Conceptual Mastery

Develop deep understanding of number through CPA, ensuring pupils grasp the “why” behind mathematical processes, not just the method.

Flexible Strategies

Equip pupils with multiple solution pathways, including decomposition and compensation, to build confidence, fluency and adaptable thinking.

Practical Impact

Implement ready-to-use classroom approaches that improve assessment, address misconceptions and enhance pupil outcomes immediately.

About the course

This practical, classroom-focused course is designed to enhance your mathematics teaching by strengthening pedagogical content knowledge, refining instructional strategies and deepening your approach to assessment — in full alignment with the IB Primary Years Programme and the IB's own commitment to inclusive education for every child. You will learn how to apply the Concrete-Pictorial-Abstract progression to build secure conceptual understanding before introducing formal written methods. The course explores structured variation, multiple solution pathways and Singapore computational strategies — including decomposition, compensation and left-to-right approaches — to develop flexibility, fluency and mathematical reasoning. You will also build expertise in bar modelling to support problem-solving, enabling learners to visualise relationships and represent unknown quantities with clarity and confidence. Directly supporting the Number strand of the IB Primary Years Programme, this course affirms that every child is mathematical. Through flexible number strategy, multiple solution paths and multiple entry points grounded in the CPA approach, Singapore Mathematics makes genuine mathematical understanding accessible to every learner — including those with additional learning needs, those working in an additional language, and diverse learning profiles — in full alignment with the IB's own guidance on learning diversity and inclusion, Universal Design for Learning and the IB's own Programme Standards and Practices for teachers' professional learning. By the end of this course, you will have a clear, structured and evidence-based approach to teaching addition and subtraction — empowering you to improve learner confidence, conceptual understanding and mathematical achievement across your school. The course is structured across five modules, totalling 20 hours of professional learning: 15 hours of course content (including pre-recorded video instruction, reading and structured activities constituting 31 chapters totalling 170 lessons) and 5 hours of independent study and reading. Each module is to be completed sequentially, building knowledge and pedagogical skill progressively across the programme. The course can be completed at each participant's own pace, independently. This is the first course of three being offered toward completion of the Singapore Mathematics Progressive Course Pathway. Primary teachers are strongly encouraged to complete all three scaffolded courses to build a comprehensive understanding of Singapore Mathematics pedagogy: - Introduction to Singapore Mathematics: Addition and Subtraction Methodologies - Singapore Mathematics: Multiplication and Division Methodologies - Singapore Mathematics: Solving Word Problems Using Bar Modelling and Heuristic Strategies Completion of this full training pathway equips teachers to make an immediate and measurable impact across all phases of the primary years, regardless of current or future class placement. It also serves to guarantee consistency and sustainability of teaching practice throughout your school. COURSE DATES Monday, 9th of November – Monday, 14th of December, 2026

Patrick Griffin - Course Trainer

Patrick Griffin is a highly experienced primary educator with 22 years of classroom teaching, special education and school leadership experience. A fully registered teacher in Ireland, Scotland and the United States, he has spent 17 years mentoring Newly Qualified Teachers across multiple education systems. Patrick holds a Master’s Degree in Primary Education. He has been selected by education authorities in the US and Scotland to share best practice in Mathematics and Science, and contributed to Scotland’s Curriculum for Excellence. Patrick brings deep expertise in curriculum development, inclusive practice and high-impact teaching methods, with a particular focus on Singapore Mathematics methodology and its transformative impact on pupil outcomes.

Curriculum

31 Chapters · 170 Lessons

    1. (Included in full purchase)

      Academic Integrity Policy

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      Overview

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      Course Aims

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      Promoting Inclusivity

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      Intellectual Property and Copyright Notice

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      Key Reference Documents

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      Course Reading List

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      Self-Directed Reading Guide and Reading Log

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      Assessment and Completion Criteria Assignment

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      Discussion Forum Protocol

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      Module 1 Overview

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      Module 1 Learning Outcomes

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      M1-S1.1: From Crisis to Global Model

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      M1-S1.2: Two Key Decisions: Language and Depth

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      M1-S1.3: The Pentagon Model

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      M1-S1.4: From the Bottom to the Summit

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      M1-S1.5 One Generation Is All It Takes

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      Module 1: Section 1 - Participant Attention Check

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      M1-S2.1: Conceptual Understanding and Metacognition

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      M1-S2.2: Inquiry-Based Learning and Mathematical Reasoning

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      M1-S2.3: Mathematical Communication and Problem Solving Competency

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      M1-S2.4: Promoting Inclusivity: Approaches to Teaching and Learning

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      M1-S2.5: Promoting Inclusivity: Learning Diversity and Inclusion

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      M1-S2.6: Collaborative Reflective Inquiry

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      M1-S2.7: Ongoing School Improvement

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      Module 1: Section 2 - Participant Attention Check

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      M1-S3.1: What is the CPA (Concrete-Pictorial-Abstract) Approach?

