CIC Mathematics Curriculum Documentation

IB Mathematical Studies

COURSE OVERVIEW

This course, designed for seniors, follows Integrated Math 3. Students in grade eleven may elect to take this course if the level of IB math methods (standard level) is unattainable, but this should be the exception and not the rule. This course prepares the student for the IB mathematical studies exam. The main goals of the year are for the students to apply previously learned concepts to real-world problems and to gain confidence in their abilities in the area of mathematics. As such, the course will reinforce basic skills, show connections between the various branches of mathematics and be composed of applications problems. In keeping with the philosophy of the math studies program, investigations, group work, and activities are used in addition to direct instruction throughout the year. Communication skills are a central theme as each student is required by the IB to complete an individual project. Topics include statistics, probability, logic, set theory, financial mathematics and sequences and series.

SKILLS OVERVIEW

As applied to real-world problems, students will be able to:

1. Solve and calculate solutions to:
   1. systems of linear equations and inequalities including linear programming problems;
   2. problems using Pythagorean theorem, right triangle trigonometric ratios including those that require a drawing in three dimensions, laws of sine and cosine and area formula for a non-right triangle including use of parallel line theorems and bearings;
   3. probability problems using tree diagrams up through binomial experiments and including the normal distribution as an approximation to the binomial distribution;
   4. statistical problems through graph reading and linear interpolation and including normal distribution;
   5. problems stemming from rounding and estimation;
   6. simple and compound interest problems and other financial applications of sequences and series.
   7. problems relating longitude, latitude, time zones and the distance on a sphere.
2. Graph
   1. histograms, cumulative frequency graphs, scatter diagrams and line of best fit by eye;
   2. linear functions and inequalities;
   3. quadratic functions using a table;
   4. sine and cosine curves with changes in period and amplitude;
   5. coordinates in three dimensions;
   6. transformations using matrix techniques;
   7. vectors.
3. Read critically
   1. statistical displays;
   2. Venn diagrams;
   3. flow charts.
4. Draw
   1. truth tables;
   2. diagrams in two and three dimensions using given information;
   3. statistical displays;
   4. Venn diagrams;
   5. tree diagrams.
5. Write, using correct vocabulary and notation
   1. comments about statistical displays
   2. logic statements;
   3. mathematical conclusions.

COURSE CONTENT

The order in which the topics are listed is roughly the order in which they have been taught. Some topics are given different placement as the result of time constraints. For example, matrices and/or vectors may be taught out of this sequence and algorithms may be left for a convenient one-day lesson before or after a vacation. More detail may be found in the IB Mathematical Studies syllabus (for testing in May 94 - May 99)

1. Computation
   1. Approximation and Error: Use of significant figures and scientific notation; Errors as a result of successive approximations; Effects of rounding.
   2. Algorithms: Reading a flowchart
2. Data Analysis
   1. Statistics: Distinction between discrete and continuous data; Collection, calculation and presentation of statistics derived from experimental data; Critical appraisal of statistical presentations; Simple and grouped data, frequency, relative frequency and cumulative frequency; Measures of central tendency, variance, standard deviation, percentiles; Scatter diagrams, line of fit by eye and interpolation; Normal distribution.
   2. Probability: Mutually exclusive events; Independent events; Conditional probability; Expectation; Binomial experiments; Approximation to binomial distribution by normal distribution.
3. Structure
   1. Sets: Vocabulary; Venn diagrams; Operations; Numeric Problems.
   2. Logic: Notation; DeMorgan's Laws; Truth tables; Quantifiers; Implications, Converse, Inverse, Contrapositives.
4. Geometry and Trigonometry
   1. Vectors: Concept; Components; Addition and multiplication by a scalar; Unit and zero vector; Length and negative of a vector.
   2. Matrices: Addition and Multiplication by a scalar; Unit and zero matrix; 2x2 Inverse matrices; Applications to data collection and transformations.
   3. Three Dimensions: Coordinates; Applications of right triangle trigonometry to problems in three dimensions.
   4. Trigonometry: Graphs of sine and cosine with changes in period and amplitude; Right triangle trigonometry and Pythagorean theorem; Sine and cosine rule and area of non-right triangles; Longitude and latitude, distances along lines of longitude and latitude and time differences.
5. Functions
   1. Basic Ideas: Function notation; Domain and range; Composite and inverse functions.
   2. Linear Functions: Meaning of slope (gradient) and y-intercept; Solving and graphing systems of equation including those that result from real life situations.
   3. Quadratic Functions: Graphical interpretation; Minimum and maximum values.
   4. Exponential Functions: Graphical treatment.
   5. Numeric Functions: Domain, range, even, odd and periodic functions; Composites and graphical treatment of inverse functions.
   6. Variation Properties: Increasing, decreasing, direct and inverse variations.
6. Business Techniques
   1. Linear Programming: usually done in conjunction with linear functions
   2. Simple Sequences and Finance: Simple interest as an application of arithmetic sequences; Compound interest as an application of geometric sequences; Sums of arithmetic sequences and series (usually done after linear functions and in conjunction with exponential functions).

