Diploma Programme subject outline—Group 5: Mathematical studies SL
School name
Westlake High School
Name of the DP subject
Mathematical Studies SL
Level
School code
Higher
(indicate with X)
Name of the teacher who
completed this outline
Bowman, Turner
Date when outline was
completed
January 2015
Standard completed in two years
X
923373
Standard completed in one year *
Date of IB training
Name of workshop
(indicate name of subject and workshop category)
Summer, 2015
Math Studies (Category I)
* All Diploma Programme courses are designed as two-year learning experiences. However, up to two standard level subjects, excluding languages ab initio and pilot subjects, can be completed in
one year, according to conditions established in the Handbook of procedures for the Diploma Programme.
1.
Course outline
–
Use the following table to organize the topics to be taught in the course. If you need to include topics that cover other requirements you have to teach (for
example, national syllabus), make sure that you do so in an integrated way, but also differentiate them using italics. Add as many rows as you need.
–
This document should not be a day-by-day accounting of each unit. It is an outline showing how you will distribute the topics and the time to ensure that
students are prepared to comply with the requirements of the subject.
–
This outline should show how you will develop the teaching of the subject. It should reflect the individual nature of the course in your classroom and should
not just be a “copy and paste” from the subject guide.
–
If you will teach both higher and standard level, make sure that this is clearly identified in your outline.
Allocated time
Topic/unit
(as identified in the IB subject
guide)
State the topics/units in the order you
are planning to teach them.
Year 1
One class is
90
In one week
there are
2-3 classes.
Contents
1.1 Natural number, N; integers, Z;
Students will be able to identify sets of numbers in 4 hours
rational number, Q; and real numbers, the Real Number System.
R.
1.2 Approximation: decimal places,
Students should be aware of the errors that can
5 hours
significant figures. Percentage errors. result from premature rounding.
Estimation.
Students should properly use functions on GDC to
eliminate potential rounding errors.
minutes.
Resources
Assessment instruments to List the main resources to be
used, including information
be used
technology if applicable.
1.1 – 1.4 Oral presentations, unit
tests, quizzes, class discussions,
debates, research papers,
projects/performance-based
activities, reflections, online
assessments (All-In-Learning,
Kahoot)
Students should be able to determine whether
results produced on GDC are reasonable values
given contexts.
For example, mass and time cannot be negative.
1.3 Expressing numbers in the form
𝑎 × 10𝑘 , where 1 ≤ 𝑎 < 10 and k is
an integer.
Students should be able to correctly write results in 4 hours
scientific notation.
Students should know how to input and read
Operations with numbers in this form. numbers in scientific notation on a GDC.
1.4 SI and other basic units of
Students should understand how to convert between 3 hours
measurement: for example, kilogram different SI and other basic units.
(kg), meter (m), second (s), liter (l),
meter per second (m/s), Celsius scale.
1.5 Currency conversions
Students should be able to perform currency
transactions involving commission.
4 hours
1.5 Video: At the airport. Students
will create a mini commercial
applying currency conversions
1.6 Use of a GDC to solve

Pairs of linear equations in
two variables

Quadratic equations
Students should be able to graph pairs of linear
equations in two variables and find the point of
intersection.
4 hours
1.6 Test on pairs of linear
equations and quadratic equations
Mathematics for the
International Student;
Mathematics Studies SL, by
Haese & Harris, 2nd edition;
Copyright June 2010
Allocated time
Topic/unit
(as identified in the IB subject
guide)
State the topics/units in the order you
are planning to teach them.
Year 1
One class is
90
In one week
there are
2-3 classes.
Contents
1.7 Arithmetic sequences and series, Students should be able to identify the common
4 hours
and their applications. Use of the
difference and first term in arithmetic sequences.
formula for the nth term and the sum of Students should be able to write geometric
the first n terms of the sequence.
sequences both recursively and with an explicit
formula, use them to model situations, and translate
between the two forms.
