High School Online Program of Studies

Mathematics Department

 PHILOSOPHY

 

 

CAC PK-12 Mathematics Philosophy Statement 

Cairo American College celebrates the beauty of mathematics, inspiring students to make sense of the fascinating elements of content knowledge, while promoting perseverance and intellectual risk taking. Learners construct deep mathematical understanding through exploration of meaningful, complex problems - both independently and in collaboration with others. Using a variety of resources and strategies, learners build new understanding by expanding and refining previous learning experiences.

We believe that: 

  • developmentally appropriate mathematics is accessible to all learners.
  • learners develop mathematical understanding by exploring strategies, questioning, explaining, and reflecting.
  • learners use a variety of mathematical representations to organize, record, and communicate their understanding.
  • learners develop and demonstrate conceptual understanding, procedural proficiency and factual knowledge.

Mathematics Teaching and Learning at CAC:

  • is anchored in research that defines the mathematically proficient student as being able to balance Conceptual Understanding, Procedural Fluency, Strategic Competence, Adaptive Reasoning, and Productive Disposition (National Research Council, Adding it Up), 
  • is grounded in a range of research-based Effective Mathematics Teaching Practices, including a balance of teacher-directed and inquiry-based teaching methodologies, 
  • is differentiated based on levels of readiness in order to meet the needs of all learners,
  • is articulated using the  AERO-CCSS Content and Practice Standards, which also emphasizes learning in four process areas: Problem Solving, Reasoning and Proof, Communication, and Connections, and
  • is aligned with the framework of the International Baccalaureate. 

 

 

 

Mathematics Courses Offered 2023-2024

INTEGRATED MATHEMATICS 1

INTEGRATED MATHEMATICS 2

INTEGRATED MATHEMATICS 3

IB APPLICATIONS AND INTERPRETATIONS II (AI SL 2) 

IB ANALYSIS AND APPROACHES I (AA SL 1) 

IB APPLICATIONS AND INTERPRETATIONS I (AI SL 1)

IB ANALYSIS AND APPROACHES II (AA SL 2)

IB ANALYSIS AND APPROACHES HL I (AA HL 1) 

IB ANALYSIS AND APPROACHES HL II (AA HL 2) 

 

 

 


INTEGRATED MATHEMATICS 3
 

Course Description:

IM3 is appropriate for students who successfully completed IM2, or an equivalent course. Topics covered in the course include the following:

Operations with Functions

Building upon concepts taught in Integrated Math 2, topics include a further study of functions (transformations, composition, inverses), and a further study of linear functions (absolute value, piecewise, inequalities) and linear systems.

Characteristics of Functions

These units focus on a study of quadratic, polynomial, rational, exponential and logarithmic functions. Topics include developing and applying the quadratic formula, solving quadratic equations, vertex form of quadratic functions. Topics related to polynomial functions explored include definitions, characteristics, graphs, simple factoring and modeling. Rational functions are defined and graphed, and properties of rational functions are explored. Also included is a review of exponential functions and introducing logarithmic functions and their relation to exponential functions, equation solving with logarithms.

Geometry: Circles, Circular Functions and Triangle Trigonometry

Topics include properties of chords, tangent lines, and central and inscribed angles of circles; radian measure of angles; and circular functions as models of periodic change. Trigonometry will be used to develop solutions to non-right triangles through the sine law and the cosine law.  Analytical trigonometry is also introduced in terms of solving simple sine and cosine equations.

Applications of Probability

Topics include Addition Rule, Multiplication Rule, independent and dependent events, and conditional probability.

 

  
 

Prerequisites:

Integrated Mathematics 2 

  
 

Credit:

1.0 credit

  
 

Length of Course:

1 year

  
 

Texts:

 

  
 

Recommendations:

Students must have a graphing calculator (TI-84 calculator is preferred).

  
  Requirements: