Appendix 5IB Diploma Programme course outlines

Teachers responsible for each proposed subject must prepare a course outline following the guidelinesbelow. While IB subject guides will be used for this exercise, teachers are expected to adapt theinformation in these guides to their own school’s context. Please be sure to use IBO nomenclaturethroughout. The name of the teacher(s) who wrote the course outline must be recorded at the top of theoutline.

Name of the teacher who prepared the outline:

Melissa Webb

Name of the course:

Mathematics SL

Course description:

This course caters for students who already possess knowledge of basic mathematical concepts, and who are equipped with the skills needed to apply simple mathematical techniques correctly. The majority of these students will expect to need a sound mathematical background as they prepare for future studies in subjects such as chemistry, economics, psychology and business administration. Students should be expected to understand mathematics conceptually as well as in application. A component of Math SL is the need for the student to make connections between several topics of mathematics in order to problem solve.

The course focuses on introducing important mathematical concepts through the development of mathematical techniques. The intention is to introduce students to these concepts in a comprehensible and coherent way. Students should, wherever possible, apply the mathematical knowledge they have acquired to solve realistic problems set in an appropriate context. Students are expected to be fluent in mathematics with and without a graphics display calculator.

Mathematics is in a sense an international language, and, apart from slightly differing notation, mathematicians from around the world can communicate within their field. Many of the foundations of modern mathematics were laid many centuries ago by Arabic, Greek, Indian and Chinese civilizations, among others and the language of mathematics continues to develop with technology. To demonstrate the universality of mathematics in a historical context, Math SL students will learn about mathematicians and the historical context in which they worked.

The internally assessed component, the exploration, offers students the opportunity for developing

independence in their mathematical learning. Students are encouraged to take a considered approach tovarious mathematical activities and to explore different mathematical ideas. The exploration also allowsstudents to work without the time constraints of a written examination and to develop the skills they need for communicating mathematical ideas. It is essential for students to communicate their appreciation for the beauty of mathematics and its place in the universe as well as a connection to a persona interest of theirs. Students must also sit for two externally graded examinations; with and without a GDC.Units:

Unit 1 – Functions and Transformations (10.5 Hours)

2.1.1 Concept of function f : x ↦ f (x) .2.1.2 Domain, range; image (value).2.1.3 Composite functions.2.1.4 Identity function. Inverse function f-1.

2.2.1 The graph of a function; its equation y = f (x) .2.2.2 Function graphing skills.2.2.3 Investigation of key features of graphs, such as maximum and minimum values, intercepts, horizontal and vertical asymptotes, symmetry, and consideration of domain and range.2.2.4 Use of technology to graph a variety of functions, including ones not specifically mentioned.2.2.5 The graph of y f-1 (x) = − as the reflection in the line y = x of the graph of y = f (x) .

2.3.1 Transformations of graphs.2.3.2 Translations: y = f (x) + b ; y = f (x − a) .2.3.3 Reflections (in both axes): y = − f (x) ; y = f (−x) .2.3.4 Vertical stretch with scale factor p: y = pf (x) .

2.3.5 Stretch in the x-direction with scale factor 1q : y = f (qx).

2.3.6 Composite transformations.

2.5.1 The reciprocal function x↦ 1

x , x ≠ 0 : its graph and self-inverse nature.

2.5.2 The rational function x↦ ax+b

cx+d and its graph.2.5.3 Vertical and horizontal asymptotes.

Optional Links to ToKToK Questions ToK ActivityIs zero the same as “nothing”? How accurate is a visual representation

of a mathematical concept? (Limits of graphs in delivering information about functions andphenomena in general, relevance of modes of representation.)

Math SL 3rd Edition: p. 236Is mathematics a formal language? Why is it important that mathematicians use the same notation? Does a mathematical argument need to read like a good piece of English? What is the difference between equal, equivalent, and the same? Are there any words which we use only in mathematics? What does this tell us about the nature of mathematics and the world around us?Mathematics and the knower. To what extent should mathematical knowledge be consistent with our intuition?Mathematics and the world. Some mathematical constants (pi, e, , Fibonacci numbers) appear consistently in nature. What does this tell us about mathematical knowledge?The nature of mathematics. Is mathematics simply the manipulation of symbols under a set of formal rules?Mathematics and knowledge claims. Does studying the graph of a function contain the same level of mathematical rigour as studying the function algebraically (analytically)?

