MATHEMATICS. ALGEBRA I: two semesters, two credits

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1 MATHEMATICS The mathematics curriculum is very broad and flexible. The program that is right for each student depends on his/her interests, abilities, and future educational/vocational plans. MATHEMATICS LAB: Grades 10-12; one semester, one credit; requires teacher recommendation and guidance approval Mathematics Lab provides students with individualized instruction designed to support success in completing mathematics coursework aligned with Indiana s Academic Standards for Mathematics. It is recommended that Mathematics Lab is taken in conjunction with a Core 40 mathematics course, usually geometry or algebra 2. This course counts as an Elective for the General, Core 40, Core 40 with Academic Honors and Core 40 with Technical Honors diplomas ALGEBRA I: two semesters, two credits Algebra I formalizes and extends the mathematics students learned in the middle grades. The following essential learnings are the focus of the Algebra 1 course: 1.) I can add, subtract, multiply and divide polynomials. AI.RNE.7: Understand polynomials are closed under the operations of addition, subtraction, and multiplication with integers; add, subtract, and multiply polynomials and divide polynomials by monomials. 2.) I can solve a linear equation/inequality in one variable. AI.L.1: Understand that the steps taken when solving linear equations create new equations that have the same solution as the original. Solve fluently linear equations and inequalities in one variable with integers, fractions, and decimals as coefficients. Explain and justify each step in solving an equation, starting from the assumption that the original equation has a solution. Justify the choice of a solution method. 3.) I can analyze and translate two variable linear functions using verbal, graphical, numerical and analytical models. AI.L.5: Represent real-world problems that can be modeled with a linear function using equations, graphs, and tables; translate fluently among these representations, and interpret the slope and intercepts. AI.L.4: Represent linear functions as graphs from equations (with and without technology), equations from graphs, and equations from tables and other given information (e.g., from a given point on a line and the slope of the line). 4.) I can solve a system of equations and apply my understanding to solve real world representations. AI.SEI.2: Understand that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. Solve pairs of linear equations in two variables using substitution and elimination.

2 AI.SEI.3: Write a system of two linear equations in two variables that represents a realworld problem and solve the problem with and without technology. Interpret the solution and determine whether the solution is reasonable. 5.) I can factor a polynomial. AI.RNE.6: Factor common terms from polynomials and factor polynomials completely. Factor the difference of two squares, perfect square trinomials, and other quadratic expressions. 6.) I can analyze and translate two variable quadratic functions using graphical, numerical and analytical models. AI.QE.4: Solve quadratic equations in one variable by inspection (e.g., for x^2 = 49), finding square roots, using the quadratic formula, and factoring, as appropriate to the initial form of the equation. AI.QE.7: Describe the relationships among the solutions of a quadratic equation, the zeros of the function, the x-intercepts of the graph, and the factors of the expression. 7.) I can analyze a function and determine if it is linear, exponential, or neither. AI.QE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. Understand that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. Compare linear functions and exponential functions that model real-world situations using tables, graphs, and equations. ALGEBRA I Enrichment: Grade 9-10; concurrent enrollment in algebra; one or two semesters, one or two credits; requires teacher recommendation; can count as a mathematics course for the General Diploma only or as an elective for the Core 40, Academic Honors, and Technical Honors Diplomas Algebra Enrichment will become a true support class for Algebra 1 and as such will be offered during the same academic year as Algebra 1. Algebra Enrichment combines standards from high school courses with foundational standards from the middle grades. The course will provide time to build the foundations necessary for high school math courses, while enriching the topics taught in Algebra 1. Since Algebra Enrichment is designed as a support course for Algebra 1, a student taking Algebra Enrichment must also be enrolled in Algebra 1 during the same academic year. ALGEBRA I HONORS*: two semesters, two credits Recommended prerequisite: B+ or higher in pre-algebra during 8 th grade The essential learnings listed in Algebra 1 are covered in this course, but Algebra I Honors provides a more rigorous and in-depth approach for a formal development of the algebraic skills and concepts necessary for students who will take other advanced courses. In particular, the instructional program in this course provides for the use of algebraic skills in a wide range of problem-solving situations. ALGEBRA II: two semesters, two credits Prerequisite: successful completion of both semesters of Algebra I

