𝗜𝗻𝘁𝗿𝗼𝗱𝘂𝗰𝘁𝗶𝗼𝗻: 𝗧𝗵𝗲 𝗣𝗼𝘄𝗲𝗿 𝗮𝗻𝗱 𝗣𝘂𝗿𝗽𝗼𝘀𝗲 𝗼𝗳 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝘀 𝗶𝗻 𝘁𝗵𝗲 𝗣𝗬𝗣
Math in the IB PYP helps students develop conceptual understanding, problem-solving, inquiry skills, and real-world connections through authentic learning experiences. Math is a language for inquiry, a tool for analysis, and a bridge to real-world understanding. In the PYP, students are encouraged to see themselves as mathematicians, using math to explore, communicate, and take action in authentic contexts.
𝟭. 𝗦𝘁𝗮𝗻𝗱𝗮𝗹𝗼𝗻𝗲 (𝗗𝗶𝘀𝗰𝗶𝗽𝗹𝗶𝗻𝗲-𝗦𝗽𝗲𝗰𝗶𝗳𝗶𝗰) 𝘃𝘀. 𝗧𝗿𝗮𝗻𝘀𝗱𝗶𝘀𝗰𝗶𝗽𝗹𝗶𝗻𝗮𝗿𝘆 𝗠𝗮𝘁𝗵 𝗶𝗻 𝘁𝗵𝗲 𝗣𝗬𝗣
Mathematics in the PYP is taught through a balanced approach that combines both standalone (also known as discipline-specific) and transdisciplinary learning. This ensures students develop strong foundational skills while also applying mathematical thinking across all areas of the curriculum.
Standalone Math refers to focused lessons on core mathematical concepts and skills that require explicit instruction and practice. These are sometimes called “subject-specific” or “discipline-specific” lessons in IB documents. They cover areas such as number sense, operations, and foundational measurement or geometry concepts that may not naturally fit into a Unit of Inquiry (UOI).
Transdisciplinary Math is authentically integrated into UOIs, where students use mathematics to make sense of real-world problems, connect with other subjects, and deepen their understanding of the central idea and lines of inquiry. This approach helps students see the relevance of math in daily life and across disciplines.
𝗘𝗳𝗳𝗲𝗰𝘁𝗶𝘃𝗲 𝗣𝗬𝗣 𝗺𝗮𝘁𝗵 𝗽𝗿𝗼𝗴𝗿𝗮𝗺𝘀 𝗯𝗹𝗲𝗻𝗱 𝗯𝗼𝘁𝗵 𝗮𝗽𝗽𝗿𝗼𝗮𝗰𝗵𝗲𝘀:
- Some strands (like number or operations) are often best taught in standalone (discipline-specific) lessons, while others (like data handling, measurement, or pattern) lend themselves to integration.
- Teachers collaboratively plan when and how to teach math within or outside the Programme of Inquiry, ensuring all strands and skills are addressed.
𝗖𝗼𝗺𝗽𝗮𝗿𝗶𝗻𝗴 𝗦𝘁𝗮𝗻𝗱𝗮𝗹𝗼𝗻𝗲 (𝗗𝗶𝘀𝗰𝗶𝗽𝗹𝗶𝗻𝗲-𝗦𝗽𝗲𝗰𝗶𝗳𝗶𝗰) 𝗮𝗻𝗱 𝗧𝗿𝗮𝗻𝘀𝗱𝗶𝘀𝗰𝗶𝗽𝗹𝗶𝗻𝗮𝗿𝘆 𝗠𝗮𝘁𝗵
This balanced structure ensures that all students experience mathematics as both foundational and relevant, supporting their growth as confident, capable mathematicians in line with the latest PYP curriculum framework.
𝟮. 𝗖𝗼𝗺𝗽𝗼𝗻𝗲𝗻𝘁𝘀 𝗼𝗳 𝗮 𝗠𝗮𝘁𝗵 𝗦𝘁𝗮𝗻𝗱𝗮𝗹𝗼𝗻𝗲 𝗣𝗹𝗮𝗻𝗻𝗲𝗿
A well-designed Math Standalone Planner in the PYP includes:
- 𝗖𝗲𝗻𝘁𝗿𝗮𝗹 𝗜𝗱𝗲𝗮: A broad conceptual statement guiding the unit (e.g., “Numbers help us describe and compare the world around us.”)