1.8 Geometric sequences and series.
Students should be able to find the first term and the 4 hours
Use of the formula for the nth term and common ratio of geometric sequences. Students
the sum of the first n terms of the
should be able to write geometric sequences both
sequence.
recursively and with an explicit formula, use them
to model situations, and translate between the two
forms.
1.9 Financial applications of geometric Students should be able to apply geometric
3 hours
sequences and series:
sequences to real-life financial problems involving
compound interest and annual depreciation.

Compound interest

Annual depreciation
Apply financial programs on GDC to solve
financial problems.
Students should understand the different scales of
compound interest.
5.1 Equation of a line in two
Students should be able to identify slope, intercepts, 5 hours
dimensions: the forms 𝑦 = 𝑚𝑥 + 𝑏 and and other points of significance in linear equations.
𝑎𝑥 + 𝑏𝑦 + 𝑑 = 0.
Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric
Gradient; intercepts.
problems (e.g.,
find the equation of a line parallel or perpendicular
Lines with gradients: 𝑚1 and 𝑚2 .
to a given line that passes through a given point).
Parallel lines: 𝑚1 = 𝑚2 .
Perpendicular lines: 𝑚1 𝑥 𝑚2 = -1.
minutes.
Resources
Assessment instruments to List the main resources to be
used, including information
be used
technology if applicable.
1.7 – 1.8 Portfolio: Students will Mathematics for the
take pictures of patterns in life and International Student;
establish whether they are
Mathematics Studies SL, by
arithmetic or geometric or neither. Haese & Harris, 2nd edition;
For arithmetic patterns, students Copyright June 2010
will compute the nth term
1.9 Investigative Task: Students
will use the compound interest
formula to take a closer look at
buying a house and investing into
real-estate.
5.1 Test 1 on linear equations with
the use of graphic calculators.
Allocated time
Topic/unit
(as identified in the IB subject
guide)
5.2 Use of sine, cosine and tangent
ratios to find the sides and angles of
right-angled triangles.
90
In one week
there are
2-3 classes.
Contents
State the topics/units in the order you
are planning to teach them.
Year 1
One class is
Students should be able to understand, that by
6 hours
similarity, side ratios in right triangles are
properties of the angles in the triangle, leading to
definitions of trigonometric ratios for acute angles.
Angles of elevation and depression.
5.3 Use of the sine rule:
Use of the cosine rule:
a2 = b2 + c2 − 2bc cos A;
Students should be able to use trigonometric ratios
and the Pythagorean Theorem to solve right
triangles in applied problems.
Students should apply rules of trigonometry to
5 hours
solve applied problems involving right triangles.
Students should be able to sketch well-labelled
diagrams to support their solutions.
minutes.
Resources
Assessment instruments to List the main resources to be
used, including information
be used
technology if applicable.
5.2 Shadow Problem investigation Mathematics for the
International Student;
Mathematics Studies SL, by
Haese & Harris, 2nd edition;
Copyright June 2010
5.3 Poster Presentations: Students
will sketch diagrams of
“Downtown Atlanta in 10 years”
with computed angles of
elevations and buildings heights
Use of area of a triangle =
Construction of labelled diagrams from
verbal statements.
5.4 Geometry of three-dimensional
Students apply rules of right-angled trigonometry to 6 hours
solids: cuboid;
questions involving three-dimensional shapes.
right prism; right pyramid; right cone;
cylinder;
sphere; hemisphere; and combinations
of these solids.
The distance between two points; ex.
between two vertices or vertices with
midpoints or midpoints with midpoints.
The size of an angle between two lines
or between a line and a plane.
5.5 Volume and surface areas of the
Students apply appropriate volume and surface area 5 hours
three-dimensional solids defined in 5.4. formulas to solve problems.
5.4 – 5.5 Students will build their
sketch of “downtown Atlanta in
10 years” while computing
volumes of complex buildings
Allocated time
Topic/unit
(as identified in the IB subject
guide)
6.1 Concept of a function, domain,
range and graph. Function notation, ex.
f (x), v(t), C(n) . Concept of a function
as a mathematical model.
