Math IA Thinking Compass — Student Handbook

IB Mathematics

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01Interest Discovery 02Mathematical Direction 03Topic Refinement 04Topic Ladder 05Data Collection 06IA Structure 07Readiness Check

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IB Mathematics · Internal Assessment Planning

Math IA Thinking Compass

Student Planning Handbook

Work through each section to develop your own IA idea — from first interest to teacher conference readiness. Your responses save automatically. The compass records your thinking; it does not write the IA.

Integrity first. This tool supports thinking and planning. All written content must represent your own ideas and understanding.

Teacher Supervision Notes

Ask students to explain why the idea matters to them before discussing methods. Genuine personal engagement must be student-generated, not teacher-suggested.

Check whether the proposed data can realistically be collected, cleaned, and analysed within the IA timeline. Feasibility issues are best caught at the planning stage.

Prompt students to justify mathematical choices in their own words. Avoid supplying a finished research question or analysis route — this compromises Criterion C and academic integrity.

Look for threads of reflection throughout: assumptions, limitations, model fit, error, and what the mathematics reveals or fails to reveal. These belong in the IA itself, not just the conclusion.

Use the Readiness Check as a formative conference guide. A student who has completed all seven sections with substantive personal responses is ready for a meaningful supervision conversation.

Interest Discovery

Begin with a broad area, then search for measurable movement, relationships, comparisons, and decisions inside it.

Broad area of interest Name the area, not a final IA topic. Examples: sport, music, environment, design, health, business.

Discovery prompts — think about each one before writing below

What can be measured in this area?
What changes over time?
What two quantities might be related?
What could be compared across groups, places, or conditions?
What prediction could mathematics help you make?

Measurable quantities you notice

Patterns, changes, or comparisons

Possible relationships between quantities

Decisions or predictions mathematics could support

Mathematical Direction

Choose the nature of your idea. The pathways are broad mathematical areas, not a prescribed solution.

Which direction best describes your idea? Select all that apply.

Possible broad pathways by direction

Changefunctions, calculus, modelling, statistics

Comparisonstatistics, geometry, trigonometry, modelling

Relationshipstatistics, regression, functions, modelling

Predictionregression, probability, functions, modelling

Optimizationcalculus, functions, geometry, modelling

Space / Designgeometry, trigonometry, modelling, functions

Uncertaintyprobability, statistics, modelling

Decision-makingstatistics, probability, modelling, functions

Important: Use only mathematics you understand and can explain. A strong IA does not need the most advanced method — it needs clear reasoning, accurate work, and honest reflection.

Which mathematics could you explain confidently right now? List topics from your current course that you understand well enough to apply and justify.

Topic Refinement

Enter your rough idea, then answer prompts that sharpen your own thinking.

Rough idea in your own words Do not write a polished research question yet. Just describe the idea informally.

Independent variable What are you changing or controlling?

Dependent variable What changes as a result?

Quantities to measure

Possible graph or representation

Possible mathematical method

Feasibility concerns

Personal connection Why does this matter to you beyond convenience? Criterion C rewards genuine engagement.

Possible limitations Name at least one limitation before collecting data. This shows proactive reflection.

Explorable Topic Ladder

Use your field to open possibilities at different depths. These are broad inquiry directions, not final research questions.

Field you want to explore Can be broad. Refinement comes through your choices and data plan.

Depth you want to attempt first Low is not weak — it means manageable and clear.

Low

Describe a measurable pattern in your field

Use clear data, graphs, summary statistics, or simple functions to show what is happening. Your challenge is precision, clarity, and honest interpretation.

Medium

Compare or connect quantities in your field

Investigate whether two measurable features appear related, different, or useful for a decision. Your challenge is choosing suitable variables and justifying the method.

High

Build, test, and critique a model for your field

Create or adapt a mathematical model, test how well it works, and evaluate assumptions, error, limitations, and possible improvements.

Your current explorable topic direction Describe the direction in your own words. Avoid writing a final research question yet.