Optional Links to InternationalismTopics International ComponentFunctions and Equations The development of functions, Rene

Descartes (France), Gottfried Wilhelm Leibniz(Germany) and Leonhard Euler (Switzerland).The Babylonian method of multiplication:

ab=(a+b )2−a2−b2

2Sulba Sutras in ancient India and the Bakhshali Manuscript contained an algebraic formula for solving quadratic equations.

Unit 2 – Quadratic Functions (12 Hours)

2.4.1 The quadratic function x↦ax2 + bx + c : its graph, y-intercept (0, c) . Axis of symmetry.2.4.2 The form x↦a(x − p)(x − q) , x-intercepts ( p, 0) and (q, 0) .2.4.3 The form x↦a(x − h)2 + k , vertex (h, k) .2.7.1 Solving equations, both graphically and analytically.2.7.2 Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach.2.7.3 Solving ax2 + bx + c = 0 , a ≠ 0 .2.7.4 The quadratic formula.2.7.5 The discriminant Δ = b2 − 4ac and the nature of the roots, that is, two distinct real roots, two equal real roots, no real roots.2.8.1 Applications of graphing skills and solving equations that relate to real-life situations.

Optional Links to InternationalismTopics International ComponentFunctions and Equations The development of functions, Rene

Descartes (France), Gottfried Wilhelm

Leibniz(Germany) and Leonhard Euler (Switzerland).The Babylonian method of multiplication:

ab= (a+b )2−a2−b2

2Sulba Sutras in ancient India and the Bakhshali Manuscript contained an algebraic formula for solving quadratic equations.

Unit 3 – Exponential and Logarithmic Laws and Functions (15 Hours)

1.2.1 Elementary treatment of exponents and logarithms.1.2.2 Laws of exponents; laws of logarithms. Change of base.2.7.6 Solving exponential equations.2.6.1 Exponential functions and their graphs: x↦ax , a > 0 , x↦ex .2.6.2 Logarithmic functions and their graphs: loga x↦ x , x > 0 , x↦ ln x , x > 0 .2.6.3 Relationships between these functions: ax = ex ln a ; logaax = x ; aloga x = x , x > 0 .2.7.1 Solving equations, both graphically and analytically.2.7.2 Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach.2.8.1 Applications of graphing skills and solving equations that relate to real-life situations.

Optional Links to ToKToK Questions ToK ActivityThe nature of mathematics and science. Were logarithms an invention or discovery?

Short-term loans at high interest rates. How can knowledge of mathematics result in individuals being exploited or protected from extortion?

Math SL 3rd Edition: p. 115Are logarithms an invention ordiscovery? (This topic is an opportunity for teachers to generate reflection on “the nature of mathematics”.)

The phrase “exponential growth” is used popularly to describe a number of phenomena. Is this a misleading use of a mathematical term?

Optional Links to InternationalismTopics International ComponentFunctions and Equations The Legend of the Ambalappuzha Paal

PayasamEulerJohn Napier

Unit 4 – Non-Right Triangle Trigonometry (10.5 Hours)

3.1.1 The circle: radian measure of angles; length of an arc; area of a sector.3.2.1 Definition of cosθ and sinθ in terms of the unit circle.

3.2.2 Definition of tanθ as sin θcosθ .

3.2.3 Exact values of trigonometric ratios of 0, π6

, π4

, π3

, π2 ,π, and their multiples.

3.6.1 Solution of triangles.3.6.2 The cosine rule.3.6.3 The sine rule, including the ambiguous case.

3.6.4 Area of a triangle, 12

ab sin C .

3.6.5 Applications.

Optional Links to ToKToK Questions ToK ActivityWhich is a better measure of angle: radian or degree? What are the “best” criteria by which to decide?

Euclid’s axioms as the building blocks of Euclidean geometry. Link to non-Euclideangeometry.

Trigonometry was developed by Math SL 3rd Edition: p. 272

successive civilizations and cultures. How is mathematical knowledge considered from asociocultural perspective?

Non-Euclidean geometry: angle sum on a globe greater than 180°.

Math SL 3rd Edition: p. 192What other measures of angle are there? Which is the most natural unit of angle measure?

