. Connect to metric measures: 1 cm = 0.01 m, since 100 cm = 1 m. Money provides a natural context: £1.47 means 1 pound, 4 tenths of a pound and 7 hundredths of a pound. Practise reading and writing decimal numbers with up to two decimal places.
Common misconceptions
Pupils often think 0.17 is 'zero point seventeen' and therefore larger than 0.9 (which they read as 'zero point nine') because 17 > 9. This is the most critical misconception in decimal place value. Pupils may also think 0.1 = 0.10 but not understand why (the zero adds no value). The connection between fraction and decimal notation (1/100 = 0.01) is often procedural rather than conceptual.
Difficulty levels
Shading hundredths on a 10×10 grid and writing the decimal as 0.01 per square, using the grid as concrete support.
Example task
Shade 23 squares on the hundredths grid. Write this as a decimal.
Model response: 0.23. Twenty-three hundredths.
Identifying the value of each digit in a number with two decimal places and understanding that 10 hundredths = 1 tenth.
Example task
What is the value of the 4 in 0.47? How many hundredths make one tenth?
Model response: The 4 is worth 4 tenths (0.4). 10 hundredths make 1 tenth (0.10 = 0.1).
Counting up and down in hundredths, comparing decimals with different numbers of decimal places, and connecting to fractions.
Example task
Which is larger, 0.7 or 0.65? Explain. Write 0.45 as a fraction.
Model response: 0.7 is larger. 0.7 = 0.70, and 70 hundredths > 65 hundredths. 0.45 = 45/100 = 9/20.
CPA Stages
concrete
Using a 10×10 hundredths grid (each small square = 0.01), place value counters labelled 0.01 and 0.1, and money (1p = £0.01) to explore hundredths physically
Transition: Child explains that 10 hundredths = 1 tenth and identifies the value of each digit in a two-decimal-place number without the grid
pictorial
Drawing hundredths grids, using place value charts with decimal columns, and placing decimals on number lines marked in hundredths
Transition: Child reads and writes any two-decimal-place number, places it on a number line, and converts between fraction and decimal notation without the grid
abstract
Working with hundredths mentally: counting in hundredths, identifying digit values, comparing decimals, and converting between fractions and decimals
Transition: Child works with hundredths fluently, never confusing 0.7 and 0.07, and converts between fraction and decimal forms instantly
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Equivalent fractions using multiples and factors
knowledge AI DirectMA-Y4-C011
Equivalent fractions can be generated by multiplying or dividing both numerator and denominator by the same non-zero number. For example, 1/2 = 2/4 = 3/6 = 4/8 (multiplying by 2, 3, 4 respectively). Families of equivalent fractions share a common value. Mastery means pupils can generate equivalent fractions systematically, recognise whether two fractions are equivalent, and use equivalence to compare and order fractions with different denominators.
Teaching guidance
Use fraction walls and fraction circles to show equivalence visually. The rule: multiplying numerator and denominator by the same number (×n/n = 1) preserves the value. Generate families: 1/3, 2/6, 3/9, 4/12... Practice: find three fractions equivalent to 2/5 (4/10, 6/15, 8/20). Connect to simplifying fractions (divide both by the same number). Use equivalent fractions to add fractions with different but related denominators: 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2.
Common misconceptions
Pupils understand that multiplying both parts works but struggle to explain why it preserves value. They may think only one specific fraction in a family is 'correct'. When using equivalence to compare fractions, pupils may use trial and error rather than a systematic approach.
Difficulty levels
Generating equivalent fractions by shading fraction walls and comparing the sizes visually.
Example task
Using the fraction wall, find a fraction equivalent to 1/2 with a denominator of 6.
Model response: 3/6. Looking at the fraction wall, 3 sixths takes up the same amount of space as 1 half.
Generating families of equivalent fractions using the rule: multiply (or divide) numerator and denominator by the same number.
Example task
Write three fractions equivalent to 2/5.