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      M1-S3.2: Why not Rote Learning and Assessment for Accuracy only?

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      M1-S3.3: Origins of the CPA Approach: Jean Piaget

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      M1-S3.4: Origins of the CPA Approach: Zoltán Dienes

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      M1-S3.5: Origins of the CPA Approach: Jerome Bruner

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      M1-S3.6: Origins of the CPA Approach: Lev Vygotsky

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      M1-S3.7: Conceptual Understanding vs. Procedural Understanding: Richard Skemp

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      M1-S3.8: Variation Theory: Conceptual Variation and Procedural Variation

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      M1-S3.9: Modelled Progression: CPA-based example of Addition

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      M1-S3.10: Reflective Discussion Forum Assignment

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      Module 1: Section 3 - Participant Attention Check

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      M1-S4.1: What is Number Sense? Define Mathematical Relationships.

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      M1-S4.2: What is Relational Understanding?

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      M1-S4.3: Counting, Number Conservation and Subitising

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      M1-S4.4: Representing Number, Combining and Partitioning

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      M1-S4.5: Why Number Bonds support Fluency, Flexibility and Understanding

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      M1-S4.6: Flexibile Thinking and Mental Strategy: Decomposition (Partitioning) - Addition and Subtraction

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      M1-S4.7: Flexibile Thinking and Mental Strategy: Compensation - Addition and Subtraction

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      M1-S4.8: Why Multiple Representations are Important (Supporting Connections through CPA)

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      Module 1: Section 4 - Participant Attention Check

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      M1-S5.1: Ensuring Equitable Access through Differentiated Instruction

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      M1-S5.2: What is Cognitive Load? What is Linguistic Demand?

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      M1-S5.3: Reducing Cognitive Load and Linguistic Demand

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      M1-S5.4: Overcoming Directionality Challenges

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      M1-S5.5: Improving Performance and Attainment

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      M1-S5.6: CPA Lesson Reflective Discussion Forum Assignment

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      M1-S5.7: Reflective Discussion Forum Assignment

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      Module 1: Section 5 - Participant Attention Check

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      Module 2 Overview

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      Module 2 Learning Outcomes

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      M2-S1.1: The Singapore Approach to Addition and Its Alignment With the IB Primary Years Programme

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      M2-S1.2 Singapore Approach: Importance of Addition Language and Maths Talk

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      M2-S1.3 Properties of Addition: Identity Property (Zero Property)

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      M2-S1.4 Properties of Addition: Commutative Property

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      M2-S1.5: Properties of Addition: Associative Property

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      M2-S1.6: Multiple Addition Structures

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      M2-S1.7: Importance of Part-Part-Whole Relationship

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      Module 2: Section 1 - Participant Attention Check

    1. (Included in full purchase)

      M2-S2.1: The Concrete–Pictorial–Abstract (CPA) Sequence of Addition (Teaching and Learning)

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      M2-S2.2: Concrete Stage: Using manipulatives to support representation and communication

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      M2-S2.3: Pictorial Stage: Using visual models to support representation and communication

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      M2-S2.4: Abstract Stage: Using abstract symbols to support representation and communication

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      M2-S2.5: Advantages of Multiple Solution Paths for Deep Conceptual Understanding of Addition

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      Module 2: Section 2 - Participant Attention Check

    1. (Included in full purchase)

      M2-S3.1: Base Ten Place Value System and Addition through Partitioning

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      M2-S3.2: Singapore Addition Approach: Dynamic Compensation (Concrete-Pictorial-Abstract)

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      M2-S3.3: Singapore Addition Approach: Number Bonds - Horizontal Orientation (Concrete-Pictorial)

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      M2-S3.4: Singapore Addition Approach: Number Bonds - Horizontal Orientation (Abstract 1-3 digit addends)

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      M2-S3.5: Singapore Addition Approach: Left to Right Vertical Orientation (1 digit addends)

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      M2-S3.6: Singapore Addition Approach: Left to Right Vertical Orientation (2 digit addends)

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      M2-S3.7: Singapore Addition Approach: Left to Right Vertical Orientation (3+ digit addends)

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      M2-S3.8: Singapore Addition Approach vs Traditional Algorithm (Vertical Column Addition)

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      M2-S4.1: Defining Structured Variation within Addition

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      M2-S4.2: Designing Differentiated Addition Tasks: Multiple Entry Points

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      M2-S4.3: Mathematical Language of Addition and Visualisation (Multilingual Learners)

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      M2-S4.4: Scaffolded Learning of Addition: Revisiting Stages to Support Understanding

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      Module 2: Section 4 - Participant Attention Check

    1. (Included in full purchase)

      M2-S5.1: Identifying and Analysing Common Misconceptions in Addition

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      M2-S5.2: Applying Formative Assessment Strategies for Addition

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      M2-S5.3: Strengthening Pupil Understanding: Evidence-Based Responsive Teaching

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      M2-S5.4: Why is Addition Competency Critical?

