Number - Fractions (including Decimals)

KS2

MA-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

AI Direct: 3

Lesson Clusters

1

Understand hundredths and extend decimal place value

introduction Curated

Hundredths 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.

2 concepts Scale, Proportion and Quantity
Decimal equivalents to common fractions Hundredths and decimal place value *
2

Generate and use equivalent fractions

practice Curated

Generating 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.

1 concepts Scale, Proportion and Quantity
Equivalent fractions using multiples and factors

Teaching Suggestions (1)

Study units and activities that deliver concepts in this domain.

Fractions and Decimals: Equivalence and Tenths/Hundredths

Mathematics Pattern Seeking
Pedagogical 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.

CPA Stage: concrete → pictorial → abstract NC Aim: reasoning
Fraction tiles (halves, quarters, fifths, tenths) Fraction wall (extending to tenths) Hundredths grid (10 x 10 square for shading) Place value chart (extended to tenths and hundredths columns) Place value counters (including 0.1 and 0.01 counters)
Fraction wall (showing equivalent fractions side by side) Hundredths grid (shading to show decimal values) Number line (0 to 1, marked in tenths and hundredths) Place value chart (ones, tenths, hundredths) Bar model (showing fractional and decimal equivalence)
Fluency targets: State common equivalent fractions (e.g., 1/2 = 2/4 = 5/10, 1/4 = 25/100); Convert between fractions with denominators of 10 or 100 and their decimal equivalents; Know decimal equivalents of 1/4, 1/2, 3/4 from memory; Order a set of fractions and decimals on a number line between 0 and 1
Decimal equivalents to common fractions Equivalent fractions using multiples and factors Hundredths and decimal place value

Prerequisites

Concepts from other domains that pupils should know before this domain.

Tenths as fractions and in place value from Number - Fractions
MA-Y3-C024
Equivalent fractions from Number - Fractions
MA-Y3-C027

Domain Vocabulary

25 terms across 3 concepts (25 domain-specific)(4 shared)

Domain-specific (25)
Concept
T3

0.01(noun)

A decimal number equal to one hundredth, written with two digits after the decimal point.

T3

1/100(noun)

A fraction representing one part out of one hundred equal parts.

T3

column(noun)

A vertical arrangement of items or digits in a table, chart, or place-value layout.

T3

common value(noun)

A value that appears in two or more sets, such as a number found in both a list of multiples of 3 and multiples of 4.

T3

convert(verb)

To change from one unit of measurement to another while keeping the same quantity.

T3

decimal equivalent(noun)

The decimal form of a fraction or percentage, showing the same value in a different notation.

T3

decimal place(noun)

The position of a digit after the decimal point, indicating its value (tenths, hundredths, etc.).

T3

decimal point(noun)

The dot in a decimal number that separates the whole-number part from the fractional part.

Shared by 2 concepts

T3

denominator(noun)

The bottom number in a fraction, showing how many equal parts the whole has been divided into.

T3

divide(verb)

To split a number into equal groups or to find how many times one number fits into another.

T3

equivalent(adjective)

Having the same value, even though it looks different.

T3

family(noun)

A set of related calculations that use the same numbers, showing the inverse relationship between operations.

T3

fraction(noun)

A number that represents part of a whole or part of a group, written with a numerator over a denominator.

Shared by 2 concepts

T3

fraction wall(noun)

A visual display showing rows of equal-length bars divided into different fractions, used to compare and find equivalences.

T3

hundredth(noun)

One of one hundred equal parts of a whole; the second digit after the decimal point represents hundredths.

T3

hundredths(noun)

The plural form referring to multiple parts each equal to one hundredth of a whole.

Shared by 2 concepts

T3

multiply(verb)

To combine equal groups to find a total; to increase a number by a given factor.

T3

numerator(noun)

The top number in a fraction, showing how many of the equal parts are being counted.

T3

one half(noun)

One of two equal parts of a whole; written as 1/2 or ½.

T3

one hundredth(noun)

A single part when a whole is divided into one hundred equal parts; equivalent to 0.01.

T3

one quarter(noun)

One of four equal parts of a whole; written as 1/4 or ¼.

T3

simplify(verb)

To reduce a fraction to its simplest form by dividing both numerator and denominator by their common factor.

T3

tenths(noun)

Parts of a whole divided into ten equal pieces; the first digit after the decimal point represents tenths.

Shared by 2 concepts

T3

three-quarters(noun)

Three out of four equal parts of a whole, written as 3/4.

T3

value(noun)

How much something is worth, either as a number or as money.

Concepts (3)

Hundredths and decimal place value

Keystone knowledge AI Direct

MA-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.

Vocabulary (10 terms)
0.01 T3 new — A decimal number equal to one hundredth, written with two digits after the decimal point.
1/100 T3 new — A fraction representing one part out of one hundred equal parts.
column T3 — A vertical arrangement of items or digits in a table, chart, or place-value layout.
decimal place T3 new — The position of a digit after the decimal point, indicating its value (tenths, hundredths, etc.).
decimal point T3 — The dot in a decimal number that separates the whole-number part from the fractional part.
hundredth T3 new — One of one hundred equal parts of a whole; the second digit after the decimal point represents hundredths.
hundredths T3 new — The plural form referring to multiple parts each equal to one hundredth of a whole.
one hundredth T3 new — A single part when a whole is divided into one hundred equal parts; equivalent to 0.01.
tenths T3 new — Parts of a whole divided into ten equal pieces; the first digit after the decimal point represents tenths.
value T3 — How much something is worth, either as a number or as money.
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

Entry

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.

Developing

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).

Expected

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 Direct

MA-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.

Vocabulary (10 terms)
common value T3 new — A value that appears in two or more sets, such as a number found in both a list of multiples of 3 and multiples of 4.
denominator T3 — The bottom number in a fraction, showing how many equal parts the whole has been divided into.
divide T3 — To split a number into equal groups or to find how many times one number fits into another.
equivalent T3 — Having the same value, even though it looks different.
family T3 new — A set of related calculations that use the same numbers, showing the inverse relationship between operations.
fraction T3 — A number that represents part of a whole or part of a group, written with a numerator over a denominator.
fraction wall T3 — A visual display showing rows of equal-length bars divided into different fractions, used to compare and find equivalences.
multiply T3 — To combine equal groups to find a total; to increase a number by a given factor.
numerator T3 — The top number in a fraction, showing how many of the equal parts are being counted.
simplify T3 — To reduce a fraction to its simplest form by dividing both numerator and denominator by their common factor.
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

Entry

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.

Developing

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.

Expected

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 Direct

MA-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.

Vocabulary (9 terms)
convert T3 — To change from one unit of measurement to another while keeping the same quantity.
decimal equivalent T3 new — The decimal form of a fraction or percentage, showing the same value in a different notation.
decimal point T3 — The dot in a decimal number that separates the whole-number part from the fractional part.
fraction T3 — A number that represents part of a whole or part of a group, written with a numerator over a denominator.
hundredths T3 — The plural form referring to multiple parts each equal to one hundredth of a whole.
one half T3 — One of two equal parts of a whole; written as 1/2 or ½.
one quarter T3 — One of four equal parts of a whole; written as 1/4 or ¼.
tenths T3 — Parts of a whole divided into ten equal pieces; the first digit after the decimal point represents tenths.
three-quarters T3 — Three out of four equal parts of a whole, written as 3/4.
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

Entry

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.

Developing

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.

Expected

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.