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```Diploma Programme subject outline—Group 5: mathematics and computer science
School name
Westlake High School
Name of the DP subject
Mathematics SL
School code
923373
Level
Higher
(indicate with X)
Name of the teacher who
completed this outline
Date when outline was
completed
January 2015
Standard completed in two years
X
Standard completed in one year *
Date of IB training
Name of workshop
(indicate name of subject and workshop category)
Summer 2014
Mathematics SL (Category 1)
* 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
(as identified in the IB subject
guide)
Contents
State the topics in the order
you are planning to teach
them.
Year 1
Topic 2: Functions and Equations
Topic 1: Algebra

Solve(2.7)

Graph (2.2)

Characteristics
o Domain/Range
o Relative extrema
o Intercepts
o Axis of symmetry

transformations(2.3)

Applications(2.8)
1.2 Elementary treatment of exponents and
logarithms.

Laws of exponents

Laws of logarithms

Change of base

Solving equations(2.7)
2.6 Exponential functions

Solve(2.7)

Graph (2.2)

Characteristics
o Domain/Range
o asymptotes
o Intercepts
o increasing/decreasing

transformations(2.3)

Applications(2.8)
2.1 Inverse function

Establish the relationship between
exponents and logarithms as inverses
algebraically and graphically.
2.6 Logarithmic functions

Solve(2.7)

Graph (2.2)

Characteristics
o Domain/Range
o asymptotes
o Intercepts
o increasing/decreasing

transformations(2.3)

Applications(2.8)
One
class is
90
In one
week
there are
2/3 classes.
5 class periods
3 class periods
3 class periods
1 class periods
3 class periods
minutes.
Resources
Assessment
List the main resources to be
instruments to be used used, including information
technology if applicable.
Students will be assessed
Safari Montage, Ti-84 Plus GDC’s,
using formative assessments, Promethean Board and Active
weekly topic quizzes, monthly expressions, All-in-Learning Student
cumulative assessments,
response remotes and data analysis.
performance assessments, the Fathom software, Calculus in motion
internal assessment
concepts. Test generator software,
USA Test prep where applicable, Text
book TBD
Allocated time
Topic
(as identified in the IB subject
guide)
Contents
State the topics in the order
you are planning to teach
them.
Year 1
Topic 1: Algebra
Topic 2: Functions and Equations
One
class is
90
In one
week
there are
2/3 classes.
1.1 Arithmetic sequences and series

Sum of a finite series using sigma
notation
Geometric sequences and series

Sum of a finite and infinite series
using sigma notation

Applications
3 class periods
1.2 The binomial theorem

Expansion of (a+b)n

Calculation of binomial coefficients
using Pascal’s triangle and (𝑛𝑟)
2 class periods
2.5 The reciprocal functions

Solve(2.7)

Graph (2.2)

Self-inverse nature(2.1)

Characteristics
o Domain/Range
o asymptotes
o Intercepts
o increasing/decreasing

Transformations(2.3)

Applications(2.8)
3 class periods
2.1 Composite Functions
1 class periods
minutes.
Resources
Assessment
List the main resources to be
instruments to be used used, including information
technology if applicable.
Students will be assessed
Safari Montage, Ti-84 Plus GDC’s,
using formative assessments, Promethean Board and Active
weekly topic quizzes, monthly expressions, All-in-Learning Student
cumulative assessments,
response remotes and data analysis.
performance assessments, the Fathom software, Calculus in motion
internal assessment
concepts. Test generator software,
USA Test prep where applicable, Text
book TBD
Allocated time
Topic
(as identified in the IB subject
guide)
Contents
State the topics in the order
you are planning to teach
them.
Year 1
Topic 3: Circular functions and
trigonometry
One
class is
90
In one
week
there are
2/3 classes.
3.1 The circle:

Degrees to radian measure of angles

Length of an arc

Area of a sector.
2
class periods
3.2 Definition of cosθ and sinθ in terms of the unit
circle

Definition of tanθ as sin θ /cos θ .

Exact values of trigonometric ratios of
π/ 6, π/4,π/3, π/2,0 and their multiples.
3
class periods
3.4 The circular functions sin x , cos x and tan x :

Solve(2.7)

Graph (2.2)

Characteristics
o Domain/Range
o Asymptotes
o amplitude
o periodic nature
o Intercepts

Transformations(2.3)

Applications(2.8)
3
class periods
3.3 Trigonometric Identities

Pythagorean identity

Double angle identity (sine and cosine)

Relationship between trigonometric ratios
3 class periods
3.5 Solving trigonometric equations on a finite
3 class periods
interval including quadratic equations in sine cosine
or tangent.