- 𝗟𝗶𝗻𝗲𝘀 𝗼𝗳 𝗜𝗻𝗾𝘂𝗶𝗿𝘆: Specific aspects of the central idea (e.g., strategies for addition/subtraction, understanding place value)
- Specified 𝗖𝗼𝗻𝗰𝗲𝗽𝘁𝘀: Guiding ideas such as form, function, causation, connection
- Additional 𝗖𝗼𝗻𝗰𝗲𝗽𝘁𝘀: Mathematical ideas like grouping, estimation, comparison
- 𝗟𝗲𝗮𝗿𝗻𝗲𝗿 𝗣𝗿𝗼𝗳𝗶𝗹𝗲 𝗔𝘁𝘁𝗿𝗶𝗯𝘂𝘁𝗲𝘀: Focused attributes (e.g., thinker, inquirer)
- 𝗔𝗽𝗽𝗿𝗼𝗮𝗰𝗵𝗲𝘀 𝘁𝗼 𝗟𝗲𝗮𝗿𝗻𝗶𝗻𝗴 (𝗔𝗧𝗟) 𝗦𝗸𝗶𝗹𝗹𝘀: Targeted skills (e.g., thinking, self-management)
- 𝗣𝗿𝗼𝘃𝗼𝗰𝗮𝘁𝗶𝗼𝗻𝘀: Engaging questions or tasks to spark curiosity (e.g., “How many ways can you show the number 100?”)
- 𝗟𝗲𝗮𝗿𝗻𝗶𝗻𝗴 𝗘𝘅𝗽𝗲𝗿𝗶𝗲𝗻𝗰𝗲𝘀: Activities and investigations planned for the unit
- 𝗔𝘀𝘀𝗲𝘀𝘀𝗺𝗲𝗻𝘁: Formative and summative tasks that measure understanding and skills
- 𝗔𝗰𝘁𝗶𝗼𝗻: Opportunities for students to apply learning in meaningful ways
𝟯. 𝗞𝗲𝘆 𝗣𝗿𝗶𝗻𝗰𝗶𝗽𝗹𝗲𝘀 𝗼𝗳 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝘀 𝗶𝗻 𝘁𝗵𝗲 𝗣𝗬𝗣
Mathematics in the IB Primary Years Programme (PYP) is not taught as an isolated subject, but rather as an interconnected discipline that supports inquiry, develops conceptual understanding, and builds essential skills for lifelong learning. The teaching and learning of mathematics in the PYP are guided by several core principles that ensure learning is meaningful, relevant, and developmentally appropriate.
(𝟯.𝟭) 𝗜𝗻𝗾𝘂𝗶𝗿𝘆-𝗕𝗮𝘀𝗲𝗱 𝗟𝗲𝗮𝗿𝗻𝗶𝗻𝗴: Mathematics in the PYP is rooted in inquiry, where students actively explore, question, and construct their own understanding. Instead of memorizing procedures, they investigate patterns and relationships to make sense of mathematical concepts. This fosters curiosity and resilience as students learn through discovery and reflection.
𝗘𝘅𝗮𝗺𝗽𝗹𝗲: In Grade 2, students use different tools to measure classroom objects and then compare their results, discussing why measurements might differ and which methods are most accurate.
(𝟯.𝟮) 𝗧𝗿𝗮𝗻𝘀𝗱𝗶𝘀𝗰𝗶𝗽𝗹𝗶𝗻𝗮𝗿𝘆 𝗖𝗼𝗻𝗻𝗲𝗰𝘁𝗶𝗼𝗻𝘀: Math is authentically integrated across all subjects, connecting learning to real-world contexts and other disciplines. This approach helps students see the relevance of mathematics beyond the math classroom and deepens conceptual understanding. Students apply math skills in meaningful, purposeful ways throughout the Programme of Inquiry.
𝗘𝘅𝗮𝗺𝗽𝗹𝗲: During a “Sharing the Planet” unit, Grade 4 students collect data on water usage at home, create graphs, and analyze patterns to understand environmental impact.
