Math

Course: Math Foundations

Description:  Students taking this course will receive instruction to prepare them to be successful in the pre-algebra course.  Teaching will focus on the number system, expressions and equations, beginning functions, and statistics and probability.  They will convert between fractions and decimals, compare units of measure and use similarity to solve problems, compute the perimeter, area, and volume of irregular geometric objects, identify relationships among variable within a data set and use probability to make predictions about the events, and make decisions about how to solve problems and communicate their ideas.

Standards

Quarter One Competency Measures:

  • Student represents real numbers as points on a number line and distinguishes rational numbers from irrational numbers.
  • Student defines a rational number as a point on the number line that can be expressed as the ratio of two integers and a point that cannot be so expressed as irrational.
  • Student classifies numbers as rational or irrational, knowing that rational numbers can be expressed as terminating or repeating decimals and irrational numbers can be expressed as non-terminating or non-repeating decimals.
  • Student computes fluently and makes reasonable estimates with rational and irrational numbers.
  • Student evaluates and simplifies numerical expressions containing rational numbers using the order of operations.
  • Student solves single variable linear equations.
  • Student solves equations for a specified variable.

Quarter Two Competency Measures:

  • Student knows that numbers that are not rational are called irrational; understands informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
  • Student solves linear equations in one variable; gives examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions; shows which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x=a, a=a, or a=b results (where a and b are different numbers).
  • Student uses proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
  • Student creates equations and inequalities in one variable and use them to solve problems.  Includes equations arising from linear and quadratic functions, and simple rational and exponential functions.

Quarter Three Competency Measures:

  • Student reasons quantitatively and uses units to solve problems.
  • Student interprets the structure of expressions.
  • Student writes expressions in equivalent forms to solve problems.
  • Student creates equations that describe numbers or relationships.
  • Student understands solving equations as a process of reasoning and explains the reasoning.
  • Student solves equations and inequalities in one variable
  • Student understands the concept of a function and uses function notation.
  • Student interprets functions that arise in applications in terms of context.
  • Student analyzes functions using different representations.
  • Student understands that a function is a rule that assigns to each input exactly one output.
  • Student interprets the equation  y=mx+b as defining a linear function whose graph is a straight line.

Quarter Four Competency Measures:

  • Student knows and applies the properties of integer exponents to generate equivalent numerical expressions.
  • Student performs operations with scientific notations including problems where both decimal and scientific notation are used.
  • Student uses square roots to represent solutions.

Course: Pre-Algebra

Description:  The goal of Pre-Algebra is to develop fluency with rational numbers and proportional relationships. Students will extend their elementary skills and begin to learn algebra concepts that serve as a transition into formal Algebra and Geometry. Students will learn to think flexibly about relationships among fractions, decimals, and percents. Students will learn to recognize and generate equivalent expressions and solve single-variable equations and inequalities. Students will investigate and explore mathematical ideas and develop multiple strategies for analyzing complex situations. Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life’s experiences.

Standards

Quarter One Competency Measures:

  • Computes fluently with understanding and makes reasonable estimates with rational numbers.
  • Analyzes relationships among rational numbers, including negative rational numbers, and operations involving these numbers.
  • Solves problems involving rational numbers using addition, subtraction, multiplication, and division.
  • Models and illustrates meanings of ratios, percents, and decimals.
  • Solves a wide variety of problems using ratios and proportional reasoning.
  • Generalizes and expresses patterns using algebraic expressions.
  • Evaluates, simplifies, and solves algebraic expressions, equations, and inequalities.
  • Represents relationships using graphs, tables, and other models.
  • Calculates probabilities of events and compares theoretical and experimental probability.

Quarter Two Competency Measures:

  • Computes fluently with understanding and makes reasonable estimates with rational numbers.
  • Understands operations involving fractions (simplifying, multiplying, dividing, changing to decimals, etc).
  • Solves problems involving numbers with negative exponents and scientific notation.
  • Adds, subtracts, multiplies, and divides with monomials.
  • Models and illustrates meanings of ratios, proportions, and percents, including solving percent equations.
  • Solves real-world problems using ratios and proportional reasoning.
  • Generalizes and expresses patterns using algebraic expressions.
  • Simplifies expressions and/or solves equations with rational numbers, ratios and percents.
  • Represents relationships using graphs, tables, and other models.

Quarter Three Competency Measures:

  • Computes fluently with understanding and makes reasonable estimates with rational numbers.
  • Analyzes relationships among rational numbers, including negative rational numbers, and operations involving these numbers.
  • Solves problems involving rational numbers using addition, subtraction, multiplication and division.
  • Evaluates, simplifies and solves algebraic expressions, equations and inequalities.
  • Represents relationships using graphs, tables and other models.

Quarter Four Competency Measures:

  • Student solves problems involving rational numbers using addition, subtraction, multiplication and division.
  • Student generalizes and expresses patterns using algebraic expressions.
  • Student evaluates, simplifies and solves algebraic expressions, equations and inequalities.
  • Student represents relationships using graphs, tables and other models.
  • Student derives formulas for surface areas of three-dimensional figures.

Course: Elementary Algebra

Description:  The main goal of Algebra is to develop fluency in working with linear equations. Students will extend their experiences with tables, graphs, and equations and solve linear equations and inequalities and systems of linear equations and inequalities. Students will extend their knowledge of the number system to include irrational numbers. Students will generate equivalent expressions and use formulas. Students will simplify polynomials and begin to study quadratic relationships. Students will use technology and models to investigate and explore mathematical ideas and relationships and develop multiple strategies for analyzing complex situations. Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life’s experiences.