Analytically

Graphically
3.6 Solutions if triangles

Law of Sines (including the ambiguous
case)

Law of Cosines
1

Area of a triangle 𝑎𝑏 𝑆𝑖𝑛 𝐶
2

Applications(2.8)
4 class periods
minutes.
Resources
Assessment
List the main resources to be
instruments to be used used, including information
technology if applicable.
Students will be assessed
Safari Montage, Ti-84 Plus GDC’s,
using formative assessments, Promethean Board and Active
weekly topic quizzes, monthly expressions, All-in-Learning Student
cumulative assessments,
response remotes and data analysis.
performance assessments, the Fathom software, Calculus in motion
internal assessment
concepts. Test generator software,
USA Test prep where applicable, Text
book TBD
Allocated time
Topic
(as identified in the IB subject
guide)
Contents
State the topics in the order
you are planning to teach
them.
Year 1
Topic 6: Calculus
One
class is
90
In one
week
there are
2/3 classes.
6.1 Informal ideas of limit and convergence
5 class periods

Investigate limits graphically, numerically
and algebraically

Definition of the derivative




o
f’(x)=lim
o
f’(x)=lim
ℎ→0
𝑥→𝑎
𝑓(𝑥+ℎ)−𝑓(𝑥)
ℎ
𝑓(𝑥)−𝑓(𝑎)
𝑥−𝑎
Interpret the derivative as a rate of change
Interpret the derivative as the slope function
Find and use the equation of tangent lines to
approximate values of functions
Find equations of normal lines
6.2 Use of Derivatives rules on polynomials,
trigonometric functions, ex, lnx, (include ax, rational
functions, radical functions, and inverse functions)

Sum and difference

Product rule

Quotient rule

Chain rule for composite functions

Second derivatives

Higher order derivatives

Implicit differentiation
3 class periods
10 class periods
6.3 Applications of Derivatives

Curve Analysis

Find local and global extrema using
derivative tests

Find points of inflection using the second
derivative test for concavity

Relate the behavior of the graphs of f f’ and
f”

Solve optimization problems

Solve Related rates problems using implicit
differentiation

Solve motion problems determining when
an object is at rest, moving in a
positive/negative direction, speeding
up/slowing down
minutes.
Resources
Assessment
List the main resources to be
instruments to be used used, including information
technology if applicable.
Students will be assessed
Safari Montage, Ti-84 Plus GDC’s,
using formative assessments, Promethean Board and Active
weekly topic quizzes, monthly expressions, All-in-Learning Student
cumulative assessments,
response remotes and data analysis.
performance assessments, the Fathom software, Calculus in motion
internal assessment
concepts. Test generator software,
USA Test prep where applicable, Text
book TBD
Allocated time
Topic
(as identified in the IB subject
guide)
Contents
State the topics in the order
you are planning to teach
them.
Year 1
Topic 6: Calculus
One
class is
90
In one
week
there are
2/3 classes.
6.4 Indefinite integration
3 class periods

Polynomials

Trigonometric functions
1

ex and
𝑥

Composite functions with a linear function

Integration using U substitution for
∫ 𝑓(𝑔(𝑥))𝑔′ (𝑥)𝑑𝑥
minutes.
Resources
Assessment
List the main resources to be
instruments to be used used, including information
technology if applicable.
Students will be assessed
Safari Montage, Ti-84 Plus GDC’s,
using formative assessments, Promethean Board and Active
weekly topic quizzes, monthly expressions, All-in-Learning Student
cumulative assessments,
response remotes and data analysis.
performance assessments, the Fathom software, Calculus in motion
internal assessment
concepts. Test generator software,
USA Test prep where applicable, Text
book TBD
6.5 Definite integration with applications
10 class periods

Analytically, graphically and using
technology

Differential equations

Slopefields

Find area under a curve

Find area between two curves

Find volumes of revolution , about
horizontal and vertical axis

Find volumes using cross sections of
different shapes using bases with different
shapes. i.e. squares, circles, triangles, and
rectangles.
3 class periods
Year 2
Topic 4: Vectors
6.6 Integration problems n involving displacement,
total distance traveled, velocity and acceleration.
4.1 Vectors as displacements in a plane and in three
dimensions

Components of a vector and column
representation

Algebraic and geometric approaches to
o Sum and difference of two
vectors,
o The zero vector,
o The negative vector
o Multiplication by a scalar
o Magnitude of a vector and
o Unit vectors i,j and k
o Position vectors
5 class periods
5 class periods
4.2 Scalar product of two vectors,

Perpendicular vectors

Parallel vectors angles between two vectors
Students will be assessed
Safari Montage, Ti-84 Plus GDC’s,
using formative assessments, Promethean Board and Active
weekly topic quizzes, monthly expressions, All-in-Learning Student
cumulative assessments,
response remotes and data analysis.
performance assessments, the Fathom software, Calculus in motion
internal assessment
concepts. Test generator software,
USA Test prep where applicable, Text
book TBD
Allocated time
Topic
(as identified in the IB subject
guide)
Contents
State the topics in the order
you are planning to teach
them.
Year 2
Topic 4: Vectors
Topic: 5 Statistics and Probability
One
class is
90
In one
week
there are
2/3 classes.
4.3 Representation of a line as r=a+tb and the angle 5 class periods
between two lines;
4.4 Distinguish between coincident and parallel lines 5 class periods

Determine if lines intersect locate the point
of intersection of two lines as the solution
to a system
5.1 Comparison of concepts
5 class periods

Population

Sample

Random sample

Discrete data

Continuous data
Graphical Representations of data

Frequency table

Frequency histograms

Box-and-whisker plots
o Use of upper and lower boundaries
o Interval widths
o Mid-interval values
5.2 Calculations of Statistical measures and make
interpretations of data using the results.