ASSESSMENT TECHNIQUES AND TEACHING METHODOLOGIES

1. Assessment Techniques
   1. Tests (80%): Tests (90%): Tests in this class are created using questions from past IB papers. They are cumulative and cover material that has been reviewed since the beginning of the school year. The marks are usually composed 50% from paper one questions and 50% from paper two questions. All tests are timed using IB timing and grading reflects the IB scale. (The square root of the raw percentage is used to convert to the CIC grading scale.) During third and fourth quarters, students should sit at least three full mock exams.
   2. Problem Sets (20%): May be graded homework assignments, practices exams, or test corrections.
   3. The Project: Refer to IB syllabus for more information about the project. It is an individual piece of work involving the collection and/or generation of data, and the analysis and evaluation of that data. It comprises 20% of the student's IB mark. It should reflect 20 hours of work, but some of the time may be class time used to learn mathematical skills used in the completion of the project. The internal grade is used to make up the bulk of the 4^th quarter course grade.
2. Teaching Methodologies:
   1. Investigations: Students work in small groups following a step-by-step process and answering thought questions in order to create an understanding about a mathematical concepts. Generally includes a follow-up discussion and/or assignment designed to check for understanding.
   2. Direct Instruction: Used in conjunction with investigations or on its own when a topic requires teacher explanation or a dialogue between teacher and students in order for the students to fully master all aspects of the topic. Usually done in a discussion format interspersed with activities designed to further understanding or check for understanding.
   3. Problem Sets: Used to prepare students for vocabulary and types of questions that will appear on the examination.

KEY RESOURCES

1. Primary Students Texts: International Baccalaureate Mathematical Studies Books 1- 4., B. Raynor (Longman Ltd. 1990)
2. Teacher Resource Texts: (packets may be copied for students)
   1. Finite Mathematics, A Search for Meaning., Egsgard, Flewelling, Newell, Warburton (Gage Educational Publishing Company 1988)
   2. Algebra and Geometry, A Search for Meaning., Egsard and Ginestier (Gage Educational Publishing Company 1994)
   3. GCSE Mathematics., Robert Powell (Letts Educational, London, England 1995)
   4. Exploring Data., Landwehr and Watkins (Dale Seymour Publications, Palo Alto , CA 1987)
   5. Exploring Probability., Newman, Obremski, Scheaffer (Dale Seymour Publications, Palo Alto , CA 1987)
3. Graphics Calculator

ESL STRATEGIES AND CONSIDERATIONS

At this level, CIC students are required to be proficient in English at grade level. Language B candidates are encouraged to use a simple translating dictionary and to attend math help labs where care is taken to review vocabulary and key words that help students to decode the problems.

FUTURE NEEDS AND CHANGES

1. For the 1999 - 2000 school year:
   1. New primary texts have been ordered
   2. Course content summary and skills overview should be modified so as to be appropriate for the level of the new IB mathematical studies syllabus
2. In general, teaching methodologies should be considered to be sure that they meet the needs and goals of the program.