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      M2-S5.5: Reflective Discussion Forum Assignment

    6. (Included in full purchase)

      Module 2: Section 5 - Participant Attention Check

    1. (Included in full purchase)

      Module 3 Overview

    2. (Included in full purchase)

      Module 3 Learning Outcomes

    1. (Included in full purchase)

      M3-S1.1: The Singapore Approach to Subtraction and Its Alignment With the IB Primary Years Programme

    2. (Included in full purchase)

      M3-S1.2: Singapore Approach: Importance of Subtraction Language and Maths Talk

    3. (Included in full purchase)

      M3-S1.3: Properties of Subtraction: Identity Property (Zero Property)

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      M3-S1.4: Properties of Subtraction: Non-Commutative Property

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      M3-S1.5: Properties of Subtraction: Non-Associative Property

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      M3-S1.6: Multiple Subtraction Structures

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      M3-S1.7: Importance of Part-Part-Whole Relationship (Inverse of Addition)

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      Module 3: Section 1 - Participant Engagement Check

    1. (Included in full purchase)

      M3-S2.1: The Concrete–Pictorial–Abstract (CPA) Sequence of Subtraction (Teaching and Learning)

    2. (Included in full purchase)

      M3-S2.2: Concrete Stage: Using manipulatives to support representation and communication

    3. (Included in full purchase)

      M3-S2.3: Pictorial Stage: Using visual models to support representation and communication

    4. (Included in full purchase)

      M3-S2.4: Abstract Stage: Using abstract symbols to support representation and communication

    5. (Included in full purchase)

      M3-S2.5: Advantages of Multiple Solution Paths for Deep Conceptual Understanding of Subtraction

    1. (Included in full purchase)

      M3-S3.1: Base Ten Place Value System and Subtraction through Partitioning

    2. (Included in full purchase)

      M3-S3.2: Singapore Subtraction Approach: Dynamic Compensation (Concrete-Pictorial-Abstract)

    3. (Included in full purchase)

      M3-S3.3: Singapore Subtraction Approach: Number Bonds - Horizontal Orientation (Concrete-Pictorial)

    4. (Included in full purchase)

      M3-S3.4: Singapore Subtraction Approach: Number Bonds - Horizontal Orientation (Abstract 1-3 digit minuends and subtrahends)

    5. (Included in full purchase)

      M3-S3.5: Singapore Subtraction Approach: Left to Right Vertical Orientation (1 digit Singapore Subtraction Approach: Left to Right Vertical Orientation (1 digit minuends and subtrahends)

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      M3-S3.6: Singapore Subtraction Approach: Left to Right Vertical Orientation (2 digit minuends and subtrahends)

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      M3-S3.7: Singapore Subtraction Approach: Left to Right Vertical Orientation (3+ digit minuends and subtrahends)

    8. (Included in full purchase)

      M3-S3.8: Singapore Subtraction Approach vs Traditional Algorithm (Vertical Column Subtraction)

    9. (Included in full purchase)

      Module 3: Section 3 - Participant Engagement Check

    1. (Included in full purchase)

      M3-S4.1: Defining Structured Variation (Subtraction)

    2. (Included in full purchase)

      M3-S4.2: Designing Differentiated Subtraction Tasks: Multiple Entry Points

    3. (Included in full purchase)

      M3-S4.3: Mathematical Language of Subtraction and Visualisation (Multilingual Learners)

    4. (Included in full purchase)

      M3-S4.4: Scaffolded Learning of Subtraction: Revisiting Stages to Support Understanding

    5. (Included in full purchase)

      Module 3: Section 4 - Participant Engagement Check

    1. (Included in full purchase)

      M3-S5.1: Identifying and Analysing Common Misconceptions in Subtraction

    2. (Included in full purchase)

      M3-S5.2: Applying Formative Assessment Strategies for Subtraction

    3. (Included in full purchase)

      M3-S5.3: Strengthening Pupil Understanding: Evidence-Based Responsive Teaching

    4. (Included in full purchase)

      M3-S5.4: Why is Subtraction Competency Critical?

    5. (Included in full purchase)

      M3-S5.5: Reflective Discussion Forum Assignment

    6. (Included in full purchase)

      Subtraction Misconception Analysis Task (Sample-Based)

    1. (Included in full purchase)

      Module 4 Overview

    2. (Included in full purchase)

      Module 4 Learning Outcomes

    1. (Included in full purchase)

      M4-S1.1: What is Bar Modelling?

