Math

Students at Decatur High School must take and pass four math courses in high school to earn a high school diploma. In general, a student’s math course in 9th grade determines the math course he or she will take in grades 10 and 11. Students are offered several math choices in 12th grade, depending on their previous studies and achievement. Students may take accelerated math courses based on their interest and meeting certain achievement and readiness criteria based on grades and MAP scores.

9th Grade

Foundations of Algebra

Previous Course: 8th-Grade Math

Next Course: Algebra 1

Foundations of Algebra is a first year high school mathematics course for students who have completed mathematics in grades 6 – 8 intended to bolster success in high school mathematics. Foundations of Algebra will provide many opportunities to revisit and expand the understanding of foundational algebra concepts, will employ diagnostic means to offer focused interventions, and will incorporate varied instructional strategies to prepare students for required high school mathematics courses. The course will emphasize both algebra and numeracy in a variety of contexts including number sense, proportional reasoning,quantitative reasoning with functions, and solving equations and inequalities.

Algebra 1

Previous Course: 8th-Grade Math

Next Course: Geometry

Algebra I is the first course in a sequence of three required high school courses designed to ensure career and college readiness. The course represents a discrete study of algebra with correlated statistics applications. The fundamental purpose of Algebra I is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, organized into units, deepen and extend understanding of functions by comparing and contrasting linear, quadratic, and exponential phenomena. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

Accelerated Algebra 1/Geometry A

Previous Course: 8th-Grade Math

Next Course: Accelerated Analytic Geometry

Placement Criteria: Two of the following: 8th-grade math grade of 6 or higher, two 8th-grade MAP Math scores 70th percentile or higher, qualifying Milestone score (TBD)

Accelerated Algebra I/Geometry A is the first in a sequence of mathematics courses designed to ensure that students are prepared to take higher‐level mathematics courses during their high school career. The fundamental purpose of Accelerated Algebra I/Geometry A is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, organized into units, deepen and extend understanding of functions by comparing and contrasting linear, quadratic, and exponential phenomena. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situation.

Accelerated Geometry B/Algebra 2

Previous Course: Accelerated Algebra 1 in 8th Grade

Next Course: AP Statistics

Placement Criteria: Students in Accelerated Analytic Geometry were identified after 7th grade.

Accelerated Geometry B/Algebra II is the second in a sequence of mathematics courses designed to ensure that students are prepared to take higher‐level mathematics courses during their high school career. It is in Accelerated Geometry B/Algebra II that students pull together and apply the accumulation of learning that they have from their previous course, with content grouped into nine critical areas, organized into units. Students continue to work with geometry concepts as the work with circles and theorems related to them. The students then move onto applying the geometric concepts they have previously learned in the coordinate plane in finding distances and writing equations of circles. They then build upon the probability concepts they learned in middle school. Students expand their repertoire of functions to include quadratic (with complex solutions), polynomial, rational, and radical functions. And, finally, students bring together all of their experience with functions to create models and solve contextual problems. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

AP Statistics

Previous Course: Accelerated Geometry B/Algebra 2 in 8th grade

Next Course: Accelerated IB Math SL/Pre-Calculus

The purpose of the AP course in statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes: Exploring data: describing patterns and departures from patterns; Sampling and Experimentation: planning and conducting a study; Anticipating patterns: exploring random phenomena using probability and simulation; and Statistical Inference: Estimating population parameters and testing hypothesis.

Summer between 9th and 10th Grade

Between 9th and 10th grades, some students may be offered an opportunity to move into Accelerated Analytic Geometry from Algebra 1. To accelerate, students must score a 6 or higher in Algebra 1, complete several units of work independently over the summer, and pass an assessment on this summer work.

Students who continue in the accelerated math sequence after 9th grade must remain in the sequence through high school and finish high school with either AP Statistics or AP Calculus. Therefore, students scoring a 3 or lower in accelerated math in 9th grade will be offered the option to move into the regularly paced math sequence in 10th grade.

