IB Maths Studies SL Course Overview (Updated 2016)

Outline of Couse Content The concepts listed below appear in: Diploma Programme Mathematical studies SL Guide, First examinations 2014 Published March 2012 Published on behalf of the Int

Appendix 5

IB Diploma Programme course outlines

Teachers responsible for each proposed subject must prepare a course outline following the guidelines below While IB subject guides will be used for this exercise, teachers are

expected to adapt the information in these guides to their own school’s context Please be sure to use IBO nomenclature throughout The name of the teacher(s) who wrote the course outline must be recorded at the top of the outline

Name of the teacher who prepared the outline:

Rachael Kasperek

Melissa Webb

Name of the course:

Mathematical Studies SL

Course description:

The course concentrates on mathematics that can be applied to contexts related as far as possible to other subjects being studied, to common real-world occurrences and to topics that relate to home, work and leisure situations While the same status as Mathematics SL, this course meets different needs It is available to students with a varied mathematical background and ability The course focuses more on the application of the mathematics in a wide array of topics and has a large portion of the curriculum devoted to statistical techniques Students are encouraged

to use logic and reasoning skills to enhance critical thinking and reach greater depth within a topic or concept Students choosing to take Mathematical Studies SL are often those individuals considering social sciences, humanities, languages and arts majors at the college/university level.

The course also includes project work: students must produce a project, a piece of written work based on personal research, guided and supervised by the teacher The project provides an opportunity for students to carry out a

mathematical investigation in the context of another course being studied, a hobby

or interest of their choice using skills learned before and during the course This process allows students to ask their own questions about mathematics and to take responsibility for a part of their own course of studies in mathematics In addition to the project, students must also sit for two externally graded examinations with a graphic display calculator (GDC)

Students electing to take Mathematics Studies SL will be required to successfully

complete rigorous courses in geometry and algebra I These courses are designed to expose

students to the IB philosophy, including a variety of assessment tools that mirror those used by the IB Along with these formal assessments, students will be required to demonstrate their learning through projects, activities, written work and cooperative learning groups This format will be carried into the Mathematical Studies SL course in conjunction with the external

requirements of the IB

Outline of Couse Content

The concepts listed below appear in:

Diploma Programme Mathematical studies SL Guide, First examinations 2014

Published March 2012

Published on behalf of the International Baccalaureate Organization

*Some concepts from Numbers and Algebra are included

Unit 1: 6 Hours

Natural Numbers, integers, rational numbers, & real numbers ( )

Approximation; decimal places, significant figures

Percent Error

Estimation

Expressing numbers in the form where and (scientific notation)

SI units & other basic units of measurement

Links to Internationalism:

 Comparison of numbers in various alphabets/notations; Babylonian, Roman, Arabic, etc

 Where did the number set notations come from ( )?

Links to ToK:

 Does math have its own language?

 Is math intuitive? Can that intuition be taught?

 Does the use of SI units make math more universal?

Unit 2: 9 Hours

Equation of a line in two dimensions: the forms y = mx+b AND ax+cx+d = 0

Linear models

Linear functions and their graphs

Use of the GDC to solve 1) pairs of linear equations in two variables 2) quadratic equations

Drawing accurate graphs

Creating a sketch from information given

Transferring a graph from GDC to paper

Reading, interpreting and making predictions using graphs

Use of the GDC to solve equations involving combinations of the functions above Links to Internationalism:

 Why is ‘x’ the unknown?

https://www.ted.com/talks/terry_moore_why_is_x_the_unknown?language=en

o Origin of the use of x in Algebraic concepts

Unit 3: 6 Hours

Concept of a function, domain, range and graph

Function notation

Concept of a function as a mathematical model

Link to ToK:

 Why can we use mathematics to describe the world and make

predictions? Is it because we discover the mathematical basis of the world or because we impose our own mathematical structures onto the world? The relationship between real-world problems and

mathematical models

Unit 4: 12 Hours

Quadratic models

Quadratic functions and their graphs

Properties of parabolas; symmetry, vertex, intercepts on the x-axis and y-axis

Equation of the axis of symmetry

Use of the GDC to solve 1) pairs of linear equations in two variables 2) quadratic equations

Drawing accurate graphs

Creating a sketch from information given

Transferring a graph from GDC to paper

Reading, interpreting and making predictions using graphs

Use of the GDC to solve equations involving combinations of the functions above Links to Internationalism:

 Study of parabolas in architecture; are they actually parabolas or is it a catenary?

