Concrete to Abstract

Overview

This 40-minute professional development session is designed for A-Level students training as future teachers, specifically focusing on enhancing Infant (KS1) maths teaching using the CPA (Concrete–Pictorial–Abstract) approach. This is a teacher training session, not specifically for direct KS1 pupils, but aimed at A-Level students who may be entering teaching or early years education, with a core focus on developing conceptual understanding of Number & Place Value and Calculation at Key Stage 1, in line with the UK National Curriculum.

The session involves both theoretical understanding and hands-on, practical activities tailored to Infant school maths. This will culminate in reflective practice and planning for implementation, impressing upon the trainee teachers the importance of engaging young learners through developmentally appropriate pedagogy.

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Lesson Information

• Class Level: A-Level (Teacher Training Focus – Early Years/Primary Education)
• Subject Focus: Mathematics – Professional Development/Teacher Training
• Stage Being Taught About: Key Stage 1 (Ages 5–7)
• Curriculum Strand: Number and Place Value / Addition & Subtraction
• Time: 40 minutes
• Group Size: 9 Students (ideal for collaborative activities)

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Learning Objectives

By the end of this session, students will be able to:

• Understand the purpose and structure of the CPA approach in early mathematics.
• Identify and differentiate between Concrete, Pictorial, and Abstract representations.
• Design and evaluate engaging activities suitable for KS1 children using the CPA model.
• Apply strategies to support all learners, including those with SEND or EAL needs.
• Use AI tools (conceptually) to support lesson planning and engagement.

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Resources Required

• Large place value counters
• Tens frames and unifix cubes
• Visual images of bar models, part-part-whole diagrams
• Laminated number cards
• Whiteboards and markers
• A printed version of the KS1 National Curriculum mathematics strands for reference
• PowerPoint Presentation (see plan below)
• Flip chart / sticky notes

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PowerPoint Presentation Overview

Slide 1 – Welcome & Session Outcomes

• Title: “Bringing Maths to Life with CPA”
• Brief objectives
  Activity: Each student writes one word they associate with ‘Maths in primary’ on a sticky note and places it on a flip chart – discussion follows.

Slide 2 – What is CPA?

• Definitions and visual model
• Examples of each stage
• Why it works – linked to Bruner's theory of enactive-iconic-symbolic representation, and Piaget’s stages of development.

Slide 3 – Concrete Examples (Hands-On)

• Demonstration with tens frames and cubes representing number bonds to 10
  Activity: Students work in pairs to model “7 + __ = 10” using cubes and tens frames.

Slide 4 – Pictorial Representations

• Visual examples: number lines, bar models
  Activity: Students draw their own representations of “13 – 4” using bar models and number lines.

Slide 5 – Abstract Concepts

• Link to equations and written methods
  Activity: Connect the equation “23 + 12” to its concrete and pictorial root.

Slide 6 – Activity Carousel

• Stations with mini tasks:
  • Station 1: Build number bonds using cubes
  • Station 2: Match visuals to equations
  • Station 3: Spot the missing step in CPA progression
    Students rotate every 4 minutes.

Slide 7 – Scaffolding & Inclusion

• Strategies for SEND and EAL learners
• Use of sentence stems, dual coding, and structured questioning
  Discussion: How can CPA reduce cognitive overload?

Slide 8 – AI in CPA Planning

• Innovative use of generative AI (e.g., ChatGPT) to help design visual representations.
  Activity: Ask ChatGPT to generate a story context for “8 + 5” for young learners – discuss outcomes.

Slide 9 – Reflect & Plan
Activity: In triads, students plan a short KS1 maths activity using CPA. Present briefly to the group.

Slide 10 – Summary & Takeaway

• Key benefits and next steps
• Handout for creating CPA-aligned lesson plans with prompt banks

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Detailed Timeline (40 minutes)

Time	Activity
0–5 mins	Introduction & Flipchart Icebreaker
5–10 mins	CPA Theory Overview + Discussion
10–16 mins	Concrete Session Demo + Paired Cube Activity
16–22 mins	Pictorial Representations + Drawing Practice
22–28 mins	Abstract Equations + Linking Activities
28–35 mins	Carousel – 3 Rotation Stations
35–38 mins	AI Use + Reflective Planning
38–40 mins	Summary & Further Questions

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Teaching Strategies Highlighted

• Modelling - Demonstrating before releasing responsibility
• Questioning - "What do you notice?", “Can you explain why…?”
• Talk Partners - Encouraging dialogue/thinking out loud
• Scaffolding - Through visual aids, manipulatives, and AI prompts
• Inclusive Practice - Supporting diverse learners through multi-sensory input

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Differentiation and Support

• Provide simplified pictorials for EAL pupils
• Encourage peer support in paired tasks
• Allow use of manipulatives throughout the task progression
• Use of visual storytelling for abstract concepts to enhance context

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Success Criteria

• Can confidently explain the difference between each CPA stage
• Can devise a CPA-rich activity tailored to a KS1 strand
• Can evaluate a sample activity for CPA completeness and inclusive value
• Have a practical understanding of how AI tools could assist planning in primary maths

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Reflection Question for Plenary Discussion

“How does using CPA support not only struggling learners but push our higher attainers as well?”

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Extension/Further Work

• Explore Dienes' theory and links to CPA
• Design a full-day KS1 maths sequence based entirely on CPA
• Investigate software for virtual manipulatives and how it may be used in remote/hybrid teaching or with SEN pupils

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Final Thought

CPA isn’t “just” a strategy, it’s a philosophy of inclusivity, a bridge from sense-making to problem-solving, and a starting point for mastery in early mathematical thinking.

Let’s bring the numbers to life—for every learner.

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Additional Notes for Presentation and Delivery

For wow factor:

• Bring in AI not as something scary but friendly and useful – for example, show students how ChatGPT was used to plan this session!
• Include a creative moment where students “ask ChatGPT” to generate a fun context for a KS1 maths problem – e.g. “Write a pirate story for 9 – 4”.
• Make sure student activities are kinaesthetic, interactive, and prospectively useful in real classrooms.

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End of Lesson Plan
Feel free to ask for editable versions of the PowerPoint or create handouts in publisher/word. All can be adapted based on setting!