(𝟯.𝟯) 𝗔𝗰𝘁𝗶𝘃𝗲 𝗮𝗻𝗱 𝗖𝗼𝗹𝗹𝗮𝗯𝗼𝗿𝗮𝘁𝗶𝘃𝗲 𝗟𝗲𝗮𝗿𝗻𝗶𝗻𝗴: Learning math in the PYP is hands-on and social, involving manipulatives, technology, and group work. Students share ideas, explain thinking, and solve problems together, building confidence and communication skills. Collaboration ensures that students learn from multiple perspectives and develop a deeper understanding.
𝗘𝘅𝗮𝗺𝗽𝗹𝗲: In Grade 1, students work in teams to create patterns with blocks, then present their patterns to classmates and explain their reasoning.
(𝟯.𝟰) 𝗖𝗼𝗻𝗰𝗲𝗽𝘁𝘂𝗮𝗹 𝗮𝗻𝗱 𝗦𝗸𝗶𝗹𝗹𝘀-𝗕𝗮𝘀𝗲𝗱 𝗙𝗼𝗰𝘂𝘀: The PYP emphasizes both deep conceptual understanding and the development of essential math skills. Students learn not just how to perform operations but also why mathematical ideas work and when to apply them. This balance prepares students for lifelong mathematical thinking and problem-solving.
𝗘𝘅𝗮𝗺𝗽𝗹𝗲: In Grade 5, students explore fractions by folding paper, drawing models, and solving real-life scenarios, connecting concrete experiences to abstract concepts.
(𝟯.𝟱) 𝗗𝗶𝗳𝗳𝗲𝗿𝗲𝗻𝘁𝗶𝗮𝘁𝗲𝗱 𝗜𝗻𝘀𝘁𝗿𝘂𝗰𝘁𝗶𝗼𝗻: The PYP recognizes that learners come from diverse backgrounds and possess varied prior knowledge, learning styles, and paces. Mathematics instruction is differentiated through the use of tiered tasks, flexible grouping, student choice, and ongoing formative assessment.
𝗘𝘅𝗮𝗺𝗽𝗹𝗲: In a unit on decimals, students may engage in different activities based on readiness: some may be identifying place values using manipulatives, others might be solving real-life shopping scenarios involving decimals, while a third group works on word problems involving multiplication and division of decimals.
These principles together ensure that mathematics in the PYP is not merely about numbers, but about thinking, reasoning, problem-solving, and making sense of the world. It nurtures confident mathematicians who understand how math connects to life, inside and outside the classroom.
𝟰. 𝗘𝘀𝘀𝗲𝗻𝘁𝗶𝗮𝗹 𝗘𝗹𝗲𝗺𝗲𝗻𝘁𝘀: 𝗖𝗼𝗻𝗰𝗲𝗽𝘁𝘀 𝗮𝗻𝗱 𝗔𝗧𝗟 𝗦𝗸𝗶𝗹𝗹𝘀 𝗶𝗻 𝗠𝗮𝘁𝗵
Mathematics in the PYP is built on key concepts and Approaches to Learning (ATL) skills, supporting holistic development.
𝟰.𝟭 𝗖𝗼𝗻𝗰𝗲𝗽𝘁𝘀 𝗠𝗮𝘁𝗿𝗶𝘅:
𝟰.𝟮 𝗔𝗽𝗽𝗿𝗼𝗮𝗰𝗵𝗲𝘀 𝘁𝗼 𝗟𝗲𝗮𝗿𝗻𝗶𝗻𝗴 𝗦𝗸𝗶𝗹𝗹𝘀 𝗠𝗮𝘁𝗿𝗶𝘅:
𝟱. 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹 𝗦𝘁𝗿𝗮𝗻𝗱𝘀 𝗶𝗻 𝘁𝗵𝗲 𝗣𝗬𝗣
The PYP mathematics curriculum is organized into five interconnected strands, each supporting a different aspect of mathematical understanding.
