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US IB Math Applications and Interpretations SL: Internal Assessments

IA Rubric

The exploration is internally assessed by the teacher and externally moderated by the IB using assessment criteria that relate to the objectives for mathematics. Each exploration is assessed against the following five criteria. The final mark for each exploration is the sum of the scores for each criterion. The maximum possible final mark is 20. Students will not receive a grade for their mathematics course if they have not submitted an exploration. 


Click the document below for a full list of example IA's provided by IB. 

The “presentation” criterion assesses the organization and coherence of the exploration. A coherent exploration is logically developed, easy to follow and meets its aim. This refers to the overall structure or framework, including introduction, body, conclusion and how well the different parts link to each other. A well-organized exploration includes an introduction, describes the aim of the exploration and has a conclusion. Relevant graphs, tables and diagrams should accompany the work in the appropriate place and not be attached as appendices to the document. Appendices should be used to include information on large data sets, additional graphs, diagrams and tables. Internal assessment Mathematics: applications and interpretation guide 85 A concise exploration does not show irrelevant or unnecessary repetitive calculations, graphs or descriptions. The use of technology is not required but encouraged where appropriate. However, the use of analytic approaches rather than technological ones does not necessarily mean lack of conciseness, and should not be penalized. This does not mean that repetitive calculations are condoned.

The “mathematical communication” criterion assesses to what extent the student has: • used appropriate mathematical language (notation, symbols, terminology). Calculator and computer notation is acceptable only if it is software generated. Otherwise it is expected that students use appropriate mathematical notation in their work • defined key terms and variables, where required • used multiple forms of mathematical representation, such as formulae, diagrams, tables, charts, graphs and models, where appropriate • used a deductive method and set out proofs logically where appropriate Examples of level 1 can include graphs not being labelled, consistent use of computer notation with no other forms of correct mathematical communication. Level 4 can be achieved by using only one form of mathematical representation as long as this is appropriate to the topic being explored. For level 4, any minor errors that do not impair clear communication should not be penalized. 

The “personal engagement” criterion assesses the extent to which the student engages with the topic by exploring the mathematics and making it their own. It is not a measure of effort. Personal engagement may be recognized in different ways. These include thinking independently or creatively, presenting mathematical ideas in their own way, exploring the topic from different perspectives, making and testing predictions. Further (but not exhaustive) examples of personal engagement at different levels are given in the teacher support material (TSM). Internal assessment 86 Mathematics: applications and interpretation guide There must be evidence of personal engagement demonstrated in the student’s work. It is not sufficient that a teacher comments that a student was highly engaged. Textbook style explorations or reproduction of readily available mathematics without the candidate’s own perspective are unlikely to achieve the higher levels. Significant: The student demonstrates authentic personal engagement in the exploration on a few occasions and it is evident that these drive the exploration forward and help the reader to better understand the writer’s intentions. Outstanding: The student demonstrates authentic personal engagement in the exploration in numerous instances and they are of a high quality. It is evident that these drive the exploration forward in a creative way. It leaves the impression that the student has developed, through their approach, a complete understanding of the context of the exploration topic and the reader better understands the writer’s intentions. 


The “reflection” criterion assesses how the student reviews, analyses and evaluates the exploration. Although reflection may be seen in the conclusion to the exploration, it may also be found throughout the exploration. Simply describing results represents limited reflection. Further consideration is required to achieve the higher levels. Some ways of showing meaningful reflection are: linking to the aims of the exploration, commenting on what they have learned, considering some limitation or comparing different mathematical approaches. Critical reflection is reflection that is crucial, deciding or deeply insightful. It will often develop the exploration by addressing the mathematical results and their impact on the student’s understanding of the topic. Some ways of showing critical reflection are: considering what next, discussing implications of results, discussing strengths and weaknesses of approaches, and considering different perspectives. Substantial evidence means that the critical reflection is present throughout the exploration. If it appears at the end of the exploration it must be of high quality and demonstrate how it developed the exploration in order to achieve a level 3. Further (but not exhaustive) examples of reflection at different levels are given in the teacher support material (TSM).

