Math Exploration ie. Internal Assessment (IA). Guidelines, DOs DONTs, Sample IA of our students…


A written paper that explores the math behind a personal interest of your choice


  • To apply and transfer skills to alternate situations, to other areas of knowledge, and to future developments
  • To appreciate the moral, social, and ethical implications of Mathematics
  • To appreciate the international dimensions & universality of Mathematics
  • Appreciate the contribution of Mathematics to other disciples


  • 6-12 pages
  • All sources must be cited in a bibliography. Please use the subsections Works Cited, Image Sources, and definition Sources.
  • Not a regurgitation of facts or a historical essay.
  • The target audience is your peers. Not expected to be a formal dissertation using ostentatiousvocabulary.
  • Use of mathematical technology or software is strongly encouraged.
  • You are not expected to use any mathematics outside the level of this course, but you may if it iscommensurate with the level of the course.
  • 20% of your IB mark


  • GeoGebra: Software for working with graphs, diagrams, functions, spreadsheets, statistics and more.
  • Desmos: Software for graphing points, functions and tables.
  • Equation Editor: Found in Microsoft Word and Google docs. Used for writing equations and other mathematical notation. (You may need to install this feature)
  • WolframAlpha/Mathematica: Computation software

Evaluation Criterion (IMP. pls read this carefully and try to implement these points as much as possible)


  • Includes Introduction, rationale (Why did you choose this topic? Why is this topic of interest to you?), aim (What do you hope your reader will learn?), and conclusion
  • Expressing ideas clearly
  • Identifying a clear aim for the exploration
  • Focusing on the aim and avoiding irrelevance
  • Structuring ideas in a logical manner
  • Editing the exploration so that it is easy to follow
  • Citing references where appropriate
  • Graphs, tables and diagrams should accompany the work in the appropriate place and not be attached asappendices to the document.


  • Using appropriate mathematical language and representation (notation, symbols, terminology)
  • Defining key terms, where required
  • Selecting appropriate mathematical tools & technology (such as graphic display calculators, screenshots, graphing software, spreadsheets, databases, drawing & word-processing software, etc)
  • Expressing results to an appropriate degree of accuracy
  • Use multiple forms of mathematical representation, such as formulae, diagrams, tables, charts, graphs and models, where appropriate.


  • Thinking independently and/or creatively
  • Asking questions, making conjectures, and investigating mathematical ideas
  • Researching areas of interest
  • Looking for and creating mathematical models for real-world situations
  • Considering historical and global perspectives
  • Demonstrating that you have “made the exploration their own”
  • Expressing ideas in an individual way
  • Addressing personal interest
  • Presenting mathematical ideas in their own way.
  • Asking and answering questions: “I wonder if…”, “What would happen if…” “Why does that happen…

D: REFLECTION (3 marks)

  • Reviewing, analysing and evaluating the exploration.
  • Discussing the implications of results
  • Considering the significance of the exploration
  • Looking at possible limitations and/or extensions
  • Making links to different fields and/or areas of mathematics
  • Making connections to TOK


  • Demonstrating knowledge and understanding
  • Producing work that is within the level of the course.
  • Applying mathematics in different contexts
  • Applying problem-solving techniques
  • Recognizing and explaining patterns, where appropriate
  • Looking at a problem from different perspectives
  • Error-free mathematics
  • Mathematical sophistication


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