http://www.intmath.com/blog/mathematics/is-the-gateway-arch-a-parabola-4306

Unit 5: 9 Hours

Exponential model

Exponential functions and their graphs

Concept and equation of a horizontal asymptote

Drawing accurate graphs

Creating a sketch from information given

Transferring a graph from GDC to paper

Reading, interpreting and making predictions using graphs

Use of the GDC to solve equations involving combinations of the functions above Links to Internationalism:

 The Science of Overpopulation: https://www.youtube.com/watch?v=dD-yN2G5BY0

Links to ToK:

 The idea of e^x and natural log; exponential growth in nature

Unit 5: 12 Hours

Models using functions of the form

Functions of this type and their graphs

The y-axis as a vertical asymptote

Drawing accurate graphs

Creating a sketch from information given

Transferring a graph from GDC to paper

Reading, interpreting and making predictions using graphs

Use of the GDC to solve equations involving combinations of the functions above Links to ToK:

 Investigation of zero

Unit 1: 12 Hours

Equation of a line in two dimensions: the forms y = mx+b AND ax+cx+d = 0

Gradient; Intercepts

Points of intersection of lines

Lines with gradients,

Parallel lines,

Perpendicular lines,

The distance between two points

The size of an angle between two lines or between a line & a plane

Links to ToK:

 Descartes showed that geometric problems can be solved algebraically and vice versa What does this tell us about mathematical representation and mathematical knowledge?

Unit 2: 12 Hours

Use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles

Angles of elevation & depression

Use of the sine rule

Use of the cosine rule

Use of the area of a triangle

Construction of labeled diagrams from verbal statements

Geometry of 3-D solids; cuboid, right prism; right pyramid; right cone; cylinder; sphere; hemisphere; and combinations of these solids

Links to Internationalism:

 Math & Art

 The origin of the ‘degree’

Links to ToK:

 The purpose of the radian & relation to degrees

 Diagrams of Pythagoras’ theorem occur in early Chinese and Indian manuscripts The earliest references to trigonometry are in Indian mathematics

 Use the fact that the cosine rule is one possible generalization of Pythagoras’

theorem to explore the concept of “generality”

*The majority of topic 1 is covered during the Mathematical Models unit

Unit 1: 12 hours

Arithmetic sequences & series; their application

Geometric sequences & series

Use of the formulae for the nth term and the sum of the first n terms of the sequence

Unit 2: 9 hours

Currency Conversions

Financial applications of geometric sequences and series:

1) compound interest 2)annual depreciation

Link to Internationalism:

 Credit cards & savings accounts

 Money systems world-wide; currency use & the Euro

 Effects of currency on trade

Links to ToK:

 How does having math knowledge/intuition assist in ensuring you are not taken advantage of or exploited?

Unit 1: 9 hours

Basic concepts of symbolic logic: definition of a proposition; symbolic notation of propositions

Compound statements: implication, equivalence, negation, conjunction, disjunction, exclusive disjunction ( )

Translation between verbal statements and symbolic form

Truth tables; concepts of logical contradiction and tautology

Converse, inverse, contrapositive

Logical equivalence

Links to ToK:

 Deductive reasoning

 Inductive reasoning

 Theoretical and experimental probability

 The perception of risk, in business, in medicine and safety in travel

Unit 2: 9 hours

Testing the validity of simple arguments through the use of truth tables

Basic concepts of set theory: elements subsets , intersection , union , complement A’

Venn diagrams and simple applications

Sample space: event A & complementary event A’

Links to Internationalism:

 Computer programming or coding

Unit 3: 9 hours

Probability of an event

Probability of a complementary event

Expected value

Probability of combined events, mutually exclusive events, independent events Use of tree diagrams, Venn diagrams, sample space diagrams and tables of outcomes Probability using “with replacement” and “without replacement”

Conditional probability

Links to Internationalism:

 Medical studies – assessing risk factors

 The ‘Monty Hall’ Problem

https://www.youtube.com/watch?v=mhlc7peGlGg

 Probablity & Poker:

http://www.intmath.com/counting-probability/poker.php

Links to ToK:

 Lottery systems – people’s mentality regarding large windfalls

 Gambler’s fallacy

Classification of data as discrete or continuous

Simple discrete data; frequency tables

Grouped discrete or continuous data; frequency tables; mid-interval values; upper & lower boundaries

Frequency histograms

Cumulative frequency tables for grouped discrete data & for grouped continuous data; cumulative frequency curves, median & quartiles

Box –and-whisker diagrams

Measures of central tendency

For simple discrete data: mean, median, mode

For grouped discrete and continuous data: estimate of a mean; modal class

Measures of dispersion: range, interquartile range, standard deviation

Links to ToK:

 Is there a difference between data and information?

 Validity of data

 Bias

 Is standard deviation a mathematical discovery or a creation of the human mind?