6.2 Linear models.
Linear functions and their graphs, f (x)
= mx + c .
6.3 Quadratic models.
Quadratic functions and their graphs
(parabolas):
Properties of a parabola: symmetry;
vertex; intercepts on the x-axis and yaxis.
Equation of the axis of symmetry,
90
In one week
there are
2-3 classes.
Contents
State the topics/units in the order you
are planning to teach them.
Year 1
One class is
minutes.
Resources
Assessment instruments to List the main resources to be
used, including information
be used
technology if applicable.
Students relate the domain and range of a function 4 hours
to its graph and, where applicable, to the
quantitative relationship it describes.
6.1 Functions with FIONA
investigative task
Students interpret key features of graphs and tables 5 hours
in terms of quantities, and sketch graphs showing
key features given a verbal description of the
relationship. Key features include: intercepts;
intervals where the function is increasing,
decreasing, positive, or negative; relative
maximums and minimums; symmetries; and end
behavior.
Students should be able to interpret quadratic
5 hours
functions in standard, intercept, and vertex form to
determine intercepts, axis of symmetry, vertex, and
other characteristics (opens up vs. down, width, end
behavior)
6.2 Test 2 on linear models
Student should be able to use this information to
graph a quadratic function.
6.4 Exponential models.
Students should be able to model exponential
5 hours
Exponential functions and their graphs: functions. Students should be able to solve applied
problems of growth and decay.
6.3 Quadratics in real life
portfolio. Students will receive
real-life problems on quadratics.
They will have to solve every
problem elaborately. At the end,
students will create their own real
life quadratic problem using a
provided rubric.
6.4 Tortoise and the Hare
investigative task. Students will
compare and contrast quadratic
models and exponential models.
Concept and equation of a horizontal
asymptote.
6.5 Models using functions of the form Students use graphical methods and GDCs to solve 5 hours
problems.
Functions of this type and their graphs.
The y-axis as a vertical asymptote.
6.5 – 6.6 Dynamic Software such
as Geometer’s Sketchpad or
Geogebra will be used to model
higher polynomial functions.
Mathematics for the
International Student;
Mathematics Studies SL, by
Haese & Harris, 2nd edition;
Copyright June 2010
Allocated time
Topic/unit
(as identified in the IB subject
guide)
90
In one week
there are
2-3 classes.
Contents
State the topics/units in the order you
are planning to teach them.
Year 1
One class is
6.6 Drawing accurate graphs. Creating Students graph linear and quadratic functions and
a sketch from information given.
show intercepts, maxima, and minima.
Transferring a graph from GDC to
paper.
minutes.
Resources
Assessment instruments to List the main resources to be
used, including information
be used
technology if applicable.
5 hours
Mathematics for the
International Student;
Mathematics Studies SL, by
Haese & Harris, 2nd edition;
Copyright June 2010
Reading, interpreting and making
predictions using graphs.
Included all the functions above and
additions and subtractions.
6.7 Use of a GDC to solve equations
involving combinations of the
functions above.
This is an ongoing skill that will be implemented in 5 hours
the linear and polynomial functions chapter. An
examination of the differences of these functions
will be explored.
7.1 Concept of the derivative as a rate Students explain how the first derivative test allows 6 hours
of change.
us to determine if a critical point is a local or
maximum or minimum point.
Tangent to a curve.
6.7 Assessment will be
implemented in the previous
sections requiring the use of
graphic calculators.
7.1 Students will create hands-on
projects that involve projectile
motions and rate of change
7.2 The principle that
Students examine various functions to investigate 4 hours
where these increase and decreasing. Be able to use
f (x) = 𝑎𝑥 𝑛 ⇒ f ′(x) = an 𝑥 𝑛−1 .
The derivative of functions of the form the GDC to analyze these functions
f (x) = 𝑎𝑥 𝑛 + 𝑏𝑥 𝑛−1 + ..., where all
exponents are integers.
7.2 Unit Test over Calculus
sections 2.2-2.5
7.3 Gradients of curves for given
values of x.
Values of x where f ′(x) is given.