Self-check — tick each one honestly

Is the topic focused enough to investigate in 12–20 pages?
Is it mathematical at its core?
Is it personally meaningful to you?
Can the necessary data realistically be collected?
Does it allow for analysis and genuine reflection?

Data Collection Planner

Clarify what your data is, where it comes from, and how another person could repeat your method.

Nature of data — select one

Data type — select one from each row

Discrete Continuous

One-variable Two-variable

Numerical Categorical

Repeated trials Single observations

How many data points will you collect?

How will you collect the data?

What tools will you use?

How will you reduce error?

What assumptions are you making?

Is the data ethical?

Can someone repeat your method? Write as if explaining to a classmate who has never seen your plan. Repeatability is a mark of rigour.

IA Structure Planner

Build your own outline by deciding what should be evident to a reader. Write notes, not paragraphs.

Criterion A: Presentation (4 marks)

Coherent organisation, a clear aim, concise development, relevant tables or graphs placed where they are discussed, and a conclusion that links back to the exploration.

Criterion B: Mathematical communication (4 marks)

Correct notation, defined variables, labelled graphs, appropriate diagrams, and mathematical language that helps the reader follow your thinking.

Criterion C: Personal engagement (3 marks)

Your own curiosity, choices, decisions, adaptations, or ways of making the exploration personally meaningful.

Criterion D: Reflection (3 marks)

Ongoing evaluation of results, assumptions, limitations, reasonableness, and what your mathematics reveals or fails to reveal.

Criterion E: Use of mathematics (6 marks)

Mathematics that is relevant, accurate, understood by you, and used to investigate rather than decorate the work.

Tip: IB assessed student work samples can help you notice how finished explorations are organised. Review them for structure and standards — not for topics to copy.

What should be evident about your aim and focus?

What should be evident about your personal engagement?

What should be evident about your data or evidence?

What should be evident about the mathematics you will use?

What should be evident about notation, graphs, diagrams, and definitions?

What should be evident about your analysis?

What should be evident about reflection during the exploration?

What should be evident in your conclusion?

Readiness Check

A planning summary to assess whether your idea is developed enough for a teacher conference. Not a grade.

Checklist before your teacher conference

I have described my interest area and can name specific measurable quantities within it.
I have chosen a mathematical direction and can name at least one pathway I understand.
I have written a rough idea with an independent and dependent variable identified.
I have identified a possible method and can explain why it fits my quantities.
I have described a personal connection to the idea beyond convenience.
I have chosen an inquiry field and depth level and written my topic direction in my own words.
I have stated the nature and type of data and can explain where it will come from.
I have described how many data points I need and how error will be reduced.
My method could be repeated by someone else following my description.
I have noted at least one limitation or assumption before collecting data.
I have completed the IA Structure Planner with notes for each section.

What to bring to your teacher conference

This completed handbook (print or download using the button above)
A clear explanation of why the idea matters to you
An honest account of your data access and collection plan
A description of the mathematics you understand and intend to use
At least one identified limitation or concern

Any remaining questions or concerns before your conference

Teacher Supervision Notes

Guidance for educators using this handbook with students.

Ask students to explain why the idea matters to them before discussing methods. Genuine personal engagement must be student-generated, not teacher-suggested.

Check whether the proposed data can realistically be collected, cleaned, and analysed within the IA timeline. Feasibility issues are best caught at the planning stage.

Prompt students to justify mathematical choices in their own words. Avoid supplying a finished research question or analysis route — this compromises Criterion C and academic integrity.

Look for threads of reflection throughout: assumptions, limitations, model fit, error, and what the mathematics reveals or fails to reveal. Criterion D rewards ongoing evaluation, not just a closing paragraph.

Use the Readiness Check as a formative conference guide. A student who has completed all seven sections with substantive personal responses is ready for a meaningful supervision conversation.

Consulting IB assessed work samples is acceptable for structural reference. It is not acceptable to replicate topics, data, or analyses from existing explorations.

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