This web-site is intended for students and teachers of IB Mathematics SL
and HL classes.

The tools are useful for IB Math students doing portfolio
work, as well as

for teachers making classroom presentations.

**"Portfolio**

A collection of two pieces of work assigned by the teacher and completed
by the student during the course.

The pieces of work must be based on
different areas of the syllabus and represent the two types of tasks:

mathematical investigation

mathematical modelling.

The portfolio is internally assessed by the teacher and externally moderated
by the IBO.....

.......**The purpose of the portfolio**

The purpose of the portfolio is to provide students with opportunities
to be rewarded for mathematics

carried out under ordinary conditions,
that is, without the time limitations and pressure associated with

written
examinations. Consequently, the emphasis should be on good mathematical
writing and thoughtful reflection.

.......**Use of technology**

The need for proper mathematical notation and terminology, as opposed
to calculator or computer

notation must be stressed and reinforced, as
well as adequate documentation of technology usage.

Students will therefore
be required to reflect on the mathematical processes and algorithms the

technology
is performing, and communicate them clearly and succinctly."

*(from
the Mathematics
SL Guide, (c) 2004 International Baccalaureate Organization)*

Your teacher will assign specific tasks by distributing guiding questions.
You will have several days to complete the task.

The teacher
may give more than two assignments, and then submit only 2 of them for the
final IA grade.

**Type Imathematical investigation**

"While many teachers incorporate a problem-solving approach into
their classroom practice, students

also should be given the opportunity
formally to carry out investigative work. The mathematical

investigation
is intended to highlight that:

the idea of investigation is fundamental
to the study of mathematics

investigation work often leads to an appreciation
of how mathematics can be applied to solve

problems
in a broad range of fields

the discovery aspect of investigation work
deepens understanding and provides intrinsic motivation

during the
process of investigation, students acquire mathematical knowledge, problem-solving

techniques,
a knowledge of fundamental concepts and an increase in self-confidence.

All investigations develop from an initial problem, the starting point.
The problem must be clearly

stated and contain no ambiguity. In addition,
the problem should:

provide a challenge and the opportunity for creativity

contain multi-solution paths, that is, contain the potential for students
to choose different

courses
of action from a range of options.

Essential skills to be assessed

Producing a strategy

Generating
data

Recognizing patterns or structures

Searching for further
cases

Forming a general statement

Testing a general statement

Justifying a general statement

Appropriate use of technology"

*(from
the Mathematics
SL Guide, (c) 2004 International Baccalaureate Organization)*

**Type IImathematical modelling**

"Problem solving usually elicits a process-oriented approach, whereas
mathematical modelling requires

an experimental approach. By considering
different alternatives, students can use modelling to arrive

at a specific
conclusion, from which the problem can be solved. To focus on the actual
process of

modelling, the assessment should concentrate on the appropriateness
of the model selected in relation

to the given situation, and on a critical
interpretation of the results of the model in the real-world

situation
chosen.

Mathematical modelling involves the following skills.

Translating
the real-world problem into mathematics

Constructing a model

Solving
the problem

Interpreting the solution in the real-world situation (that
is, by the modification or amplification of the problem)

Recognizing
that different models may be used to solve the same problem

Comparing
different models

Identifying ranges of validity of the models

Identifying the possible limits of technology

Manipulating data

Essential skills to be assessed

Identifying the problem variables

Constructing relationships between these variables

Manipulating data
relevant to the problem

Estimating the values of parameters within
the model that cannot be measured or calculated from the data

Evaluating the usefulness of the model

Communicating the entire process

Appropriate use of technology "

*(from
the Mathematics
SL Guide, (c) 2004 International Baccalaureate Organization)*

" *(from
the Mathematics
SL Guide, (c) 2004 International Baccalaureate Organization)*