10th Grade

Algebra 1

Previous Course: Foundations of Algebra

Next Course: Geometry

Algebra I represents a discrete study of algebra with correlated statistics applications. The fundamental purpose of Algebra I is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, organized into units, deepen and extend understanding of functions by comparing and contrasting linear, quadratic, and exponential phenomena. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

Geometry

Previous Course: Algebra 1

Next Course: Algebra 2

Geometry is the second course in a sequence of three required high school courses designed to ensure career and college readiness. The course represents a discrete study of geometry with correlated statistics applications. The standards in the three-course high school sequence specify the mathematics that all students should study in order to be college and career ready. Additional mathematics content is provided in fourth credit courses and advanced courses including pre-calculus, calculus, advanced statistics, discrete mathematics, and mathematics of finance courses. High school course content standards are listed by conceptual categories including Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. Conceptual categories portray a coherent view of high school mathematics content; a student’s work with functions, for example, crosses a number of traditional course boundaries, potentially up through and including calculus. Standards for Mathematical Practice provide the foundation for instruction and assessment.

Accelerated Geometry B/Algebra 2

Previous Course: Accelerated Algebra 1/Geometry A

Next Course: IB Math SL/Pre-Calculus

The focus of Accelerated Analytic Geometry B/Advanced Algebra is organized into 10 critical areas. The need for extending the set of rational numbers arises and real and complex numbers are introduced so that all quadratic equations can be solved. Quadratic expressions, equations, and functions are developed; comparing their characteristics and behavior to those of linear and exponential relationships from Coordinate Algebra. Circles return with their quadratic algebraic representations on the coordinate plane. The link between probability and data is explored through conditional probability. They apply methods from probability and statistics to draw inferences and conclusions from data. Students expand their repertoire of functions to include polynomial, rational, and radical functions. They expand their study of right triangle trigonometry to model periodic phenomena. And, finally, students bring together all of their experience with functions and geometry to create models and solve contextual problems. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics

AP Statistics

Previous Course: Accelerated Geometry B/Algebra 2

Next Course: Accelerated IB Math SL/Pre-Calculus

IB Math SL/Pre-Calculus

Previous Course: AP Statistics

Next Course: AP Statistics

The IB DP mathematics standard level (SL) 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, rather than insisting on the mathematical rigor required for mathematics HL. Students should, wherever possible, apply the mathematical knowledge they have acquired to solve realistic problems set in an appropriate context.

11th Grade

Geometry

Previous Course: Algebra 1

Next Course: Algebra 2

Algebra 2

Previous Course: Geometry

Next Course: Pre-Calculus OR IB Math Studies OR Pre-Calculus and AP Statistics OR Advanced Mathematical Decision-making

The Advanced Algebra standards taught within this course are the same standards as the GSE Algebra II standards. The Advanced Algebra course may be substituted for the GSE Algebra II course. It is in Advanced Algebra that students pull together and apply the accumulation of learning that they have from their previous courses, with content grouped into six critical areas, organized into units. They apply methods from probability and statistics to draw inferences and conclusions from data. Students expand their repertoire of functions to include polynomial, rational, and radical functions. They expand their study of right triangle trigonometry to model periodic phenomena. And, finally, students bring together all of their experience with functions and geometry to create models and solve contextual problems. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

IB Math SL/Pre-Calculus

Previous Course: Accelerated Geometry B/Algebra 2 or AP Statistics

Next Course: AP Statistics (12th grade only), AP Calculus AB, AP Calculus BC

AP Calculus AB

Previous Course: IB Math SL/Pre-Calculus

Placement Criteria: 4 or higher in IB Math SL/Pre-Calculus

This is the entire AP Calculus AB course! Students need to have already had four years of high school math including algebra, geometry, trig and a fourth year of study including advanced topics of the aforementioned along with functions. This course is primarily concerned with developing the student's understanding of the concepts of calculus and providing experience with its methods and applications. Three major areas will be studied in depth: limits, derivatives and integrals. Upon completion of this course, students will have everything they need to sit for the AP Exam.

