Mastering Fractions: A Comprehensive Guide for EYFS to Year 6 Teachers

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The Fractions Learning Journey: From Early Years to Year 6

Understanding fractions is a critical part of mathematics education, and the journey begins in the Early Years Foundation Stage (EYFS) before progressing steadily through the primary curriculum to Year 6. This development emphasises not only the conceptual understanding of fractions but also the connections to place value and the decimal number system. Fewer representations are employed across this flightpath, helping children see consistent structures, linking them to place value knowledge and reinforcing memory retention. This approach ensures that children know more and remember more as they build their knowledge progressively.

Early Years Foundation Stage (EYFS): Building the Foundation

In the Early Years, children’s exposure to fractions is not formal, but they begin by exploring foundational concepts that later underpin their understanding of fractions. At this stage, the focus is on developing an understanding of equal and unequal groups and doubling. These activities lay the groundwork for recognizing the concept of parts of a whole.

1. Equal and Unequal Groups: Children start to recognize when a group of objects is divided equally or unequally. This might happen through everyday activities like sharing toys or snacks. Teachers emphasize fairness, using language like “the same” and “different,” which helps children understand when quantities are equal or unequal.

2. Doubling: Another early step is the concept of doubling, where children are introduced to the idea of making two equal groups from one. They are encouraged to practice doubling simple quantities, like doubling the number of toys. This early work in doubling leads naturally into the concept of halving, which links directly to the idea of fractions.

Year 1: Introducing Halves and Quarters

In Year 1, children are formally introduced to fractions, starting with halves and quarters. The focus remains on using concrete representations and simple language to help them grasp these early fraction concepts.

1. Recognizing Halves: Children begin by recognizing halves as one of two equal parts. Practical activities—like cutting shapes or dividing objects (such as sandwiches)—help children visualize and understand halves. They learn to identify halves of shapes and quantities, using simple, consistent representations like physical objects or drawings.

2. Recognizing Quarters: As children become comfortable with halves, they are introduced to quarters. Here, the idea of dividing something into four equal parts is introduced, again using hands-on activities. These early activities establish a strong visual and conceptual link to how parts of a whole can be divided into equal segments.

Year 2: Expanding to Thirds and Equivalence

Year 2 builds on the foundations laid in Year 1 by introducing new fractions and beginning to explore equivalence between fractions.

1. Recognizing Thirds and Fractions of a Set: Children now begin working with fractions like thirds, as well as continuing their work with halves and quarters. Practical tasks, like finding fractions of a discrete set of objects (e.g., ⅓ of 9 apples), help deepen their understanding.

2. Equivalence (½ = 2/4): A key learning point in Year 2 is recognizing the equivalence between ½ and 2/4. Children use visual representations—like folding paper or fraction walls—to see how two quarters can equal one half. This early work with equivalence sets the stage for more complex fraction concepts later in the curriculum.

Year 3: Introducing Tenths and Equivalent Fractions

In Year 3, children’s understanding of fractions begins to deepen, as they are introduced to new concepts, including tenths and the idea of using fractions as numbers.

1. Counting in Tenths: Children are introduced to tenths, which arise from dividing objects into ten equal parts. The consistent use of number lines and bead strings helps them visualize tenths as steps between whole numbers. This idea of dividing into tenths also begins to establish a connection with the decimal system.

2. Equivalent Fractions: Year 3 also introduces equivalent fractions, allowing children to explore how different fractions can represent the same quantity (e.g., ½ = 2/4 = 3/6). Visual aids, like fraction walls or bar models, are used to make these relationships clear.

3. Adding and Subtracting Fractions: Children begin to work on simple operations with fractions, starting with adding and subtracting fractions with the same denominator. This helps to reinforce their understanding of fractions as numbers that can be manipulated just like whole numbers.

Year 4: Developing Fluency with Hundredths and Decimals

In Year 4, children’s understanding of fractions continues to expand, with a particular emphasis on decimal equivalents and making connections between fractions and decimals.

1. Counting in Hundredths: By dividing objects into hundredths, children begin to grasp the link between fractions and decimals. They start to see how fractions like ⅕ or ½ can be represented as decimals (e.g., ½ = 0.5, ¼ = 0.25). The use of number lines and bar models remains crucial in making these connections clear.

2. Adding and Subtracting Fractions: Children continue to add and subtract fractions with the same denominator, now using fractions with denominators of 10 or 100. This continued practice helps solidify their operational fluency with fractions.

3. Decimal Equivalents: Year 4 introduces decimal equivalents for common fractions, such as ¼, ½, and ¾. These conversions between fractions and decimals are supported by visual representations and links to place value, reinforcing the idea that fractions and decimals are interconnected parts of the same system.

Year 5: Working with Mixed Numbers and Improper Fractions

By Year 5, children are ready to work with more complex fractions, including mixed numbers and improper fractions. They also begin to explore fractions as they relate to percentages.

1. Mixed Numbers and Improper Fractions: Children learn to convert between mixed numbers (e.g., 1⅓) and improper fractions (e.g., 4/3), using diagrams and visual models to support this process. This ability to move between different representations of fractions is critical as they advance into more complex mathematical operations.

2. Multiplying Fractions by Whole Numbers: Another key development in Year 5 is the introduction of multiplying fractions by whole numbers. Visual models, such as bar diagrams, help children understand this concept, reinforcing their understanding of fractions as numbers.

3. Percentages as Fractions and Decimals: Children are introduced to percentages, and they learn how to convert between fractions, decimals, and percentages (e.g., 25% = ¼ = 0.25). This begins to bridge the gap between fractions and real-world applications, such as in financial literacy.

Year 6: Mastery and Application

In Year 6, the focus shifts to achieving mastery of fractions and applying this understanding in complex, multi-step problems.

1. Simplifying and Comparing Fractions: Children learn to simplify fractions using common factors and to compare fractions, including those greater than one, by finding common denominators. This fluency with fractions helps them solve more complex problems.

2. Multiplying and Dividing Fractions: Year 6 introduces the multiplication of pairs of fractions (e.g., ⅔ × ½ = ⅓) and division of fractions by whole numbers (e.g., ⅓ ÷ 2 = ⅙), using visual aids to reinforce these processes.

3. Linking to Place Value and Decimals: The culmination of the journey involves linking fractions to place value knowledge, particularly in terms of decimals and percentages. By using fewer, consistent representations—such as number lines and bar models—children can see how fractions fit within the broader structure of the decimal number system.