Overview of Internal Assessment for Mathematics HL: The Exploration
Note: Much of this overview is taken from IBO Math HL documents (2012).
Main features:
 An investigation that focuses on an area of mathematics that interests you: you
choose the topic.
 Written report 6-12 pages long, excluding bibliography; however, it is the quality
of the writing that matters, not the length
 Done individually
 Your audience is your classmates—they must be able to follow your report
 Emphasis is on:
 Mathematical communication (formulae, diagrams, graphs)
 Accompanying commentary with good mathematical writing
 Thoughtful reflection
Purpose: To give you the opportunity to apply your skills and knowledge and pursue
your personal interests in mathematics without the pressure of time limitations or other
constraints associated with tests.
Students should use the exploration to show that they can:
 Apply and transfer skills to alternative situations, to other areas of knowledge and
to future developments
 Appreciate how developments in technology and mathematics have influenced
each other
 Appreciate the moral, social and ethical implications arising from the work of
mathematicians and the applications of mathematics
 Appreciate the international dimension in mathematics through an awareness of
the universality of mathematics and its multicultural and historical perspectives
When it’s done: You will begin the exploration in HL1 by considering possible topics,
reading and researching, and narrowing your ideas down to a short list of topics by May
in HL1. You will complete a first draft in the fall of the HL2 year. The final version is
due in January of HL2. You may complete things earlier than this if you wish.
What it’s worth: The exploration counts for 20% of your IB grade. The other 80%
comes from the final IB math exams: Papers 1, 2, and 3. Altogether your IB grade
counts for 30% of the final grades for your Grade 12 courses, MHF4U and MCV4U, so
this means the exploration counts for 6% of the final grades for your Grade 12 courses.
You will not receive a grade for Math HL if you do not submit an exploration.
Time Required
 Approximately 10 hours of class/school time: Includes an introduction to the
requirements and the process, time to explore possible topics and choose one,
time to consult with teacher
 Approximately 10 hours outside class
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Authenticity:
 All work connected with the exploration, including the writing, should be your
own.
 In any given grade, no two explorations should be on the same particular topic.
 Direct quotes must be acknowledged.
 You must include a detailed bibliography.
 Be able to provide evidence that the exploration is your own work and that you
worked on it independently.
 Save all rough drafts labelled by date. Have them available until June of the year
you graduate.
 Be prepared to explain any aspects of your work with the teacher as you are
writing your report and after you have submitted it. The teacher could ask you to
explain the methods used and to summarize your results and conclusions. You
could also be asked to replicate part of the analysis using different data.
 Both the student and the teacher must sign a cover sheet regarding authenticity. If
the teacher has doubts about authenticity, no grade will be awarded for the report.
 The math exploration cannot be the same work as the EE.
How it’s marked: Each task is marked using a rubric with five criteria. Your HL2 teacher
will mark all the explorations and then the IBO will select several reports from the class
to be mailed off for external moderation. The marks for the entire set of explorations
may then be adjusted.
A
B
C
D
E
Criterion
Communication
Mathematical presentation
Personal engagement
Reflection
Use of mathematics
Maximum total mark
Maximum mark
4
3
4
3
6
20
Criterion A: Communication
Achievement Level
0
1
2
3
4


Descriptor
The exploration does not reach the standard described by the
descriptors below.
The exploration has some coherence.
The exploration has some coherence and shows some
organization.
The exploration is coherent and well-organized.
The exploration is coherent and well-organized, concise and
complete.
This criterion assesses the organization and coherence of the exploration
Organization:
o The title should not be too general. For example, rather than just “Water,”
use “Water—Predicting Storm Surges.”
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
o Include an introduction, a rationale (which explains why you chose this
topic), a clear description of the aim, a conclusion, and a bibliography.
o Number your pages.
o Number your tables: Table 1, Table 2, ,,,
o Number your diagrams and graphs: Figure 1, Figure 2, …
o Include tables, diagrams, graphs, and algebraic steps in the body of your
report where they are mentioned; they should not be simply attached to the
back of your report.
o Use sentences such as: “The results are summarized below in Table 4.”
o Cite references where appropriate.
Coherence:
o Be concise. A 12-page report will not automatically earn more than 6
pages.
o Focus on the aim of the exploration and avoid repetition; do not include
any irrelevant material.
o Structure your ideas in a logical manner.
o Edit your report so that it is easy to follow. You should write to an
audience consisting of your classmates.
Criterion B: Mathematical presentation
Achievement Level
0
1
2
3
Descriptor
The exploration does not reach the standard described by the
descriptors below.
There is some appropriate mathematical presentation.
The mathematical presentation is mostly appropriate.
The mathematical presentation is appropriate throughout.

This criterion assesses the use of appropriate mathematical language (notation,
symbols, and terminology) and representation (formulae, diagrams, tables, charts,
graphs, and models).