Nature of mathematics. If the angles of a triangle can add up to less than 180°, 180° or more than 180°, what does this tell us about the “fact” of the angle sum of a triangle and about the nature of mathematical knowledge?

Mathematics and the knower. Why do we use radians? (The arbitrary nature of degree measure versus radians as real numbers and the implications of using these two measures on the shape of sinusoidal graphs.)Mathematics and knowledge claims. If trigonometry is based on right triangles, how can we sensibly consider trigonometric ratios of angles greater than a right angle?Mathematics and knowledge claims. How can there be an infinite number of discrete solutions to an equation?

Optional Links to InternationalismTopics International ComponentCircular Functions and Trigonometry Seki Takakazu calculating π to ten

decimal places.Hipparchus, Menelaus and Ptolemy.Why are there 360 degrees in a completeturn? Links to Babylonian mathematics.The first work to refer explicitly to thesine as a function of an angle is theAryabhatiya of Aryabhata (ca. 510).Cosine rule: Al-Kashi and Pythagoras.The origin of degrees in the mathematics of Mesopotamia and why we use minutes and seconds for time.Why did Pythagoras link the study of music and mathematics?The use of triangulation to find the curvature of the Earth in order to settle a dispute between England and France over Newton’s gravity.

Unit 5 – Trigonometric Functions (21 Hours)

3.4.1 The circular functions sin x , cos x and tan x: their domains and ranges; amplitude, their periodic nature; and their graphs.3.4.2 Composite functions of the form f (x) = asin(b(x + c) )+ d .3.4.3 Transformations.3.4.4 Applications.3.5.1 Solving trigonometric equations in a finite interval, both graphically and analytically.3.5.2 Equations leading to quadratic equations in sin x, cos x or tan x .3.5.3 The general solution of trigonometric equations.3.3.1 The Pythagorean identity cos2θ+sin2θ =1. Double angle identities for sine and cosine.2.7.1 Solving equations, both graphically and analytically.2.7.2 Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach.2.8.1 Applications of graphing skills and solving equations that relate to real-life situations.

Optional Links to ToKToK Questions ToK ActivityMathematics and the world. Music can be expressed using mathematics. Does this mean that music is mathematical, that mathematics is musical or that both are reflections of a common “truth”?

Optional Links to InternationalismTopics International ComponentCircular Functions and Trigonometry Michael Faraday and electric current

Unit 6 – Patterns in Algebra (10.5 Hours)

1.1.1 Sequences and series; sum of finite arithmetic series; geometric sequences and series; sum of finite and infinite geometric series.1.1.2 Sigma notation.1.1.3 Applications.1.3.1 The binomial theorem: expansion of (a + b)n , n∈ℵ .

1.3.2 Calculation of binomial coefficients using Pascal’s triangle and (nr ).

Optional Links to ToKToK Questions ToK ActivityMath SL 3rd Edition: p. 347What is Zeno’s dichotomy paradox? How far can mathematical facts be fromintuition?

How did Gauss add up integers from 1 to 100? Discuss the idea of mathematical intuition as the basis for formal proof.

The nature of mathematics. The unforeseen links between Pascal’s triangle, counting methods and the coefficients of polynomials. Is there an underlying truth that can be found linking these?

Math SL 3rd Edition: p. 174Debate over the validity of the notion of “infinity”: finitists such as L. Kronecker consider that “a mathematical object does not exist unless it can be constructed from naturalnumbers in a finite number of steps”.Math SL 3rd Edition: p. 89Prove √2 is irrationalHow many different tickets are possible in a lottery? What does this tell us about the ethics of selling lottery tickets to those who do not understand the implications of these large numbers?

Optional Links to InternationalismTopics International ComponentAlgebra The chess legend (Sissa ibn Dahir).