6 hours
7.3 Quiz over gradients of curves
7.4 Increasing and decreasing
Students examine various functions to investigate 5 hours
functions.
where these increase and decreasing. Be able to use
Graphical interpretation of f ′(x) > 0, f the GDC to analyze these functions
′(x) = 0 and f ′(x) < 0.
7.4 Quiz over graphical
interpretation of decreasing and
increasing functions with graphic
calculators
Students explain methods for finding gradients of
given values or x, equation of tangent at a given
point. Point out the connection with this concept
and previous topics of slope (gradient)
Equation of the tangent at a given
point.
Equation of the line perpendicular to
the tangent at a given point (normal).
www.heinemann.com/math ;
open-ended Assessment
Database
Mathematics for the
International Student;
Mathematics Studies SL, by
Haese & Harris, 2nd edition;
Copyright June 2010
Allocated time
Topic/unit
(as identified in the IB subject
guide)
7.5 Values of x where the gradient of a
curve is zero.
Solution of f ′(x) = 0.
Stationary points.
90
In one week
there are
2-3 classes.
Contents
State the topics/units in the order you
are planning to teach them.
Year 1
One class is
Students understand that a local
maximum/minimum will not necessarily be the
greatest/least value of the function in the given
domain.
4 hours
minutes.
Resources
Assessment instruments to List the main resources to be
used, including information
be used
technology if applicable.
7.5 and 7.6 Project on efficient
use of material in packaging with
an emphasis on Physics
(kinematics).
Mathematics for the
International Student;
Mathematics Studies SL, by
Haese & Harris, 2nd edition;
Copyright June 2010
2.1 Internal Assessment Training
Activities: Practice on
commenting on the validity of a
data using data from Psychology
and Biology.
Mathematics for the
International Student;
Mathematics Studies SL, by
Haese & Harris, 2nd edition;
Copyright June 2010
Local maximum and minimum points. Students manipulate points of inflexion with zero.
7.6 Optimization problems.
Year 2
Students work on problems that involve
maximizing profit, minimizing cost, and
maximizing volume for given surface area.
5 hours
2.1 Classification of data as discrete or Students explore the concepts of population and of 5 hours
continuous.
representative and random sampling.
2.2 Simple discrete data: frequency
tables.
Students explore geographical datasets to further
understand frequency tables
4 hours
2.3 Grouped discrete or continuous
data: frequency tables; mid-interval
values; upper and lower boundaries.
Frequency histograms.
Students use GDC to produce histograms and box
and-whisker diagrams
5 hours
2.4 Cumulative frequency tables for
grouped discrete data and for grouped
continuous data; cumulative frequency
curves, median and quartiles. Boxand-whisker diagram
2.5 Measures of central tendency. For
simple discrete data: mean, median;
mode. For grouped discrete and
continuous data: estimate of a mean;
modal class.
2.6 Measures of dispersion: range,
interquartile range, standard deviation.
Students use mid-interval values to estimate the
mean of grouped data.
4 hours
3.1 Basic concepts of symbolic logic:
definition of a proposition; symbolic
notation of propositions.
Students calculate and analyze percentiles and
quartiles in data.
Students review how to compare and contrast
measures of central tendency.
4 hours
Students will develop a survey and calculate the
measures of central tendency
Students will understand the significance of
5 hours
dispersion in data. Determine, analyze and interpret
range, interquartile range, and standard deviation
Students are introduced to mathematical symbols 6 hours
for: or, and, not.
2.5 Mini Project: Students design
surveys. In this assessment,
students will be assessed on
identifying the errors in using
statistics to mislead.
Activity; we use students’ shoe
size and compute measures of
dispersion
3.1 – 3.2 Quiz on logic
Allocated time
Topic/unit
(as identified in the IB subject
guide)
90
In one week
there are
2-3 classes.
Contents
State the topics/units in the order you
are planning to teach them.
Year 2
One class is
minutes.
Resources
Assessment instruments to List the main resources to be
used, including information
be used
technology if applicable.