Take care to use appropriate mathematical notation symbols, not computer
notation or calculator notation. For example, use x 2 instead of x^2. Report
values in scientific notation correctly (i.e., 3.21  1012 ). Use symbols such as 
and = appropriately. Use subscripts correctly (tn , not tn).
Take care to use mathematical terminology appropriately and correctly; watch
choice of words, such as equation versus expression, and point versus coordinate.
Avoid casual language; use “substitute” rather than “sub in” or “plug in.”
Include concise definitions of key mathematical terms if we have not studied them
yet in class. Also define terms related to your topic (e.g., music, science) that
your classmates may not know.
Choose and use appropriate ICT tools such as GDCs, screenshots, graphing,
spreadsheets, databases, drawing and word-processing software, as appropriate.
Label graphs completely, in pen if necessary: Label the axes with correct
variables (with units, if appropriate), and write numbers beside the tick marks to
indicate scale. Write in arrows if necessary. If more than one relationship is
shown on a graph, label each one clearly and use colour to help your reader.
Express results to an appropriate degree of accuracy.
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Criterion C: Personal engagement
Achievement Level
0
1
2
3
4
Descriptor
The exploration does not reach the standard described by the
descriptors below.
There is evidence of limited or superficial personal engagement.
There is evidence of some personal engagement.
There is evidence of significant personal engagement.
There is evidence of outstanding personal engagement.

This criterion assesses the extent to which the student engages with the
exploration and makes it her own; for example, to what extent she:
o Thinks independently and/or creatively
o Asks questions, makes conjectures, and investigates mathematical ideas
o Reads about mathematics and researches areas of interest
o Looks for and creates mathematical models for real-world situations
o Considers historical and global perspectives
o Explores unfamiliar mathematics.



Keep a detailed Exploration Journal.
Meet all deadlines.
In your report:
o Clearly describe/explain your personal interest in the topic
o Present mathematical ideas in your own way
o Include an aspect of international-mindedness
Criterion D: Reflection
Achievement Level
0
1
2
3
Descriptor
The exploration does not reach the standard described by the
descriptors below.
There is evidence of limited or superficial reflection.
There is evidence of meaningful reflection.
There is substantial evidence of critical reflection.

This criterion assesses how the student reviews, analyses, and evaluates the
exploration.

Evidence of reflection can be found throughout the exploration or in the
conclusion.
Explain, analyse, and assess your calculations; include sources of error if
appropriate.
Discuss the implications of your results; discuss any limitations of your results;
consider the significance of your exploration.
Make links to different fields of mathematics.
Describe any generalizations reached.
Discuss possible extensions.
Make an informed conclusion.
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4
Criterion E: Use of mathematics
Achievement Level
0
1
2
3
4
5
6







Descriptor
The exploration does not reach the standard described by the
descriptors below.
Some relevant mathematics is used.
Some relevant mathematics is used. Limited understanding is
demonstrated.
Relevant mathematics commensurate with the level of the course
is used. Limited understanding is demonstrated.
Relevant mathematics commensurate with the level of the course
is used. The mathematics explored is partially correct. Some
knowledge and understanding are demonstrated.
Relevant mathematics commensurate with the level of the course
is used. The mathematics explored is mostly correct. Good
knowledge and understanding are demonstrated.
Relevant mathematics commensurate with the level of the course
is used. The mathematics explored is correct. Thorough
knowledge and understanding are demonstrated.
Demonstrate knowledge and understanding that is relevant to the exploration; be
thorough in showing steps and explaining them
Apply mathematics in different contexts
Apply problem-solving techniques
Recognize and explain patterns, where appropriate
Generalize and justify conclusions
Produce work that is commensurate with the level of the course (corresponds with
the level of difficulty of the course); explore part of the syllabus or some
mathematics outside of the syllabus at a similar level of difficulty or beyond.
If the level of the mathematics is not commensurate with the level of the course, a
maximum of two marks can be awarded here.
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Process and Timeline:

January – February, HL1: Make regular entries in your Exploration Journal in
OneNote. Your ability to maintain this journal and to meet deadlines along the
way will help your teachers to assess your personal engagement.
Checkpoint 1: End of February—Progress in Journal
Checkpoint 2: End of April—Long list
 Create a long list of possible topics that you have found in class or on your own.
 Keep track of where the ideas come from (e.g., brain-storming in class, NCTM
October 2012 issue, CSI show on forensics, Environmental Sciences class on
global warming).
Checkpoint 3: End of May—Short list
 From the long list, make a short list of 3-4 topics that interest you.
 Explain why each of these topics appeals to you.
The writing and completion of the exploration will take place in HL2.
By Oct. 9 – Choose a topic and write a one-paragraph description of the mathematics
involved, with an outline of what your exploration can include. Include at least two
sources.
Nov. 4 – First version due.
Jan. 26 – Final version due.
Submission (in HL2):
1. The report is due by 8:30 a.m. on the firm due date.
2. If you cannot be in school on the due date, just email your teacher and attach the
report by the required time. Then be sure to provide the paper copy to the teacher
first thing next morning.
3. If you do not submit your report by 3:30 p.m. on the firm due date, you will be
expected to work at the library after school until the report has been completed or
until 5:30 p.m.
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