Aryabhatta is sometimes considered the“father of algebra”. Compare withal-Khawarizmi.The so-called “Pascal’s triangle” wasknown in China much earlier than Pascal.Koch’s snowflake

Unit 7 – Statistics (12 Hours)

5.1.1 Concepts of population, sample, random sample, discrete and continuous data.5.1.2 Presentation of data: frequency distributions (tables); frequency histograms with equal class intervals;5.1.3 box-and-whisker plots; outliers.5.1.4 Grouped data: use of mid-interval values for calculations; interval width; upper and lower interval boundaries; modal class.5.2.1 Statistical measures and their interpretations.5.2.2 Central tendency: mean, median, mode.5.2.3 Quartiles, percentiles.5.2.4 Dispersion: range, interquartile range, variance, standard deviation.5.2.5 Effect of constant changes to the original data.5.2.6 Applications.5.3.1 Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles.5.4.1 Linear correlation of bivariate data.5.4.2 Pearson’s product–moment correlation coefficient r.5.4.3 Scatter diagrams; lines of best fit.5.4.4 Equation of the regression line of y on x.5.4.5 Use of the equation for prediction purposes.5.4.6 Mathematical and contextual interpretation.

Optional Links to ToKToK Questions ToK ActivityDo different measures of centraltendency express different properties of the data? Are these measures invented ordiscovered? Could mathematics make alternative, equally true, formulae? What does this tell us about mathematical truths?

How easy is it to lie with statistics?

Mtah SL 3rd Edition: p. 561Is mathematics useful to measure risks?

Does the use of statistics lead to an overemphasis on attributes that can easily be measured over those that cannot?

The nature of mathematics. Why have mathematics and statistics sometimes been treated as separate subjects?

Misleading statistics in media reports.

The nature of knowing. Is there a difference between information and data?

Optional Links to InternationalismTopics International ComponentStatistics and Probability The St Petersburg paradox,

Chebychev,Pavlovsky.Discussion of the different formulae forvariance.Blaise Pascal and Pierre de Fermat

Unit 8 – Probability (24 Hours)

5.5.1 Concepts of trial, outcome, equally likely outcomes, sample space (U) and event.

5.5.2 The probability of an event A is P ( A )= n ( A )

n (U ) .5.5.3 The complementary events A and A′ (not A).5.5.4 Use of Venn diagrams, tree diagrams and tables of outcomes.5.6.1 Combined events, P(A∪ B) .5.6.2 Mutually exclusive events: P(A∩ B) = 0 .

5.6.3 Conditional probability; the definition P ( A|B )=

P ( A∩B )P ( B )

5.6.4 Independent events; the definition P( A| B) = P(A) = P( A| B′) .5.6.5 Probabilities with and without replacement.5.7.1 Concept of discrete random variables and their probability distributions.5.7.2 Expected value (mean), E(X ) for discrete data.5.7.3 Applications.

Optional Links to ToKToK Questions ToK ActivityMath SL 3rd Edition: p. 603In what ways can mathematics model the world without using functions? How

Can gambling be considered as an application of mathematics? (This is a good opportunity to generate a debate

does a knowledge of probability theory affect decisions we make? Do ethics play a role in the use of mathematics?

on the nature,role and ethics of mathematics regarding itsapplications.)

Mathematics and knowledge claims. Is independence as defined in probabilistic terms the same as that found in normal experience?

Math SL 3rd Edition: p. 538Analyzing charts and graph for bias and deception

Mathematics and the real world. Is the binomial distribution ever a useful model for an actual real-world situation?

Why has it been argued that theories based on the calculable probabilities found in casinos are pernicious when applied to everyday life (eg economics)?

Mathematics and knowledge claims. To what extent can we trust mathematical models such as the normal distribution?

Use of probability methods in medical studies to assess risk factors for certain diseases.

Why might the misuse of the normal distribution lead to dangerous inferences and conclusions?

Optional Links to InternationalismTopics International ComponentStatistics and Probability The St Petersburg paradox,

Chebychev,Pavlovsky.Discussion of the different formulae forvariance.Blaise Pascal and Pierre de Fermat

Unit 9 – Vectors (15 Hours)

4.1.1 Vectors as displacements in the plane and in three dimensions.

4.1.2 Components of a vector; column representation;

v=(v1

v2

v3)=v1 i+v2 j+v3 k

.4.1.3 Algebraic and geometric approaches to the following:

a. the sum and difference of two vectors; the zero vector, the vector −v ;b. multiplication by a scalar, kv ; parallel vectors;c. magnitude of a vector, |v| ;d. unit vectors; base vectors; i, j and k;e. position vectorsO⃗A=a ;f. A⃗B=O⃗B−O⃗A=b−a .

