Wales’ Curriculum for Wales represents a transformative shift in how we teach and understand mathematics. Central to this reform are the Five Proficiencies—key capabilities learners should develop to become confident, capable mathematicians. For teachers at Key Stage 3, understanding and incorporating these proficiencies into daily lessons is crucial to nurturing well-rounded, numerate learners.
In this post, we’ll explore each of the five proficiencies and share practical strategies to integrate them into your KS3 classroom.
1. Conceptual Understanding
What it means:
Learners should grasp why maths works, not just how to do it. It's about understanding the underlying principles and connections between mathematical ideas.
In the classroom:
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Use concrete-pictorial-abstract (CPA) approaches to introduce new topics.
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Encourage students to explain their reasoning using multiple representations (e.g., diagrams, number lines, algebra tiles).
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Ask open-ended questions like “Why does this method work?” or “Can you show it in a different way?”
Example activity:
Use visual models to explore the distributive property, showing how 3 × (4 + 2) is the same as (3 × 4) + (3 × 2), and let students build their own examples.
2. Communication Using Symbols
What it means:
Students should be fluent in the language of mathematics—numbers, symbols, notation—and able to use them precisely to represent and solve problems.
In the classroom:
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Regularly model correct mathematical notation during explanations.
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Create sentence starters or maths vocabulary banks.
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Use “error spotting” tasks where learners identify and correct symbolic errors.
Example activity:
Give students a multi-step equation with errors in symbol usage (like misplaced equal signs or incorrect order of operations) and ask them to explain and correct it.
3. Fluency
What it means:
This is not just about speed. Fluency means efficiency, accuracy, and flexibility in mathematical processes.
In the classroom:
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Practice retrieval with spaced, low-stakes quizzes.
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Use fluency starters at the beginning of lessons.
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Encourage multiple strategies for solving the same problem.
Example activity:
Challenge students to solve 48 × 25 in at least two different ways, such as using doubling and halving (48 × 25 = 96 × 12.5) or partitioning.
4. Logical Reasoning
What it means:
Students should be able to make and follow arguments, justify their thinking, and understand mathematical proof at an appropriate level.
In the classroom:
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Introduce “always, sometimes, never” questions to promote reasoning.
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Use Venn diagrams to sort mathematical statements.
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Let students peer critique each other’s solutions with reasoning prompts.
Example activity:
Pose the statement: “If a number is divisible by 4, it is also divisible by 2.” Ask students to provide examples, counterexamples (if possible), and justifications.
5. Strategic Competence
What it means:
Learners should develop problem-solving strategies and be able to plan and carry out investigations or tackle unfamiliar problems.
In the classroom:
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Incorporate rich problem-solving tasks that require planning.
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Teach and model problem-solving heuristics (e.g., working backwards, drawing diagrams).
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Use collaborative group work for extended tasks.
Example activity:
Provide a real-world scenario like planning a school trip within a budget and let students work through the mathematics involved (percentages, estimation, ratio).
Final thoughts
Embedding the Five Proficiencies into Key Stage 3 maths lessons doesn’t require a complete curriculum overhaul—it’s about thoughtful, deliberate teaching that develops deep mathematical thinking. By aligning lesson planning with these proficiencies, we prepare learners not just for assessments, but for real-life mathematical reasoning and lifelong numeracy.
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