Model response: 4/10, 6/15, 8/20. I multiplied top and bottom by 2, then 3, then 4.
Using equivalent fractions to compare and order fractions with different denominators.
Example task
Which is larger, 3/4 or 5/6? Show your working using a common denominator.
Model response: Common denominator of 4 and 6 is 12. 3/4 = 9/12. 5/6 = 10/12. So 5/6 > 3/4.
CPA Stages
concrete
Using fraction walls, fraction strips and fraction circles to find equivalent fractions by overlaying and comparing, generating families of equivalent fractions physically
Transition: Child generates equivalent fractions by multiplying numerator and denominator by the same number, verifying with strips only to confirm
pictorial
Drawing fraction bars to show equivalence, recording the multiplicative relationship in a table, and using equivalence to compare fractions with different denominators
Transition: Child generates equivalent fractions and uses them to compare fractions with different denominators, recording on paper without fraction strips
abstract
Generating equivalent fractions mentally, simplifying fractions by dividing, and using equivalence to compare and order fractions
Transition: Child generates, simplifies and uses equivalent fractions fluently to compare any two fractions, selecting the most efficient common denominator
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.
Decimal equivalents to common fractions
knowledge AI DirectMA-Y4-C012
Certain common fractions have well-known decimal equivalents: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/10 = 0.1, 1/100 = 0.01. These equivalences must be known to automaticity. Mastery means pupils can convert between fraction and decimal notation for these key fractions instantly and use these equivalences in measurement and money contexts.
Teaching guidance
Use money as the most natural context: £0.50 = £1/2; £0.25 = £1/4 (25p is a quarter of a pound). Use the hundredths grid: shade 50 squares for 1/2 = 0.50; shade 25 squares for 1/4 = 0.25. Connect to division: 1 ÷ 2 = 0.5; 1 ÷ 4 = 0.25. Extend to any tenths: 3/10 = 0.3, 7/10 = 0.7. Display a reference table until these are memorised.
Common misconceptions
Pupils often write 1/4 = 0.4 (reading the denominator as the decimal digit rather than dividing). They may know 1/2 = 0.5 but not connect 3/4 = 0.75 (which requires recognising it as 3 × 0.25). The equivalence 1/10 = 0.1 is usually secure; 1/100 = 0.01 is less so.
Difficulty levels
Using money to establish key equivalences: 50p = half of £1, 25p = quarter of £1.
Example task
What fraction of £1 is 50p? What fraction of £1 is 25p? Write them as decimals.
Model response: 50p = 1/2 of £1 = £0.50. 25p = 1/4 of £1 = £0.25.
Knowing decimal equivalents of tenths and key fractions: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/10 = 0.1.
Example task
Write 3/4 as a decimal. Write 0.1 as a fraction.
Model response: 3/4 = 0.75. 0.1 = 1/10.
Converting fluently between fraction and decimal forms for all tenths and key fractions, in measurement and money contexts.
Example task
Convert 7/10 to a decimal. A plank is 0.75 m long. What fraction of a metre is that?
Model response: 7/10 = 0.7. 0.75 m = 3/4 of a metre.
CPA Stages
concrete
Using money (£1 = 100p) and hundredths grids to discover key fraction-decimal equivalences: half = 50p = 0.50, quarter = 25p = 0.25, three-quarters = 75p = 0.75
Transition: Child states the decimal equivalents of 1/2, 1/4, 3/4, 1/10 and 1/100 from memory without money or grids
pictorial
Drawing hundredths grids and number lines to show fraction-decimal equivalences, recording conversions in a reference table
Transition: Child converts between fraction and decimal notation for all tenths and the key quarter fractions without reference materials
abstract
Converting instantly between common fractions and their decimal equivalents, and applying these in measurement and money contexts
Transition: Child converts between fractions and decimals instantly and applies equivalences in context without any visual aids
Delivery rationale
Upper primary maths (Y4) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.