Mathematics Courses

The major purpose of this course is to serve as a vehicle by which students will master the four Critical Areas
of Instruction. In grade six, instructional time should focus on four critical areas: (1) connecting ratio, rate,
and percentage to whole number multiplication and division and using concepts of ratio and rate to solve
problems; (2) completing understanding of division of fractions and extending the notion of number to the
system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions
and equations; and (4) developing understanding of statistical thinking. Students also work toward fluency with multi-digit division and multi-digit decimal operations.

In grade seven instructional time should focus on four critical areas: (1) developing understanding of and
applying proportional relationships, including percentages; (2) developing understanding of operations
with rational numbers and working with expressions and linear equations; (3) solving problems involving
scale drawings and informal geometric constructions and working with two- and three-dimensional
shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about
populations based on samples. Students also work towards fluently solving equations of the form px + q =
r and p(x + q) = r.

In grade eight, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence and understanding and applying the Pythagorean Theorem. Students also work towards fluency with solving simple sets of two equations with two unknowns by inspection.

 

Students will understand informally the rational and irrational numbers and use rational numbers approximation of irrational numbers. Students will use rational numbers to determine an unknown side in triangles. They apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons. Students use radicals and integers when they apply the Pythagorean Theorem in real word. Students understand the connections between proportional relationships and linear equations involving bivariate data. Students will analyze and solve linear equations and pairs of simultaneous linear equations. Students use similar triangles to explain why the slope is the same between two distinct points on a non-vertical line in the coordinate plane as well as derive the equation of a line.

 

Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representations may be partial representations), and they describe how aspects of the function are reflected in the different representations. Students use ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems. Students show that the sum of the angles in a triangle is the angle formed by a straight line, and that various configurations of lines give rise to similar triangles because of the angles created when a transversal cuts parallel lines. Students understand the statement of the Pythagorean Theorem and its converse, and can explain why the Pythagorean Theorem holds, for example, by decomposing a square in two different ways. Students complete their work on volume by solving problems involving cones, cylinders, and spheres.

The purpose of Algebra I is for students to use reasoning about structure to define and make sense of rational exponents and explore the algebraic structure of the rational and real number systems. They understand that numbers in real world applications often have units attached to them, that is, they are considered quantities. Students explore the structure of algebraic expressions and polynomials. They see that certain properties must persist when working with expressions that are meant to represent numbers, now written in an abstract form involving variables. When two expressions with overlapping domains are set equal to each other, resulting in an equation, there is an implied solution set (be it empty or nonempty), and students not only refine their techniques for solving equations and finding the solution set, but they can clearly explain the algebraic steps they used to do so.

In Algebra I, students extend this knowledge to working with absolute value equations, linear inequalities, and systems of linear equations. After learning a more precise definition of function in this course, students examine this new idea in the familiar context of linear equations (for example, by seeing the solution of a linear equation as solving 𝑓(𝑥) = 𝑔(𝑥) for two linear functions 𝑓 and 𝑔). Students continue building their understanding of functions beyond linear ones by investigating tables, graphs, and equations that build on previous understandings of numbers and expressions. They make connections between different representations of the same function. They learn to build functions in a modeling context, and solve problems related to the resulting functions. Note that the focus in Algebra I is on linear, simple exponential, and quadratic equations.

 

This course is offered to students who demonstrate a thorough understanding of Pre- algebra concepts. The intent of the course is to develop skill and understanding of the language of algebra, functions, number operations, solving and graphing equations and inequalities involving real-world concepts, ratios, quadratic functions, factoring terms, completing the square, using the quadratic formula, monomial and polynomial expressions, exponents and rational expressions, and problem solving. Through the study and use of Algebra, the learner develops an understanding of the symbolic language of mathematics and the sciences. Algebra 1 develops the skills and concepts to help solve a wide variety of problems.

 

Goals:

A) To help students own and command the language of Algebra;

B) To prepare students for the study of higher mathematics and for those who are college bound, to provide a basic understanding of the symbolic nature of algebra;

C) To focus on the big ideas of Algebra1.

Finally, students extend their prior experiences with data, using more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit.

In this course, students expand understanding of expressions including rewriting, interpreting and examining rational, radical, polynomial expressions and deriving the formula of the sums of finite geometric series. Students continue expanding their knowledge of rational, polynomial, radical, exponential and logarithmic functions; they learn to represent functions algebraically, graphically, in numerical tables and by verbal descriptions. Students expand their knowledge of the real numbers to model/ solve a variety of equations/inequalities and the systems of equations with two or more variables. Students practice creating equations for the real world situations, learn how to solve them, interpret the solutions and explain the reasoning. Students learn about complex numbers and explore real /complex roots of polynomial functions using the Fundamental Theorem of Algebra. Students explore/ apply the Remainder Theorem and the Binomial Theorem with the polynomial expressions and equations. Students explore the relationship between the exponential functions and their inverses, the logarithmic functions.

 

Students explore all conic sections and learn how to express geometric properties with equations. Students extend their trigonometry knowledge: they learn how to interpret the radian measure of angles in the unit circle, graph all six trigonometric functions, model the periodic phenomena of the graphs, and prove/apply trigonometric identities.

 

Finally, students continue expanding their knowledge of statistics by summarizing, representing, and interpreting data using the normal distribution. Moreover, students make inferences and justify conclusions based on sampling, experiments and observational studies.

The standards in this Algebra II course cover the following conceptual categories: Modeling, Functions, Number and Quantity, Algebra, and Statistics and Probability. The standards are developed to help educators implement mathematical practices of reasoning abstractly/ quantitatively, constructing viable arguments, modeling with mathematics, analyzing the structure of algebraic problems and persevering in solving them. This course content provides the rich instructional experiences for students and helps them to succeed beyond the high school and compete in the 21st century job market.

 

Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning

 

 

The essential purpose of this Geometry course is to introduce students to formal geometric proofs and the study of plane figures, with an emphasis on plane Euclidean geometry—both synthetically and analytically. Furthermore, transformations of rigid motion are the foundations of proof for congruency and similarity. Concepts included in this course are geometric transformations, proving geometric theorems, congruence and similarity, analytic geometry, right triangle trigonometry, and probability and statistics. Students are expected to model real world situations and make decisions using these ideas.

 

Course Purpose:
The purpose of this course is to formalize and deepen a students’ understanding of how transformational geometry, trigonometry, probability and statistics can be used to model and interpret the real world. Students will be able to grasp abstract Euclidean proofs, transformational proofs, and apply them to understand real world, geometric relationships—including relationships between two and three dimensional objects. Students will continue to develop mathematical ways of thinking through the Mathematical Practice Standards and content standards. Students will be expected to make sense of real world situations and apply mathematics to develop solutions.