The “Use of mathematics” SL criterion assesses to what extent students use mathematics that is relevant to the exploration. Relevant refers to mathematics that supports the development of the exploration towards the completion of its aim. Overly complicated mathematics where simple mathematics would suffice is not relevant. Students are expected to produce work that is commensurate with the level of the course, which means it should not be completely based on mathematics listed in the prior learning. The mathematics explored should either be part of the syllabus, or at a similar level. A key word in the descriptor is demonstrated. The command term demonstrate means “to make clear by reasoning or evidence, illustrating with examples or practical application”. Obtaining the correct answer is not sufficient to demonstrate understanding (even some understanding) in order to achieve level 2 or higher. For knowledge and understanding to be thorough it must be demonstrated throughout. The mathematics can be regarded as correct even if there are occasional minor errors as long as they do not detract from the flow of the mathematics or lead to an unreasonable outcome. Students are encouraged to use technology to obtain results where appropriate, but understanding must be demonstrated in order for the student to achieve higher than level 1, for example merely substituting values into a formula does not necessarily demonstrate understanding of the results. The mathematics only needs to be what is required to support the development of the exploration. This could be a few small elements of mathematics or even a single topic (or sub-topic) from the syllabus. It is better to do a few things well than a lot of things not so well. If the mathematics used is relevant to the topic being explored, commensurate with the level of the course and understood by the student, then it can achieve a high level in this criterion.

Steps of IA Process

         Step 3:  Data Gathering and Structuring an IA

Most students writing for the IA begins with data.

Data can be gathered through:
     secondary research, primary research
     (ex: surveying), using a tool or program to
      generate the data, or experimentation

No matter how you gather data, there is a recommended structure
that is to be followed in an IA, much of which connects to your data.

This structure includes the following:

- an aim (and sometimes, hypotheses)

- a rationale (why it is important) and implications

- data gathering process (including sampling)

- reflection on reliability, validity and bias

- appropriate presentation of and analysis of data

- conclusion connecting back to the aim

Websites we recommend

Evaluating web sources

Anyone can put information on the web, so how can we tell if it's reliable and accurate?

  • Who is the author?  Do they have qualifications/a reputation in the relevant area?
  • Is the website affiliated with an organisation?  If so, what is the mission of that organisation?
  • Has the information been properly referenced?  Are the references authoritative?
  • When was the site last updated?
  • Is there any reason for bias on this web site?
  • Has the website been well presented in an appropriately academic style?
  • Has anyone recommended this website to you?
  • Does the information match what you have learned from other sources?

Watch this short video:

Social Media


Social media can include any of the following:

  • Blogs
  • Discussion forums
  • Microblogs (i.e. Twitter)
  • News aggregators (i.e. Digg)
  • Photo sharing
  • Podcasts
  • RSS
  • Social networks
  • Video sharing
  • Wikis

All of these types of social media have their own merits and drawbacks when searching for information. As the field is still growing, there is an abundance of ways to use these sites.

Some sites you could use in your studies or research include:

Follow these links for information on how to use social media in your studies or research:

Internal Assessment Examples


Florence Nightingale (20/20)






Tea Cup Example



A4—Brief aim. Easy to read, logical, detailed. Clear aim (although the student does stray from it slightly). Coherent work through transformations required to obtain model. Returns to original question at end to fulfil aim – complete.

B2—Tables displaying data and units and clear. Labels on axes not always clear but appropriate graphs throughout. Misuse of words “scatter graph”, “constants”. Variables clearly defined.

C3—Application of area of mathematical interest to real-life situation. Conducts own experiment. Comparison of different approaches to produce models. Looks for different ways to explore problem.

D3—Reflects on nature of problem. Reflects on degree of accuracy of results. Constantly comparing models. Reflects on possible reasons for discrepancies between model and real-life data and considers ways to analyse this.

E6—Good initial analysis of results. Understanding of transformations of graphs and exponentials/natural logarithms (commensurate with syllabus) clearly demonstrated. Correct calculations throughout.





A4—The exploration is concise and easy to follow. A couple of typing errors does not detract from the flow.

B3—Multiple forms are well used.

C4—The work is highly original, and the student used historical idea to create her own similar situation. She is clearly engaged in the work.

D3—There is critical reflection, where the student tries to resolve contradictions discovered.

E6—Areas of sectors using radians and descriptive statistics are commensurate with the mathematics SL course, and are done well enough at achieve level 6.

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