AP Calculus BC

Previous Course: IB Math SL/Pre-Calculus

Placement Criteria: 6 or higher in IB Math SL/Pre-Calculus

Broad concepts and widely applicable methods are emphasized. The focus of the courses is neither manipulation nor memorization of an extensive taxonomy of functions, curves, theorems, or problem types. Thus, although facility with manipulation and computational competence are important outcomes, they are not the core of these courses. Technology should be used regularly by students and teachers to reinforce the relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results.Through the use of the unifying themes of derivatives, integrals, limits,approximation, and applications and modeling, the course becomes a cohesive whole rather than a collection of unrelated topics. These themes are developed using all the functions listed in the prerequisites.

12th Grade

Algebra 2

Previous Course: Geometry

Advanced Mathematical Decision-Making (AMDM)

Previous Course: Algebra 2

Placement Criteria: Students are placed in AMDM based on teacher recommendation and grades in Advanced Algebra. The primary goal of AMDM is to prepare students for life beyond high school by developing and applying real-world math skills.

This is a course designed to follow the completion of Algebra II, Advanced Algebra, Accelerated Geometry B/Algebra II or Accelerated Analytic Geometry B/Advanced Algebra. The course will give students further experiences with statistical information and summaries, methods of designing and conducting statistical studies, an opportunity to analyze various voting processes, modeling of data, basic financial decisions, and use network models for making informed decisions.

Pre-Calculus

Previous Course: Algebra 2

Pre-Calculus focuses on standards to prepare students for a more intense study of mathematics. The critical areas organized in seven units delve deeper into content from previous courses. The study of circles and parabolas is extended to include other conics such as ellipses and hyperbolas. Trigonometric functions are further developed to include inverses, general triangles and identities. Matrices provide an organizational structure in which to represent and solve complex problems. Students expand the concepts of complex numbers and the coordinate plane to represent and operate upon vectors. Probability rounds out the course using counting methods, including their use in making and evaluating decisions. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

AP Statistics/IB Math Studies

Previous Course: IB Math SL/Pre-Calculus, Algebra 2

Placement Criteria: 3 or higher in IB Math SL/Pre-Calculus, 5 or higher in Algebra 2

AP Calculus AB

Previous Course: IB Math SL/Pre-Calculus

Placement Criteria: 4 or higher in IB Math SL/Pre-Calculus

AP Calculus BC

Previous Course: Accelerated IB Math SL/Pre-Calculus

Placement Criteria: 4 or higher in Accelerated IB Math SL/Pre-Calculus or 6 or higher in IB Math SL/Pre-Calculus

IB Math Studies

Previous Course: Algebra 2 or IB Math SL/Pre-Calculus

Placement Criteria: 4 or higher in Advanced Algebra or 3 or higher in IB Math SL/Pre-Calculus. This course is a requirement for students in the IB Diploma or IB Career Programs who will not take AP Statistics or AP Calculus.

The IB DP mathematical studies standard level (SL) course focuses on important interconnected mathematical topics. The syllabus focuses on: placing more emphasis on student understanding of fundamental concepts than on symbolic manipulation and complex manipulative skills; giving greater emphasis to developing students’ mathematical reasoning rather than performing routine operations; solving mathematical problems embedded in a wide range of contexts; using the calculator effectively. There is an emphasis on applications of mathematics and statistical techniques. It is designed to offer students with varied mathematical backgrounds and abilities the opportunity to learn important concepts and techniques and to gain an understanding of a wide variety of mathematical topics, preparing them to solve problems in a variety of settings, develop more sophisticated mathematical reasoning and enhance their critical thinking.

Dual Enrollment Math Course

Previous Course: AP Calculus

Seniors who have completed the DHS Math curriculum with terminates at AP Calculus and still need to earn a fourth math credit will do so through Dual Enrollment. See the instructions for Dual Enrollment HERE.