Unit 1: 12 Hours

The normal distribution

The concept of a random variable: of the parameters ; the bell shape; the symmetry about

Diagrammatic representation

Normal distribution calculations

Expected value

Inverse normal calculations

Links to Internationalism:

 What are some issues caused by the misuse of normal distribution?

Links to ToK:

 To what extent can models like normal distribution be trusted?

Unit 2: 18 hours

Bivariate data; the concept of correlation

Scatter diagrams; line of best fit, by eye, passing through the mean point

Pearson’s product-moment correlation coefficient, r

Interpretation of positive, zero, and negative, strong or weak correlations

The regression line for y on x

Use of the regressions line for prediction purposes

The test of independence: formulation of null & alternative hypothesis;

significance levels; contingency tables; expected frequencies, degrees of freedom, p-values

Links to Internationalism:

 How Stats Fools Juries: http://ed.ted.com/lessons/peter-donnelly-shows-how-stats-fool-juries

Links to ToK:

 To what extent can we trust data?

 Does correlation imply causation?

 Can we reliably use the equation of the regression line to make predictions?

 Scientific method

The project is an individual piece of work involving the collection of information or the generation of measurements, and the analysis and evaluation of the information

or measurements

Links to Real World Applications:

 Sampling

http://www.intmath.com/blog/mathematics/sampling-to-create-mathematical-function-graphs-10381

Volume and surface area of the 3-D solids described above

Introduction to Differential Calculus Total Hours: 30

Unit 1: 12 hours

Concept of the derivative of rate of change

Tangent to a curve

The principle that

The derivative of functions of the form where are the exponents are integers

Gradients of curves for given values of x

Values of x where f’(x) is given

Equation of a tangent ant a given point

Equation of the line perpendicular to the tangent at a given point (normal)

Links to Internationalism:

 Newton & Liebniz

Links to Internationalism:

 Is calculus abstract?

Unit 2: 18 hours

Increasing and decreasing functions

Graphical interpretation of

Values of x where the gradient of the curve is zero

Solution to f’(x)=0

Stationary points

Local maximum & minimum points

Optimization problems

Examine curriculum guide to determine areas of weaknesses & strengths

Concept review by topic/unit – 7 in all

Practice Exams

Activities to review concepts of course

Total Hours: 261

Links to the Learner Profile

The Mathematics Learner Profile taken from:

henricowarriors.org/ /2011/12/The-Mathematics-Learner-Profile.pdf

IB External Assessment

EXTERNAL ASSESSMENT – GDC allowed & encouraged on both papers

o PAPER 1, a 90 minute exam consisting of fifteen short response questions based on the

whole syllabus

o PAPER 2, a 90 minute exam consisting of approximately five compulsory extended-response

questions based on the whole syllabus

The external assessment is 80% (40% paper 1 & 40% paper 2) of the overall grade towards the

IB diploma These papers are given in May according to the IB schedule The marks are given externally and are awarded for method, accuracy, answers and reasoning, including

interpretation These papers will be completed at the end of the students second year

INTERNAL ASSESSMENT

o PROJECT – The project is an individual, authentic piece of work by the student involving

the collection of information or the generation of measurements, and the analysis and evaluation

of the information or measurements collected

This assessment, as graded by the teacher, is 20% of the overall grade towards the IB diploma and will be completed the second year of the course The project will be moderated by the IBO

IB Internal Assessment Timeline

Internal assessment is an integral part of the course and is compulsory for all

students It enables students to demonstrate the application of their skills and knowledge, and to pursue their personal interests, without the time limitations and other constraints that are associated with written examinations

Internal assessment in mathematics SL is an individual exploration This is a piece

of written work that

involves investigating an area of mathematics It is marked according to five

assessment criteria (Communication, Mathematical Presentation, Personal

Engagement, Reflection, Use of Mathematics).

The process is divided into the following parts:

o Students are given the rules and guidelines

o Students are provided the rubric

o Review exemplar projects & review construction of document

o Brainstorm potential topics for data collection

o Students research the brainstormed topics to verify ‘enough’ data is available to continue with the theme for a project

o Discussion of the math processes – simple and further to assist in choosing topic

o Student choose topics and begin data collection

o All sources must be turned in on a bibliography; citations included

o Task and portion of plan are expected at this time

o Microsoft Equation Editor and Excel are reviewed

o Students continue with data collection and begin the analysis phase

o Students are provided time to use school technology

o The plan is adjusted to include the processes chosen

o Math processes are expected to be attempted/completed by the end of week 15

o The concept of interpretation is discussed

o Rough draft is expected at the end of 18 weeks