These strands are addressed both in standalone lessons and through integration with the Programme of Inquiry, ensuring students see math as relevant and connected to their world
𝟲. 𝗜𝗻𝘁𝗲𝗴𝗿𝗮𝘁𝗶𝗻𝗴 𝗠𝗮𝘁𝗵 𝗶𝗻𝘁𝗼 𝘁𝗵𝗲 𝗣𝗿𝗼𝗴𝗿𝗮𝗺𝗺𝗲 𝗼𝗳 𝗜𝗻𝗾𝘂𝗶𝗿𝘆 (𝗣𝗢𝗜): 𝗘𝘅𝗮𝗺𝗽𝗹𝗲𝘀 𝗳𝗼𝗿 𝗔𝗹𝗹 𝗧𝗵𝗲𝗺𝗲𝘀 𝗮𝗻𝗱 𝗚𝗿𝗮𝗱𝗲𝘀
Mathematics is authentically integrated into each transdisciplinary theme at every grade level. This approach helps students apply mathematical thinking in real-life contexts, deepening both conceptual understanding and engagement
How to use this matrix: Each cell provides a concrete example of how math can be authentically embedded in a UOI under a specific transdisciplinary theme, ensuring that students experience math as purposeful and relevant at every stage of their PYP journey.
𝟳. 𝗛𝗮𝗻𝗱𝘀-𝗢𝗻 𝗧𝗼𝗼𝗹𝘀 𝗮𝗻𝗱 𝗕𝗲𝘀𝘁 𝗥𝗲𝘀𝗼𝘂𝗿𝗰𝗲𝘀 𝗳𝗼𝗿 𝗣𝗬𝗣 𝗠𝗮𝘁𝗵
Effective math teaching in the PYP uses a range of manipulatives and digital tools to make learning concrete, engaging, and accessible for all learners.
How to use this matrix: Select tools based on the learning objective and grade level. Manipulatives support hands-on exploration, while digital tools foster engagement, differentiation, and real-world application.
𝗥𝗲𝗺𝗼𝘃𝗶𝗻𝗴 𝗕𝗮𝗿𝗿𝗶𝗲𝗿𝘀 𝘁𝗼 𝗟𝗲𝗮𝗿𝗻𝗶𝗻𝗴 (𝗗𝗶𝗳𝗳𝗲𝗿𝗲𝗻𝘁𝗶𝗮𝘁𝗶𝗼𝗻) 𝗮𝗻𝗱 𝗣𝗲𝗿𝘀𝗼𝗻𝗮𝗹𝗶𝘇𝗲𝗱 𝗟𝗲𝗮𝗿𝗻𝗶𝗻𝗴 𝗶𝗻 𝘁𝗵𝗲 𝗣𝗬𝗣
In the IB PYP, creating an inclusive environment means proactively removing barriers to learning so that every student can participate fully and achieve their potential. What was previously referred to as “differentiation” is now more commonly described in IB documentation as “removing barriers to learning.” The emphasis is on designing learning experiences that are accessible, equitable, and responsive to the diverse needs, backgrounds, and interests of all learners.
- Removing barriers to learning involves identifying and addressing obstacles – whether cognitive, linguistic, physical, or emotional, that might prevent students from engaging with mathematical concepts or the wider curriculum. This includes providing multiple entry points, flexible pathways, and a range of resources and supports.
- Personalized learning is at the heart of this approach. Teachers recognize each student’s unique strengths, interests, and learning profiles, and adapt instruction accordingly. In mathematics, this might mean offering choices in how students explore or represent mathematical ideas, using manipulatives or digital tools, or designing open-ended tasks that allow for multiple strategies and solutions.
𝗞𝗲𝘆 𝘀𝘁𝗿𝗮𝘁𝗲𝗴𝗶𝗲𝘀 𝗳𝗼𝗿 𝗿𝗲𝗺𝗼𝘃𝗶𝗻𝗴 𝗯𝗮𝗿𝗿𝗶𝗲𝗿𝘀 (𝗗𝗶𝗳𝗳𝗲𝗿𝗲𝗻𝘁𝗶𝗮𝘁𝗶𝗼𝗻) 𝗮𝗻𝗱 𝗽𝗲𝗿𝘀𝗼𝗻𝗮𝗹𝗶𝘇𝗶𝗻𝗴 𝗹𝗲𝗮𝗿𝗻𝗶𝗻𝗴 𝗶𝗻 𝗺𝗮𝘁𝗵 𝗮𝗻𝗱 𝗮𝗰𝗿𝗼𝘀𝘀 𝘁𝗵𝗲 𝗣𝗬𝗣 𝗶𝗻𝗰𝗹𝘂𝗱𝗲:
- Universal Design for Learning (UDL): Planning lessons that offer various ways for students to access content, engage with learning, and demonstrate understanding.
