An Interactive Guide to Year 5 Maths
Exploring the curriculum, pedagogy, and practice for pupils aged 9-10.
The Pedagogical Framework
Effective teaching in Year 5 is not just about delivering content; it’s about **how** that content is taught. The core goal is to build deep, connected, and flexible mathematical understanding. This is achieved through a ‘Teaching for Mastery’ approach, ensuring all pupils can achieve a high standard by moving through content together and exploring concepts in depth. This section explores the key ideas that underpin this powerful pedagogical framework, forming the foundation of high-quality maths education.
The ‘Teaching for Mastery’ Approach
Promoted by the NCETM, this approach is built on the belief that all children can succeed in mathematics. The whole class progresses through content at a similar pace, with differentiation achieved by providing greater depth and more complex problems, not by accelerating pupils through topics. It is defined by Five Big Ideas:
Concrete, Pictorial, Abstract (CPA)
The CPA model is the engine that drives mastery in the classroom. It’s a dynamic, cyclical process that helps pupils build deep understanding by connecting tangible experiences to abstract mathematical symbols. Effective teaching involves moving flexibly between these stages.
🧱 Concrete: The “Doing” Stage
Pupils physically manipulate objects (e.g., counters, blocks) to model problems. This is for all learners when encountering a new concept, grounding their understanding in physical reality.
🖼️ Pictorial: The “Seeing” Stage
Pupils use visual representations (e.g., drawings, bar models) to bridge the gap between the physical and the abstract, helping them to organise their thoughts visually.
🔣 Abstract: The “Symbolic” Stage
Pupils use conventional numbers and symbols ($+, -, \times, \div$) to represent their calculations, connecting the concrete and pictorial stages to formal mathematics.
Curriculum Explorer
The Year 5 curriculum represents a major step up, introducing larger numbers, more complex procedures, and increasingly abstract concepts. This explorer allows you to dive into the main domains of study. Select a topic to see key learning objectives, effective teaching strategies, and an interactive example to bring the concept to life. The focus is on building deep, interconnected knowledge across all areas of mathematics.
Number: Fractions, Decimals & Percentages
A major conceptual leap in Year 5 is understanding the relationship between fractions, decimals, and percentages. Teaching must explicitly focus on the fact they are different ways of representing the same value. Number lines and hundred squares are key tools to make these connections visible and secure.
Key Objectives:
- ✓ Compare and order fractions with related denominators.
- ✓ Convert between improper fractions and mixed numbers.
- ✓ Multiply proper fractions and mixed numbers by whole numbers.
- ✓ Read, write, and order decimals up to 3 decimal places.
- ✓ Recognise that % relates to ‘parts per hundred’ and write percentages as fractions and decimals.
Equivalence: 1/2 = 0.5 = 50%
Measurement: Conversions & Calculations
Measurement provides a rich, real-world context for reinforcing number skills. Converting between units is a direct application of place value (multiplying/dividing by 10, 100, 1000), while calculating area and perimeter requires both precise calculation and deductive reasoning.
Key Objectives:
- ✓ Convert between different units of metric measure (km/m, kg/g, l/ml).
- ✓ Understand and use approximate equivalences with imperial units (inches, pounds, pints).
- ✓ Calculate the perimeter of composite rectilinear shapes.
- ✓ Calculate and compare the area of rectangles (including squares).
Metric Unit Converter
Geometry: Properties of Shapes & Angles
The focus in geometry shifts from simple identification to justification and reasoning. A significant focus is on angles: pupils learn to estimate, compare, measure with a protractor, and use key angle facts (e.g., angles on a straight line) to find missing angles and solve problems.
Key Objectives:
- ✓ Distinguish between regular and irregular polygons.
- ✓ Know angles are measured in degrees (°) and use a protractor.
- ✓ Estimate, compare, draw and measure acute, obtuse, and reflex angles.
- ✓ Use facts about angles at a point (360°), on a straight line (180°), and multiples of 90°.
- ✓ Identify, describe and represent reflections and translations.
Angle: Acute (<90°)
Statistics: Interpreting Data
The focus is on interpretation and solving problems using data. Pupils learn to read complex tables (like timetables) and are introduced to line graphs, which are used to show changes over time. Questions are often multi-step, requiring pupils to find multiple pieces of information and perform a calculation.
Key Objectives:
- ✓ Solve comparison, sum, and difference problems using information presented in a line graph.
- ✓ Complete, read, and interpret information in tables, including timetables.
Change Over Time: Classroom Temperature
Classroom in Practice
Translating theory into effective practice requires careful planning and resources. This section explores the structure of a typical mastery-aligned lesson and highlights the essential hands-on manipulatives that help pupils explore and understand mathematical concepts deeply. These tools are not just for support, but for deepening understanding for all learners.
Anatomy of a Mastery Lesson
Anchor Task:
An accessible problem to spark curiosity and explore initial ideas.
Recap Prior Learning:
Quick questions to activate prior knowledge essential for the new concept.
Teacher Input:
Modeling the new concept using a fluid CPA approach, making connections explicit.
Intelligent Practice:
Carefully varied questions to build procedural fluency and conceptual understanding.
Independent Practice:
Applying learning. Differentiation is through providing deeper, more complex problems.
Plenary:
Consolidating learning, sharing strategies, and addressing misconceptions.
Essential Manipulatives
Click a card to see its use.
Place Value Counters
Use: Place Value, 4 Operations, Decimals. Physically shows movement of digits when x/÷ by powers of 10, making the abstract rule concrete.
Fraction Walls
Use: Equivalence, Comparing, Adding & Subtracting Fractions. Makes equivalence (e.g. 2/4 = 1/2) visually obvious and easy to prove.
1 cm³ Blocks
Use: Volume, Square & Cube Numbers. Makes concepts like 3³ tangible by building a physical cube, revealing the structure of cubed numbers.
Protractors
Use: Measuring & Drawing Angles. An essential hands-on tool for developing accuracy and an intuitive feel for the size of different angles.
The Road to SATs
High-quality, pedagogy-driven teaching in Year 5 is the most effective preparation for the KS2 SATs taken in Year 6. It builds the deep, secure knowledge required for success, rather than relying on superficial test-drilling. The Reasoning and Arithmetic papers directly assess the skills developed through a mastery approach. This section maps Year 5 learning objectives directly to the style of questions pupils will encounter, showing the clear link between good teaching and assessment success.