4.2.1 The scalar product of two vectors.4.2.2 Perpendicular vectors; parallel vectors.

4.2.3 The angle between two vectors.4.3.1 Vector equation of a line in two and three dimensions: r = a + tb .4.3.2 The angle between two lines.4.4.1 Distinguishing between coincident and parallel lines.4.4.2 Finding the point of intersection of two lines.4.4.3 Determining whether two lines intersect.

Optional Links to ToKToK Questions ToK ActivityHow do we relate a theory to the author? Who developed vector analysis: JW Gibbs or O Heaviside?

Vectors are used to solve many problems in position location. This can be used to save a lost sailor or destroy a building with a laser-guided bomb.

Math SL 3rd Edition: p. 337Are algebra and geometry two separate domains of knowledge? (Vector algebra is agood opportunity to discuss how geometrical properties are described and generalized byalgebraic methods.)

The nature of mathematics. Why might it be argued that vector representation of lines is superior to Cartesian?

Mathematics and knowledge claims. You can perform some proofs using different mathematical concepts. What does this tell us about mathematical knowledge?

Mathematics and the knower. Why are symbolic representations of three-dimensional objects easier to deal with than visual representations? What does this tell us about our knowledge of mathematics in other dimensions?

Unit 10 – Introduction to Calculus (16.5 Hours)

6.1.1 Informal ideas of limit and convergence.6.1.2 Limit notation.

6.1.3 Definition of derivative from first principles as f ' ( x )=limh→0

f (x+h )−f ( x )h

.

6.1.4 Derivative interpreted as gradient function and as rate of change.6.1.5 Tangents and normals, and their equations.6.2.1 Derivative of xn (n∈Q) 6.2.2 Differentiation of a sum and a real multiple of these functions.6.2.3 The chain rule for composite functions.6.2.4 The product and quotient rules.6.2.5 The second derivative.6.2.6 Extension to higher derivatives.

Optional Links to ToKToK Questions ToK ActivityWhat value does the knowledge of limits have? Is infinitesimal behavior applicable to real life?The nature of mathematics. Does the fact that Leibniz and Newton came across the calculus at similar times support the argument that mathematics exists prior to its discovery?Mathematics and the knower. What does the dispute between Newton and Leibniz tell us about human emotion and mathematical discovery?Mathematics and knowledge claims. Euler was able to make important advances in mathematical analysis before calculus had been put on a solid theoretical foundation by Cauchy and others. However, some work was not possible until after Cauchy’s work. What does this tell us about the importance of proof and the nature of mathematics?Mathematics and the real world. The seemingly abstract concept of calculus allows us to create

mathematical models that permit human feats, such as getting a man on the Moon. What does this tell us about the links between mathematical models and physical reality?

Optional Links to InternationalismTopics International ComponentCalculus Successful calculation of the volume of

the pyramidal frustum by ancient Egyptians(Egyptian Moscow papyrus).Use of infinitesimals by Greek geometers.Accurate calculation of the volume of acylinder by Chinese mathematician Liu Hui.Ibn Al Haytham: first mathematician tocalculate the integral of a function, in order tofind the volume of a paraboloid.How the Greeks’ distrust of zero meant that Archimedes’ work did not lead to calculus.Investigate attempts by Indian mathematicians (500–1000 CE) to explain division by zero.

Unit 11 – Calculus Curve Properties and Applications (18 Hours)

6.3.1 Local maximum and minimum points.6.3.2 Testing for maximum or minimum.6.3.3 Points of inflexion with zero and non-zero gradients.6.3.4 Graphical behaviour of functions, including the relationship between the graphs of f , f ' , f ' ' .6.3.5 Optimization.6.3.6 Applications.6.6.1 Kinematic problems involving displacement s, velocity v and acceleration a.6.6.2 Total distance travelled.

Optional Links to ToKToK Questions ToK ActivityMath SL 3rd Edition: p. 436 Opportunities for discussing hypothesis

Is optimization unique to mathematics? How does mathematics fit into the scientific method? Does mathematics have a prescribed method of its own? Is mathematics a science?

formation and testing, and then the formalproof can be tackled by comparing certain cases, through an investigative approach

Unit 12 – Calculus of Exponential, Logarithmic, and Trigonometric Functions (16.5 Hours)

6.2.1 Derivative of sin x , cos x , tan x , ex and ln x .6.2.2 Differentiation of a sum and a real multiple of these functions.6.2.3 The chain rule for composite functions.6.2.4 The product and quotient rules.6.2.5 The second derivative.6.3.6 Applications.

