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.

The portfolio is also intended to provide students with opportunities to increase their understanding of

mathematical concepts and processes. It is hoped that, by doing portfolio work, students benefit from

these mathematical activities and find them both stimulating and rewarding.

The specific purposes of portfolio work are to:

• develop students’ personal insight into the nature of mathematics and to develop their ability to

ask their own questions about mathematics

• provide opportunities for students to complete extended pieces of mathematical work without

the time constraints of an examination

• enable students to develop individual skills and techniques, and to allow them to experience the

satisfaction of applying mathematical processes on their own

• provide students with the opportunity to experience for themselves the beauty, power and

usefulness of mathematics

• provide students with the opportunity to discover, use and appreciate the power of a calculator

or computer as a tool for doing mathematics

• enable students to develop the qualities of patience and persistence, and to reflect on the

significance of the results they obtain

• provide opportunities for students to show, with confidence, what they know and what they can

do.

Objectives

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

criteria have been developed to relate to the mathematics objectives. In developing these criteria,

particular attention has been given to the objectives listed here, since these cannot be easily addressed

by means of timed, written examinations.

Where appropriate in the portfolio, students are expected to:

• know and use appropriate notation and terminology

• organize and present information and data in tabular, graphical and/or diagrammatic forms

• recognize patterns and structures in a variety of situations, and make generalizations

• demonstrate an understanding of and the appropriate use of mathematical modelling

• recognize and demonstrate an understanding of the practical applications of mathematics

• use appropriate technological devices as mathematical tools.

Requirements

The portfolio must consist of two pieces of work assigned by the teacher and completed by the student

during the course.

Each piece of student work contained in the portfolio must be based on:

• an area of the syllabus

• type II—mathematical modelling.

The level of sophistication of the students’ mathematical work should be similar to that contained in

the syllabus. It is not intended that additional topics are taught to students to enable them to complete a

particular task.

Each portfolio must contain two pieces of student work, each of the two types of task: the portfolio

must contain one type I and one type II piece of work.

This is the required type of math.

Type II—mathematical 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

The criteria will be attached after this submission. The Math should be high level Calculus/Statistics

NOTE: THIS ASSIGNMENT SHOULD TAKE UP 10 PAGES INCLUDING GRAPHS AND MATH WORKING OUT.