3 1) I understand systems of equations. 2) I understand the concept of a function. 3) I understand quadratic functions. 4) I understand polynomial functions. 5) I understand radicals and inverse functions. 6) I understand exponential and logarithmic functions. 7) I understand rational functions. 8) I understand sequences and series. 9) I understand counting techniques and probability. 10) I understand radian measure and the unit circle. ALGEBRA II HONORS*: two semesters, two credits; Prerequisite: C or better in Algebra I Honors and Geometry Honors or A in regular algebra and geometry without retesting Algebra 2 Honors covers the same ELs as regular algebra 2, but more application of skills are required. Algebra 2 honors is recommended for students planning on Calculus AP in the future. 1) I understand systems of equations. 2) I understand the concept of a function. 3) I understand quadratic functions. 4) I understand polynomial functions. 5) I understand radicals and inverse functions. 6) I understand exponential and logarithmic functions. 7) I understand rational functions. 8) I understand sequences and series. 9) I understand counting techniques and probability. 10) I understand radian measure and the unit circle. GEOMETRY: two semesters, two credits; prerequisite - Algebra I Geometry provides students with experiences that deepen the understanding of two- and threedimensional objects and their properties. The essential learning covered in this course are: Unit 1: Segments, lines, rays, parallel and perpendicular 1. (Q1) I can find the distance and midpoint in a variety of situations. I can state and apply the relationship between distance and congruence. Unit 2: Angles, angle pairs 2. (Q1) I can identify complementary, supplementary and vertical angle pairs and solve problems involving the relationship between their measures. Unit 3: Parallel lines and transversals, angle pairs

4 3. (Q1) I can identify alternate interior, alternate exterior, corresponding and consecutive interior angle pairs. I can solve problems involving the relationship between angles created by two parallel lines cut by a transversal. Unit 4: Introduction to Triangles 4. (Q1)I can solve problems involving the sum of the interior angles of a triangle, properties of isosceles triangles, Triangle Inequality Theorem, Exterior Angle Theorem, Hinge Theorem, and angle-side relationships within triangles. Unit 5: Logic 5. (Q2) I can state, use, and examine the validity of the converse, inverse, and contrapositive of conditional ( if then ) and bi-conditional ( if and only if ) statements. Unit 6: Congruent Triangles 6. (Q2) I can write geometric and algebraic two-column direct proofs including proofs of triangle congruence by SAS, SSS, AAS, and ASA. Unit 7: Similar Polygons 7. (Q2) I can prove triangles are similar by SAS, AA and SSS. I can use the properties of similar figures to find missing sides and angles in similar polygons. Unit 8 Quadrilaterals 8. (Q3) I can identify and apply properties of a parallelogram, rhombus, rectangle, trapezoid, and square. Unit 9 Right Triangles 9. (Q3) I can use geometric means with altitudes in right triangles to find missing pieces. 10. (Q3) I can state and use the Pythagorean Theorem to solve problems involving right triangles. 11. (Q3) I can use sine, cosine and tangent to find missing sides and angles in right triangles. 12. (Q3) I can use special right triangle relationships to find the missing sides of 45, 45, 90 and 30, 60, 90 triangles. Unit 10 Transformations 13. (Q3) I can apply transformations to basic geometric figures including reflection, rotation, translation and dilation. Unit 11 Surface Area and Volume 14. (Q4) I can find the area of geometric shapes including a square, rectangle, triangle, trapezoid, rhombus, kite, circle, sector and composite figures. 15. (Q4) I can find the surface area and volume of prisms, cylinders, pyramids, cones and spheres.