- Flexible Grouping: Allowing students to work individually, in pairs, or in groups based on their needs and preferences.
- Multiple Representations: Using visuals, manipulatives, technology, and real-life contexts to make abstract concepts concrete.
- Scaffolded Support: Providing just-right challenges, prompts, or tools for students who need them, and opportunities for extension for those ready to go further.
- Student Agency and Voice: Encouraging students to set goals, make choices about their learning, and reflect on their progress.
- Assistive Technology: Leveraging digital tools and apps to support access and expression, especially for students with additional needs.
𝗘𝘅𝗮𝗺𝗽𝗹𝗲 𝗶𝗻 𝗠𝗮𝘁𝗵: A Grade 3 class is exploring multiplication. Some students use arrays and counters, others draw pictures, while a few use a multiplication app. The teacher offers challenge problems for those who are ready and provides sentence starters for students who need support in explaining their thinking. All students reflect on their strategies in a math journal, choosing the format that works best for them, writing, drawing, or voice recording.
𝟵. 𝗔𝘀𝘀𝗲𝘀𝘀𝗺𝗲𝗻𝘁 𝗶𝗻 𝗣𝗬𝗣 𝗠𝗮𝘁𝗵 in IB PYP (𝘄𝗶𝘁𝗵 𝗘𝘅𝗮𝗺𝗽𝗹𝗲𝘀)
Assessment in PYP math is ongoing, authentic, and varied, supporting both process and product. Here are some assessments and examples:
- Math Journals: Students record their strategies, solutions, and reflections in a dedicated math journal. (Example: After a lesson on patterns, students write or draw how they recognized and extended a pattern in the classroom.(
- Performance Tasks: Authentic, real-world problems or projects that require students to apply mathematical skills. (Example: Students design a school garden, calculating the area and perimeter needed for each planting bed.(
- Portfolios: Collections of student work over time that show progress and growth in mathematical understanding. (Example: Students gather their best work, including math projects, quizzes, and reflections, into a portfolio binder.)
- Observations and Anecdotal Records: Teachers observe students during activities and record notes about their thinking, strategies, and participation. (Example: During a group problem-solving task, the teacher notes how a student explains their reasoning to peers.)
- Self-Assessment: Students reflect on and rate their own learning and understanding. (Example: After a unit on fractions, students use a rubric to assess how confident they feel about adding and comparing fractions.(
- Peer Assessment: Students review and provide feedback on each other’s work. (Example: Partners check each other’s solutions to word problems and discuss the different strategies they used.)
- Quizzes and Exit Tickets: Short assessments to quickly check for understanding at the end of a lesson or unit. (Example: Before leaving class, students answer a question about today’s math concept on a sticky note.)
- Digital Assessments: Online platforms and apps for interactive math tasks and instant feedback. (Example: Students complete multiplication challenges on Mathletics and receive immediate results.)
- Conceptual Rubrics: Clear criteria used by teachers to assess students’ understanding of key math concepts. (Example: A rubric is used to evaluate how well students understand place value during a number unit.)
- Projects: Extended tasks that integrate multiple math skills and often other disciplines. (Example: Students conduct a survey, collect data, and present their findings using graphs and charts.)
- Presentations: Opportunities for students to explain their mathematical thinking to others. (Example: Students present their solution to a multi-step word problem using a poster and answer classmates’ questions.)
- Pre-Assessments: Assessments given before a new unit to gauge prior knowledge and inform instruction. (Example: Students complete a mind map showing everything they know about shapes before starting a geometry unit.)
- Human Graphs or Physical Models: Using students’ bodies or physical objects to represent mathematical data or concepts. (Example: The class forms a human bar graph to show everyone’s favorite type of fruit.)