Mean, median, mode,

Range, interquartile range, quartiles,
percentiles, variance and standard deviation
5.3 Find median, quartiles and percentiles from
cumulative frequencies and their graphs
5 class periods
5 class periods
5.8 Binomial distribution

Binomial probabilities
5 class periods

Mean and Variance of the binomial
distribution
Determine when random variables are best described
using binomial distributions
5 class periods
5.9 Normal distribution and the “Bell” curve

Standardization of normal variables

Z-values and z-scores

Characteristics of a normal distribution
minutes.
Resources
Assessment
List the main resources to be
instruments to be used used, including information
technology if applicable.
Students will be assessed
Safari Montage, Ti-84 Plus GDC’s,
using formative assessments, Promethean Board and Active
weekly topic quizzes, monthly expressions, All-in-Learning Student
cumulative assessments,
response remotes and data analysis.
performance assessments, the Fathom software, Calculus in motion
internal assessment
concepts. Test generator software,
USA Test prep where applicable, Text
book TBD
Allocated time
Topic
(as identified in the IB subject
guide)
Contents
State the topics in the order
you are planning to teach
them.
Year 2
Topic: 5 Statistics and Probability
One
class is
90
In one
week
there are
2/3 classes.
Various Math Exploration Activities
10 class periods
5.4 Linear correlation of bivariate data
5 class periods

Pearson’s product-moment correlation
coefficient r

Scatter plots and linear regression equations

Use regressions lines to make predictions

Use mathematical findings to make
interpretations in the context of the
problem.
5 class periods
5.5 Probability Concepts

trials, outcomes, equally likely outcomes,
sample space and event

probability of an event and its complement
Use of Venn diagrams, tree diagrams and
tables to solve problems
5 class periods
5.6 Find probabilities

Combined events

Mutually exclusive events

Conditional probability definition

Independent events definition

Probabilities with and without replacement
5.7 Concept of discrete random variables and their
probability distributions

Find expected value for discrete data
Investigate real world uses of probability
distribution and expected value
IB Exam Review
5 class periods
15 class periods
minutes.
Resources
Assessment
List the main resources to be
instruments to be used used, including information
technology if applicable.
Safari Montage, Ti-84 Plus GDC’s,
Promethean Board and Active
expressions, All-in-Learning Student
response remotes and data analysis.
Fathom software, Calculus in motion
concepts. Test generator software,
USA Test prep where applicable, Text
book TBD
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.
The internal assessment (IA) will involve investigations and problem solving assignments. Students will be assessed on their ability to read, interpret and solve a given problem using appropriate
mathematical terms, organize and present information and data in tabular, graphical and/or diagrammatic forms, using appropriate notation and terminology, formulate a mathematical argument and
communicate it clearly, select and use appropriate mathematical strategies and techniques, demonstrate an understanding of both the significance and the reasonableness of results, recognize patterns and
structures, make generalizations, recognize and demonstrate an understanding of the practical applications of mathematics, use appropriate technological devices as mathematical tools and demonstrate an
understanding of and the appropriate use of mathematical modeling. The topic will be introduced and students will begin working on the IA when Calculus is introduced. The IA will be due at the
beginning of the second semester of the second year.
3.
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)
1.1 Arithmetic sequences and Students in pairs would be challenged to find the sum of the first 100 integers without the use of a calculator. After they work on the task for a few minutes I’ll let them
series: Sum of a finite
know that an 8 year old was able to find the sum in his head. After pairs arrive at their conclusions we will discuss their methods and any patterns they observed. Students
series using sigma notation will be prompted to find an equation that describes their pattern or process and verify that it works for any number of integers. We will then discuss the idea of mathematical
intuition and the basis for formal proof.
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 analyze it from different cultural perspectives. Briefly explain the reason for your choice and what resources you will use to achieve this goal.
Topic
3.1 Circular functions and
trigonometry
Contribution to the development of international mindedness (including resources you will use)
Students will investigate the origins of the metric system and countries willingness to adopt the metric system for their units of measure for distance, weight and capacity.
Students will then investigate the answer the question. Why haven’t circular functions been converted to the metric system? Students will research the Babylonian origins of
the 360 degree circle and its influences on the world.
5.
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
Random sampling from
populations; graphical displays
of data
6.
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.
Sampling from populations and then displaying the results requires a fundamental knowledge of the tools necessary to achieve accurate results. Clear presentation is also
necessary. The impact of displaying accurate versus inaccurate results on public opinion and elections throughout the world will be discussed. Suggestions for presenting
and displaying clear and meaningful results will be debated.
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.
Students and the teacher will utilize various resources such as Safari Montage, Ti-84 Plus GDC’s,
Promethean Board and Active expressions; All-in-Learning Student response remotes and data analysis, Fathom software, Calculus in motion Sketchpad to visually display
concepts. Test generator software, USA Test prep where applicable, Text book TBD
```
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