Unit 13 – Integral Calculus (28.5 Hours)

6.4.1 Indefinite integration as anti-differentiation.

6.4.2 Indefinite integral of xn (n∈Q) , sin x , cos x ,1x

, ex

.6.4.3 The composites of any of these with the linear function ax + b .

6.4.4 Integration by inspection, or substitution of the form ∫ f ( g (x ) ) g' (x ) dx .6.5.1 Anti-differentiation with a boundary condition to determine the constant term.6.5.2 Definite integrals, both analytically and using technology.6.5.3 Areas under curves (between the curve and the x-axis).6.5.4 Areas between curves.6.5.5 Volumes of revolution about the x-axis.6.6.1 Kinematic problems involving displacement s, velocity v and acceleration a.6.6.2 Total distance travelled.

Optional Links to ToKToK Questions ToK ActivityMathematics, sense, perception and reason. If we can find solutions in higher dimensions, can we reason that these spaces exist beyond our sense perception?

Links to the Learner ProfileThe Mathematics Learner Profile taken from: henricowarriors.org/.../2011/12/The-Mathematics-Learner-Profile.pdf

Assessment:

IB External Assessment PAPER 1

o 90 minute exam consisting of two sections and no calculator is allowed Section A is approximately 7 – 9 short response questions based on the whole

syllabus Section B is approximately 3 – 4 long response questions based on the whole

syllabus PAPER 2

o 90 minute exam consisting of two sections and a Graphing Display Calculator is required

Section A is approximately 7 – 9 short response questions based on the whole syllabus

Section B is approximately 3 – 4 long response questions based on the whole syllabus

The external assessment is 80% 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.

IB Internal Assessment 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 thatinvolves 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 broken up into the following process Introduction (.5

Hours)o During 1st Quartero Students are given the rules and guidelines o Students are provided the rubric

Stimuli (1.5 Hours)

o During 2nd quarter students participate in multiple activities World Café MindMaps

o Students are given time to read through exemplars Topic (.25

Hours)o During 3rd quartero Students must choose two possible topics based on previous stimuli activity o Individual meetings with the instructor to decide on the best topic

Research/Data (.25 Hours)

o During 3rd quartero Students are given time to either find data to model or research a topic to investigateo All sources must be turned in on a bibliography

Mathematical Work (.25 Hours)

o During 4th quartero Students are to work out their mathematical work on paper

Rough Draft (6.75 Hours)

o During 4th quartero Students are to type out a rough draft and include the following subtopics

Introduction – why this topic Rationale – individual and global value Aim – mathematic s to be used Data/Research – tables/graphs/research Mathematics – all work shown and screenshots of the GDC Analysis/Reflection – results and meaning of mathematics Conclusion including limitations and further research

o Rough draft due before the end of the junior year and must be submitted to turnitin.com Final Draft (.5

Hours)o Students will have an individual meeting with the instructor discussing strengths and

weaknesses of the rough drafto Students will not be provided with an annotated versiono Students will have 9 – 10 days to turn in a final draft to the instructor and turnitin.com

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.

In-Class Formative AssessmentFormative 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 Questioning Discussion Graphic Organizers Self-Assessment Think-Pair-Share Order Share

World Café Think Aloud Talk to the Text Mind Map White-Boarding Practice Problems Entrance/Exit Cards

In-Class Summative AssessmentSummative assessment is used to summarize and record overall achievement at the end of a course, forpromotion 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 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 Math SL 2nd edition for students- Haese & Harris Math SL 3rd edition as teacher resource material- Agnesi to Zeno – 100 vignettes from History of Math, Sanderson and Smith as teacher

resource material (Internationalism)- TI-84Plus Graphics Display Calculator- Oxford Math SL Course Companion teacher resource material - IBID Press 3rd Edition Math SL as teacher resource material- NTK Learning Center IB Study Guide- IB QuestionBank (CD) and past IB Examinations available through IBO- Online Curriculum Center