5 Unit 12 Circles 16. (Q4) I can solve problems involving circles that include radius, diameter, and circumference. 17. (Q4) I can find measures of central angles, inscribed angles and circumscribed angles and their arcs. 18. (Q4) I can define a chord, secant and tangent of a circle. GEOMETRY HONORS*: two semesters, two credits Prerequisite: C or better in Algebra I Honors or A in regular algebra without retesting The essential learnings listed in Geometry are covered in this course, but Geometry Honors offers a more rigorous and in-depth approach to provide students with experiences that deepen the understanding of two-and three-dimensional objects and their properties. Deductive and inductive reasoning as well as investigative strategies in drawing conclusions are stressed. Additional topics in the Geometry Honors course include proofs, special segments in triangles, and additional characteristics of circles. Following Algebra I, Algebra II, and Geometry, students who do not choose to take Pre- Calculus, Pre-Calculus Honors, or AP Statistics, may take one semester of Finite Mathematics plus one semester of Probability and Statistics to meet the fourth-year mathematics requirement for the Academic Honors Diploma. FINITE MATHEMATICS: Grades 11-12; one semester, one credit Prerequisite - Algebra 2 or Algebra 2 Honors. A C or better in Algebra II is strongly encouraged. Finite Mathematics is an umbrella of mathematical topics. It is a course designed for students who will undertake higher-level mathematics in college that may not include calculus. Some of the college-preparatory mathematics topics included are counting techniques, matrices, and recursion. PROBABILITY AND STATISTICS: Grades 11-12; one semester, one credit Prerequisite - Algebra 2 or Algebra 2 Honors.. A C or better in Algebra II is strongly encouraged. Probability and Statistics includes the concepts and skills needed to apply statistical techniques in the decision- making process. Topics include: (1) descriptive statistics; (2) probability; and (3) statistical inference. Practical examples based on real experimental data are used throughout. Students plan and conduct experiments or surveys and analyze the resulting data. The use of graphing calculators and computer programs is employed. PRE-CALCULUS/TRIGONOMETRY: two semesters, two credits Prerequisite: C or better in Algebra II and Geometry without retesting

6 Pre-calculus/Trigonometry blends together all of the concepts and skills that must be mastered prior to enrollment in a college-level calculus course. This course is designed to fulfill the fourth year of mathematics credit required by many four- year colleges. The course includes the study of relations and functions, exponential and logarithmic functions, trigonometry in triangles, trigonometric identities and equations, polar coordinates and complex numbers, and data analysis. PRE-CALCULUS/TRIGONOMETRY HONORS*: two semesters, two credits; Prerequisite : C or better in Algebra II Honors or A in regular Geometry and regular Algebra II without retesting Pre-Calculus/Trigonometry Honors is a rigorous course that blends together all of the concepts and skills that must be mastered prior to enrollment in a college level calculus course. In addition, it is a prerequisite for Calculus AP. The course includes the study of relations and functions, exponential and logarithmic functions, trigonometry in triangles, trigonometric functions, trigonometric identities and equations, polar coordinates, vectors, conic sections, complex numbers and matrices. STATISTICS, ADVANCED PLACEMENT: two semesters, two credits; AP Statistics is a two semester elective course designed for two types of students. 1. Any honors track mathematics students who has successfully completed Algebra I Honors. An honors track mathematics students will be encouraged to take this course in conjunctions with Algebra II Honors, Geometry Honors, Pre-calculus honors, or AP Calculus. 2. Any college bound regular track mathematics student who has completed Algebra I, Geometry, and Algebra II. Students do not have to be top rate mathematicians because the course does not depend heavily on mathematics. Rather, students are asked to explore and explain concepts with the help of hands-on investigation while technology lowers the drudgery of computation. Students do not have to memorize formulas and they use a graphing calculator almost every day. Students will be strongly encouraged to take the Statistics AP Exam at the end of the course. Components of the course include the use of technology, projects, laboratories, cooperative group problem solving, and writing as a part of the concept-oriented instruction and assessment. The topics for AP Statistics are divided into five major themes: exploratory data analysis, planning and conducting a study, probability, anticipating patterns, and statistical inference. CALCULUS AB, ADVANCED PLACEMENT *: two semesters, two credits Prerequisite -Pre-Calculus Honors Calculus AB, Advanced Placement is a course based on content established by the College Board. Calculus AB is primarily concerned with developing the students understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations also are important. Topics include: (1) functions, graphs, and limits; (2)

7 CALCULUS BC, ADVANCED PLACEMENT: Grade 12; two semesters, two credits: recommended prerequisite - AP Calculus AB AP Calculus BC is a course based on content established by the College Board. AP Calculus BC is primarily concerned with developing the student s understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations also are important. Topics include: (1) functions, graphs, and limits; (2) derivatives; (3) integrals; and (4) polynomial approximations and series. 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. A comprehensive description of this course can be found on the College Board AP Central Course Description web page at: derivatives; and (3) integrals. 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. A comprehensive description of this course can be found on the College Board AP Central Course Description web page at

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