    2. (Included in full purchase)

      M4-S1.2: Alignment with PYP Priorities: Problem Solving

    3. (Included in full purchase)

      M4-S1.3: Alignment with PYP Priorities: Reasoning

    4. (Included in full purchase)

      M4-S1.4: Alignment with PYP Priorities: Representation and Communication

    5. (Included in full purchase)

      M4-S1.5: Part-Whole Bar Model

    6. (Included in full purchase)

      M4-S1.6: Comparison Bar Model

    7. (Included in full purchase)

      Module 4-Section 1: Participant Engagement Check

    1. (Included in full purchase)

      M4-S2.1: What are Problem-Solving Heuristics?

    2. (Included in full purchase)

      M4-S2.2: Common Addition Problem-Solving Heuristics

    3. (Included in full purchase)

      M4-S2.3: Common Subtraction Problem-Solving Heuristics

    4. (Included in full purchase)

      M4-S2.4: Word Problem Sequencing: Recommended Progression for Addition and Subtraction

    5. (Included in full purchase)

      M4-S2.5: Importance of Teaching Strategic Thinking and Growth Mindset

    6. (Included in full purchase)

      Module 4 - Section 2: Participant Engagement Check

    1. (Included in full purchase)

      M4-S3.1: Use of the Concrete–Pictorial–Abstract (CPA) approach within Word Problem Solving

    2. (Included in full purchase)

      M4-S3.2: Part Whole Bar Model Examples of Addition Problem Solving (Concrete and Pictorial)

    3. (Included in full purchase)

      M4-S3.3: Part Whole Bar Model Drawing Examples for Addition (Abstract)

    4. (Included in full purchase)

      M4-S3.4: Part Whole Bar Model Examples of Subtraction Problem Solving (Concrete and Pictorial)

    5. (Included in full purchase)

      M4-S3.5: Part Whole Bar Model Drawing Examples for Subtraction (Abstract)

    6. (Included in full purchase)

      M4-S3.6: Comparison Bar Model Example involving Addition

    7. (Included in full purchase)

      M4-S3.7: Comparison Bar Model Examples involving Subtraction

    1. (Included in full purchase)

      M4-S4.1: Inclusive Teaching: Multiple Entry Points for Problem Solving

    2. (Included in full purchase)

      M4-S4.2: The Importance of Visualisation and Reducing Linguistic Complexity

    3. (Included in full purchase)

      M4-S4.3: Restating the Problem and Forming Representations

    4. (Included in full purchase)

      M4-S4.4: Procedure for Step-by-Step Reasoning

    5. (Included in full purchase)

      M4-S4.5: Simplifying the Problem - Identifying Necessary Operations to Solve

    6. (Included in full purchase)

      Module 4 - Section 4: Participant Engagement Check

    1. (Included in full purchase)

      M4-S5.1: Reflective Discussion Forum Assignment

    2. (Included in full purchase)

      Course Summative Singapore Methodology Proficiency Task

    1. (Included in full purchase)

      Module 5 Overview

    2. (Included in full purchase)

      Module 5 Learning Outcomes

    1. (Included in full purchase)

      M5-S1.1: Opportunities for Teaching Singapore Mathematics Methodologies Within PYP Framework

    1. (Included in full purchase)

      M5-S2.1: Expert Modelling Presentation Event

    1. (Included in full purchase)

      M5-S3.1: Final Course Reflection Assignment

    1. (Included in full purchase)

      M5-S4.1: Enhanced Teacher Practice = Improved Pupil Achievement

    2. (Included in full purchase)

      M5-S4.2: Collaborative Planning and Reflection — Singapore Mathematics Integration in IB PYP Schools

    3. (Included in full purchase)

      M5-S4.3: Pupil Records Review: Pace and Challenge, Opportunities, Knowledge Gaps

    4. (Included in full purchase)

      M5-S4.4: Embedding CPA in Daily Instruction in the IB PYP Mathematics Classroom

    5. (Included in full purchase)

      M5-S4.5: Ongoing Assessment for Learning and Responsive Teaching

    1. (Included in full purchase)

      M5-S5.1: Mapping the Curriculum

    2. (Included in full purchase)

      M5-S5.2: Establishing Baseline

    3. (Included in full purchase)

      M5-S5.3: Timelines

    4. (Included in full purchase)

      M5-S5.4: Building Teacher Pedagogical Capacity

    5. (Included in full purchase)

      M5-S5.5: Reflective Implementation

    6. (Included in full purchase)

      Paddy Teacher Course Participant Evaluation Form

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