IB Maths Studies SL Course Overview (Updated 2016)

Appendix 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 Mathematical Models Total Hours: 54 *Some concepts from Numbers and Algebra are included Unit 1: 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: Hours Equation of a line in two dimensions: the forms y = mx+b AND ax+cx+d = 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: 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: 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 Geometry and Trigonometry Total Hours: 24 Unit 1: 12 Hours Equation of a line in two dimensions: the forms y = mx+b AND ax+cx+d = 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” Number and Algebra total hours: 21 *The majority of topic 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: 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? Logic, Sets & Probability total hours: 27 Unit 1: 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: hours Testing the validity of simple arguments through the use of truth tables Basic concepts of set theory: elements union subsets , complement A’ Venn diagrams and simple applications Sample space: event A & complementary event A’ Links to Internationalism:  Computer programming or coding Unit 3: hours Probability of an event Probability of a complementary event Expected value , intersection , 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 Descriptive Statistics Total Hours: 18 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? Statistical Applications Unit 1: 12 Hours The normal distribution Total Hours: 30 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, pvalues Links to Internationalism:  How Stats Fools Juries: http://ed.ted.com/lessons/peter-donnelly-shows-how-statsfool-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 Project Total Hours: 26 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-mathematicalfunction-graphs-10381 Geometry Total Hours: 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 IB Exam Preparation Total Hours: 22 Examine curriculum guide to determine areas of weaknesses & strengths Concept review by topic/unit – 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-MathematicsLearner-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 & 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:  Weeks 1-5: Senior year (3 Hours) 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  Weeks 6-10: Senior Year (5 Hours) 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  Weeks 11-15: Senior Year (6 Hours) 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  Weeks 16 – 20: Senior Year (6 Hours) o The concept of interpretation is discussed o Rough draft is expected at the end of 18 weeks   Rough draft needs to have completed mathematical processes in order to be submitted for review o Rough draft is expected at the end of 18 weeks  Rough draft meetings occur from weeks 19-23  Students are provided with feedback regarding the strengths & weaknesses of their project  Students are to submit the rough draft to turnitin.com for verification of originality Weeks 21- 25: Senior Year (6 Hours) o Rough draft meetings continue through weeks 19-23  Students are provided with feedback regarding the strengths & weaknesses of their project  Students are to submit the rough draft to turnitin.com for verification of originality o Students are provided time to use school technology to revise projects o Students are given weeks from the date of their rough draft meeting to submit a hard copy of their project & upload the project to turnitin.com to verify originality All work submitted to the IB for moderation or assessment must be authenticated by a teacher, and must not include any known instances of suspected or confirmed malpractice Each student must sign the coversheet for internal assessment to confirm that the work is his or her authentic work and constitutes the final version of that work Once a student has officially submitted the final version of the work to a teacher (or the coordinator) for internal assessment, together with the signed coversheet, it cannot be retracted NON-IB MONITORING o Periodic evaluation of skills using group discussions quizzes, tests, and end of quarter, semester & year exams o Daily in-class activities and investigations along with practice homework In-Class Formative Assessment Formative Assessment is used to recognize achievements and difficulties at the beginning or during a course, so that teachers and students can take appropriate action This type of assessment forms an integral part of all learning  Observations  Entrance/Exit Cards  Questioning  Discussion  Graphic Organizers  Self-Assessment  Think Aloud  Talk to the Text  Mind Map  White-Boarding  Practice Problems In-Class Summative Assessment Summative assessment is used to summarize and record overall achievement at the end of a course, for promotion and certification Most ‘high stakes’ tests and external examinations are designed for this purpose Summative assessment is also used to evaluate the relative effectiveness of a particular course, teaching method, or even an institution  End of unit tests built from questions from the IB test bank  Quarter exams  Midterms exams  Final Exams  ACT/SAT testing  M-STEP Testing Resources: List the books and other resource materials and software that will be used in the course Information should include what is currently available as well as what is being ordered             Haese & Harris Mathematical Studies SL 2nd edition for students Haese & Harris Mathematical Studies SL 3rd edition as teacher resource material Agnesi to Zeno – 100 vignettes from History of Math, Sanderson and Smith as teacher resource material (Internationalism) TED-Ed talks (Internationalism & ToK links) TI-84Plus Graphics Display Calculator Barron’s IB Math Studies (2014) teacher resource material NTK Learning Center IB Study Guide IB QuestionBank (CD) and past IB Examinations available through IBO Online Curriculum Center The Handy Math Answer Book by Patricia Barnes-Svarney & Thomas E Svarney c 2006 Mathematics: An Illustrated History of Numbers; Edited by Tom Jackson c.21012 Interactice Mathematics website; http://www.intmath.com/ ... 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,... Display Calculator Barron’s IB Math Studies (2014) teacher resource material NTK Learning Center IB Study Guide IB QuestionBank (CD) and past IB Examinations available through IBO Online Curriculum... 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