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Mathematics

The mathematics program at DCIS is designed to support the mission and values of the Denver Center for International Studies.  That is–it prepares students for success at college and features the use of DCIS stated values and skills like collaboration and reflection in most daily learning activities. Additionally, students will use and understand the math skills and concepts of statistics in order to empower their analyses of global issues and facts. Students are required to complete 4 years of high school mathematics.

Algebra 1
Credit: 5 hours
Grade Levels: 9, 10, 11, and 12
Prerequisites: None
Graduation Information: Applies toward requirement for Algebra
Notes: Algebra 1X and 2X in middle school fulfills 10 hours of required high school math

Discovering Algebra is a first year algebra course in which students will learn the power of math in its abstract and its application to real world scenarios.  The key content area involves problem solving using different methods such as factoring, graphing, linear and quadratic equations.  Students will be presented with real life scenarios and through a series of lessons be able to solve the problems and present their solutions with written proofs, and student taught lessons.   Students will demonstrate their ability to reason symbolically.  Students will learn different methods to solve quadratic equations including factoring, completing the square, graphically, or through application of the quadratic formula. The course also includes study of monomial and polynomial expressions, inequalities, exponents, functions, rational expressions, ratio, and proportion.  This is a required course for graduation.

Course: Algebra 2
Prerequisites: Algebra 2 and usually Geometry 2 or its equivalent
Course Description:

This two-semester course sequence reviews and expands the topics of first year algebra and some from geometry. The topics covered are linear and quadratic equations and inequalities in one variable, rational expressions and equations, radical expressions and equations, equations and slopes of lines, conic,  systems of linear and quadratic equations and inequalities, secons and third degree polynomials, logarithmic and exponential functions. (Optional topics may include sequences, series, probability and statistics, matrices and determinants).

Advanced Algebra
Credits: 5 hours
Grade Level(s):
Prerequisites: Algebra 2 and usually Geometry 2 or its equivalent
Graduation Info: This course is applicable toward the graduation requirement for Mathematics (gen.)

Like the geometry course, it is also discovery-based and its algebra rigor prepares students for trigonometry/ pre-calculus or AP classes the following years. Textbook is Discovering Advanced Algebra.  Students will deepen content knowledge in advanced algebra, develop an understanding of the connections among mathematical representations, focus on problem solving, logic and reasoning, and communication. Develop understanding of technology as applied to advanced algebra topics. This is a required course for graduation.

Geometry
Credit: 5
Grade Levels: 9, 10, 11, and 12
Prerequisites: Algebra 2
Graduation Information: Applies toward requirement for Geometry
Course Description:

This course is based upon the textbook Discovering Geometry by Michael Serra, one of the most rigorous and currently highly recognized texts due to its centerpiece of hypotheses or conjectures. Students use constructions both with compass and the software program, Geometer’s Sketchpad to examine and prove or disprove each conjecture.  The Discovering Geometry course provides students with the knowledge, language, and logic of inductive geometry using an inquiry based learning strategy.  Students will apply reasoning to line and angle relationships, polygons, circles and geometric constructions.  Informal proofs are investigated.  Second semester builds on concepts covered in the first semester and such as studying area, Pythagorean Theorem, special right triangles, volume, similarity, trigonometry, circular relationships and tessellations.  It expands students’ abstract and critical thinking in mathematics. This course includes an art infusion unit featuring perspective using multi-cultural images. This is a required course for graduation.

Probability and Statistics
Credit: 5
Grade Levels: 11, 12
Graduation Information: This course is applicable toward the graduation requirement for Mathematics (gen.)
Prerequisites: Algebra 3
Course Description:

Statistics Through Applications is the ideal alternative for juniors and seniors not going into high level courses such as calculus, but who are interested in an introduction to the important topics of statistics.   The course’s data analysis approach moves students away from monotonous computation to focus on the statistical thinking behind data gathering and interpretation.  This approach more accurately reflects the way working statisticians contribute to our understanding of the world.  It also helps students be more discerning consumers of statistics, teaching them to look closely at what the numbers from surveys, election polls, and medical studies are really saying.

Pre-calculus
Credits: 5
Grade Level(s): 11, 12
Prerequisites: Advanced Algebra 2
Course Description:

This two-semester course is designed to provide students with a strong background in functions (trigonometric, linear, quadratic, absolute value, power, square root, exponential, rational, and logarithmic) and is designed to prepare students for a calculus course.  Textbook for this class is Precalculus; Seventh Edition by Demana, Waits, Foley and Kennedy.

Advanced Placement Calculus
Grade Level(s): 11, 12
Special Grading: AP credit
Prerequisites: Pre-Calculus 1, 2 or Pre-Calculus 1X, 2X
Course Description:

Advanced Placement Calculus is year long course comparable to calculus courses offered in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement or both, from institutions of higher learning.  Calculus AB is primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and application.  The course emphasizes a multi-representational approach to calculus with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally.  Throughout the course connections among these representations will be established.  Graphing calculator will be used frequently for the purpose of exploration and investigation of concepts, and verification of conclusions.  Textbook for this class is Calculus by Finney, Deamana, Waits and Kennedy.

Notes

Students in honors level classes are expected to complete more extensive course work and meet with the teacher during office hours as pre-arranged to receive and turn in work.

Each semester students will select one artifact for inclusion in their graduation portfolio. Graphing calculators are required for high school courses and may be used for middle school.  It is preferred that each high school student purchase his or her own calculator to become familiar with its programs and preferences.