3.2 Compound statements: implication, Students use compound statements to translate
6 hours
between verbal statements and symbolic statements
⇒;
equivalence, ⇔ ; negation, ¬ ;
conjunction,
∧ ; disjunction, ∨ ; exclusive
disjunction .
Translation between verbal statements
and symbolic form.
Tests, quizzes, and hands-on
activities.
3.3 Truth tables: concepts of logical
contradiction and tautology.
3.3 Students explore computer
programing mini projects in order
to apply truth tables
Truth tables are used to illustrate the associative and 6 hours
distributive properties of connectives, and for
variations of implication and equivalence
statements.
3.4 Converse, inverse, contrapositive. Appl: Use of arguments in developing a logical
Logical equivalence.
essay structure.
Appl: Computer programming; digital circuits;
Physics HL 14.1; Physics SL C1.
TOK: Inductive and deductive logic, fallacies.
Testing the validity of simple arguments through
the use of truth tables.
3.5 Basic concepts of set theory:
elements x∈ A,
subsets A ⊂ B ; intersection A∩B ;
union
A∪B ; complement A′.
Venn diagrams and simple
applications.
3.6 Sample space; event A;
complementary event,
A′.
Probability of an event.
Probability of a complementary event.
Expected value.
6 hours
Tests, quizzes, and hands-on
activities.
6 hours
Tests, quizzes, and hands-on
activities.
Probability is introduced and taught in a practical 6 hours
way using coins and other examples to demonstrate
random behavior.
3.6 Students research on actuarial
studies, probability of life
spans and their effect on
insurance.
Mathematics for the
International Student;
Mathematics Studies SL, by
Haese & Harris, 2nd edition;
Copyright June
Allocated time
Topic/unit
(as identified in the IB subject
guide)
90
In one week
there are
2-3 classes.
Contents
State the topics/units in the order you
are planning to teach them.
Year 2
One class is
3.7 Probability of combined events,
Students work on word problems involving
mutually exclusive events, independent probability questions using diagrammatic
events.
representations.
Use of tree diagrams, Venn diagrams,
sample space diagrams and tables of
outcomes.
Probability using “with replacement”
and “without replacement”.
Conditional probability.
4.1 The normal distribution.
Students will use the GDC when calculating
The concept of a random variable; of probabilities and inverse normal.
the parameters μ and σ; of the bell
shape; the symmetry about x = μ .
minutes.
Resources
Assessment instruments to List the main resources to be
used, including information
be used
technology if applicable.
6 hours
3.7 Students create a game show
such as who wants to be a
millionaire with probability
questions
9 hours
4.1 Students will be tested on
normal computations using their
graphic calculators. Questions will
be pooled from real life
application questions in biology,
psychology, and social studies.
9 hours
4.2 Students will use the internet
to find two sets of data that may or
may not be related. Students will
be required to make a scatter plot,
find of line of best fit, and
interpret the data.
Diagrammatic representation.
Normal probability calculations.
Expected value.
Inverse normal calculations.
Not required:
Transformation of any normal variable
to the standardized normal.
4.2 Bivariate data: the concept of
Investigate and analyze various sets of data to
correlation. Scatter diagrams; line of determine a best fit line and the correlation
best fit, by eye, passing through the
coefficient.
mean point. Pearson’s productmoment correlation coefficient, r.
Interpretation of positive, zero and
negative, strong or weak correlations.
4.3 The regression line for y on x.
Analyze the regression line for researched data. Be 9 hours
able to make predictions based on the regression
Use of the regression line for prediction line.
purposes.
4.3 Students use business models
to compute regression models.
Mathematics for the
International Student;
Mathematics Studies SL, by
Haese & Harris, 2nd edition;
Copyright June
Allocated time
Topic/unit
(as identified in the IB subject
guide)
One class is
90
In one week
there are
2-3 classes.
Contents
State the topics/units in the order you
are planning to teach them.
minutes.
Resources
Assessment instruments to List the main resources to be
used, including information
be used
technology if applicable.
4.4 The χ 2 test for independence:
formulation of null and alternative
hypotheses; significance levels;
contingency tables; expected
frequencies; degrees of freedom; pvalues.
Students determine how to use the chi square to test 9 hours
the association between two categorical variables.
4.4 Students collect categorical
International Student;
data and use the chi square test for Mathematics Studies SL, by
the analysis of their data
Haese & Harris, 2nd edition;
Copyright June 2010
Project
Individual piece of work involving the collection of 25 hours
information or the generation of measurements, and
the analysis and evaluation of the information or
measurements.
Students compile their statistical
mini projects into one portfolio
which will be checked for
thorough analysis and accurate
computations.
2.
IB internal assessment requirement to be completed during the course
Briefly explain how and when you will work on it. Include the date when you will first introduce the internal assessment requirement to your students, the different
stages and when the internal assessment requirement will be due.








October, 2016 (2nd year of course) – Project introduction. Review of project samples and grading rubric. Students will have four weeks to declare project topic.
End of October – Topic declaration
3rd week of November – Each student will meet with project mentor to discuss progress.
4th week of November – Students will spend two class days conducting peer reviews of projects.
2nd week of December – Students will submit a status report for project. Students will receive feedback before Winter Break.
3rd week of January – Students will submit second status report for project.
4th week of January – Two class days will be spent discussing projects. One of these class days will be the second round of peer reviews.
Internal assessment will be due February 8, 2017.
3.
Links to TOK
You are expected to explore links between the topics of your subject and TOK. As an example of how you would do this, choose one topic from your course
outline that would allow your students to make links with TOK. Describe how you would plan the lesson.
Topic
Link with TOK (including description of lesson plan)
Currency Conversions What is money? What is the history of money as we know it? In what ways does it govern our society? How can I give people some slips of green paper in
exchange for food? How can I just swipe a card in exchange for food? Students will critically explore these questions as a class, developing a better
understanding of world economics and society.
4.
International mindedness
Every IB course should contribute to the development of international mindedness in students. As an example of how you would do this, choose one topic from
your outline that would allow your students to analyse it from different cultural perspectives. Briefly explain the reason for your choice and what resources you will
use to achieve this goal.
Topic
Exponential functions
and their graphs.
5.
Contribution to the development of international mindedness (including resources you will use)
In today’s world, human population growth is a key issue facing the future of our species. While some countries, like China, have created legal incentives and
disincentives to address the issue, other countries think it is ethically wrong. In a Socratic seminar setting, students will discuss the ethics of existing and
hypothetical policy regarding population growth. Students will then model population growth using exponential functions and their graphs. Students will
compare trends in countries over a span of 50 years.
Development of the IB learner profile
Through the course it is also expected that students will develop the attributes of the IB learner profile. As an example of how you would do this, choose one
topic from your course outline and explain how the contents and related skills would pursue the development of any attribute(s) of the IB learner profile that you
will identify.
Topic
1.9 Financial applications of
geometric sequences and series:

Compound interest

Annual depreciation
Contribution to the development of the attribute(s) of the IB learner profile
Contribution to the development of the attribute(s) of the IB learner profile: Inquiry, risk-taking, reflection.
Students will be granted a small amount of fake money (~$1000). Students in groups will have a small investment competition. Students will learn
about different methods of investment, decide how they want to invest their money, and watch it grow (or fall).
6.
Resources
Describe the resources that you and your student will have to support the subject. Indicate whether they are sufficient in terms of quality,
quantity and variety. Briefly describe what plans are in place if changes are needed.
The following textbooks will be used during the two years of this course:
McDougal-Littel Georgia High School Mathematics 3, by Holt, Rinehart, and Winston, Copyright 2008
McDougal-Littel Georgia High School Mathematics 2, by Holt, Rinehart, and Winston, Copyright 2008
In addition to the text, resources found on the online curriculum center (OCC) will be used; occ.ibo.org.
- Both textbooks are in sufficient quality, quantity, and variety, but I will be requesting Mathematics for the International Student; Mathematics Studies SL.