- Math Talks: Structured discussions where students explain and justify their reasoning. (Example: Students share different ways to solve a subtraction problem and discuss which method is most efficient.)
- Investigations and Inquiry Tasks: Open-ended explorations that encourage students to discover and present mathematical patterns or relationships. (Example: Students investigate patterns in multiplication tables and share their discoveries with the class.)
This variety of assessment strategies ensures a comprehensive understanding of each student’s mathematical thinking, growth, and ability to apply concepts in multiple ways.
𝟭𝟬. 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹 𝗗𝗶𝘀𝗰𝗼𝘂𝗿𝘀𝗲 𝗮𝗻𝗱 𝗖𝗼𝗺𝗺𝘂𝗻𝗶𝗰𝗮𝘁𝗶𝗼𝗻
Mathematical discourse is central to PYP math. Students are encouraged to articulate their thinking, explain strategies, and justify solutions. Math talk, group discussions, and presentations build confidence, deepen understanding, and develop communication skills essential for lifelong learning.
𝟭𝟭. 𝗔𝗰𝘁𝗶𝗼𝗻 𝗧𝗵𝗿𝗼𝘂𝗴𝗵 𝗠𝗮𝘁𝗵: 𝗠𝗮𝗸𝗶𝗻𝗴 𝗮 𝗗𝗶𝗳𝗳𝗲𝗿𝗲𝗻𝗰𝗲
PYP students use their mathematical understanding to take meaningful action – solving real-life problems, advocating for causes, or improving their community. Math becomes a tool for inquiry, reflection, and positive change.
𝗘𝘅𝗮𝗺𝗽𝗹𝗲: Grade 4 students use data to create persuasive graphs for a school recycling campaign, presenting their findings to inspire action.
𝟭𝟮. 𝗧𝗲𝗮𝗰𝗵𝗲𝗿 𝗣𝗿𝗼𝗳𝗲𝘀𝘀𝗶𝗼𝗻𝗮𝗹 𝗗𝗲𝘃𝗲𝗹𝗼𝗽𝗺𝗲𝗻𝘁
Ongoing professional learning ensures teachers are confident and current in best practices for inquiry-based math. Collaboration, reflection, and training in new tools and strategies empower teachers to create rich, engaging math experiences for every learner.
𝟭𝟯. 𝗩𝗶𝘀𝘂𝗮𝗹 𝗘𝘅𝗮𝗺𝗽𝗹𝗲: 𝗠𝗮𝘁𝗵 𝗜𝗻𝘁𝗲𝗴𝗿𝗮𝘁𝗶𝗼𝗻 𝗣𝗿𝗼𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻 (𝗣𝗿𝗲-𝗞 𝘁𝗼 𝗚𝗿𝗮𝗱𝗲 𝟱)
A visual progression map shows how mathematical skills and concepts build from early exploration in Pre-K to advanced problem-solving and data analysis in Grade 5. This progression supports coherent, connected, and developmentally appropriate math learning.
𝗖𝗼𝗻𝗰𝗹𝘂𝘀𝗶𝗼𝗻: 𝗧𝗵𝗲 𝗙𝘂𝘁𝘂𝗿𝗲-𝗥𝗲𝗮𝗱𝘆 𝗣𝗬𝗣 𝗠𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗶𝗮𝗻
Mathematics in the PYP is a dynamic, inquiry-driven journey that prepares students to think critically, solve problems, and make connections in a complex world. By embedding math in real-life contexts, fostering agency, and supporting all learners, PYP educators empower students to become confident, creative, and reflective mathematicians – ready for the challenges of the future.
𝗥𝗲𝗳𝗲𝗿𝗲𝗻𝗰𝗲𝘀:
- [ISOP PYP Mathematics Scope and Sequence]
- [Integrating Math into an IB PYP Unit of Inquiry]
- [Toddle: PYP Mathematics Planning]
- [Integrating ATL in Math]
- [Integrating Inquiry-Based Math in the IB PYP]
- [IBO: Inquiry Strategies for Math]
- [DISV IB PYP Curriculum Handbook 2024-25]
This handbook is designed as a practical, inspirational reference for every PYP math teacher – helping you bring math to life in your classroom, every day.