 Standards

Quarter One Competency Measures:

  • Student extends the properties of exponents to rational exponents.
  • Student uses properties of rational and irrational numbers.
  • Student performs arithmetic operations with complex numbers.
  • Student represents complex numbers and their operations on the complex plane.
  • Student uses complex numbers in polynomial identities and equations.
  • Student writes expressions in equivalent forms to solve problems.
  • Student performs arithmetic operations on polynomials.
  • Student understands the relationship between zeros and factors of polynomials.
  • Student understands solving equations as a process of reasoning and explains the reasoning.

Quarter Two Competency Measures:

  • Student uses units as a way to understand problems and to guide the solution of multi-step problems; chooses and interprets units consistently in formulas; chooses and interprets the scale and the origin in graphs and data displays.
  • Student understands that numbers that are not rational are called irrational; understands informally that every number has a decimal expansion; for rational numbers shows that the decimal expansion repeats eventually, and converts a decimal expansion which repeats eventually into a rational number.
  • Student creates equations and inequalities in one variable and uses them to solve problems. Includes equations arising from linear and quadratic functions, and simple rational and exponential functions.
  • Student constructs a function to model a linear relationship between two quantities; determines the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph; interprets the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
  • Student graphs functions expressed symbolically and shows key features of the graph, by hand in simple cases and using technology for more complicated cases.
  • Student graphs linear and quadratic functions and shows intercepts, maxima and minima.
  • Student summarizes, represents, and interprets data on a single count or measurement variable.
  • Student summarizes, represents, and interprets data on two categorical and quantitative variables.
  • Student makes inferences and justifies conclusions from sample surveys, experiments and observational studies.

Quarter Three Competency Measures:

  • Student reasons quantitatively and uses units to solve problems.
  • Student interprets the structure of expressions.
  • Student writes expressions in equivalent forms to solve problems.
  • Student creates equations that describe numbers or relationships.
  • Student understands solving equations as a process of reasoning and explains the reasoning.
  • Student solves equations and inequalities in one variable
  • Student understands the concept of a function and uses function notation.
  • Student interprets functions that arise in applications in terms of context.
  • Student analyzes functions using different representations.
  • Student understands that a function is a rule that assigns to each input exactly one output.
  • Student interprets the equation  y=mx+b as defining a linear function whose graph is a straight line.

Quarter Four Competency Measures:

  • Student extends the properties of exponents to rational exponents.
  • Student uses properties of rational and irrational numbers.
  • Student performs arithmetic operations with complex numbers.
  • Student represents complex numbers and their operations on the complex plane.
  • Student uses complex numbers in polynomial identities and equations.
  • Student writes expressions in equivalent forms to solve problems.
  • Student performs arithmetic operations on polynomials.
  • Student understands the relationship between zeros and factors of polynomials.
  • Student understands solving equations as a process of reasoning and explains the reasoning.

Course: Geometry

Description:  The main goal of Geometry is for students to develop a Euclidean geometric structure and apply the resulting theorems and formulas to address meaningful problems. Students will use experimentation and inductive reasoning to construct geometric concepts, discover geometric relationships, and formulate conjectures. Students will employ deductive logic to prove theorems and justify conclusions. Students will extend their pre-existing experiences with algebra and geometry to trigonometry, coordinate geometry, and probability. Students will use dynamic geometry software, compass and straightedge, and other tools to investigate and explore mathematical ideas and relationships and develop multiple strategies for analyzing complex situations. Students will apply mathematical skills and make meaningful connections to life’s experiences.

Standards

Quarter One Competency Measures:

  • Student uses inductive and deductive reasoning to develop mathematical arguments.
  • Student analyzes characteristics and properties of lines and angles.
  • Student performs basic geometric constructions, describing and justifying the procedures used.
  • Student describes the properties and attributes of lines and line segments using coordinate geometry.
  • Student finds measurements of plane and solid figures.
  • Student solves real-world problems using visualization and spatial reasoning.

Quarter Two Competency Measures:

  • Student proves congruency and similarity of geometric figures.
  • Student investigates geometric relationships using constructions, copies and bisects angels and segments, constructs perpendicular and parallel lines.
  • Student identifies medians, altitudes and angle bisectors of a triangle.
  • Student proves congruency and similarity of geometric figures.
  • Student classifies angle pairs formed by two lines and a transversal.
  • Student proves lines parallel or perpendicular using angle relationships.
  • Student classifies triangles by sides and angles.
  • Student identifies and determines relationships in adjacent, complementary, supplementary or vertical angles and linear pairs.
  • Student writes an equation of a line perpendicular or a line parallel to a line through a given point.
  • Student writes the equation for a line in standard form.

Quarter Three Competency Measures:

  • Student understands congruence in terms of rigid motions.
  • Student proves geometric theorems.
  • Student makes geometric constructions.
  • Student understands similarity in terms of similarity transformations.
  • Student uses coordinates to prove simple geometric theorems algebraically.
  • Student visualizes relationships between two-dimensional and three-dimensional objects.

Quarter Four Competency Measures:

  • Student analyzes characteristics and properties of triangles.
  • Student analyzes characteristics and properties of polygons.
  • Student performs basic geometric constructions, describing and justifying the procedures used.
  • Student uses triangle relationships to solve problems.

Course: Algebra II

Description:  The focus of Mathematics II is on quadratic expressions, equations, and functions; comparing their characteristics and behavior to those of linear and exponential relationships from Mathematics I as organized into 6 critical areas, or units. 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. The link between probability and data is explored through conditional probability and counting methods, including their use in making and evaluating decisions. The study of similarity leads to an understanding of right triangle trigonometry and connects to quadratics through Pythagorean relationships. Circles, with their quadratic algebraic representations, round out the course. 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.

Standards

Quarter One Competency Measures:

  • Student demonstrates understanding of Algebra 1 concepts of proportion and linear relationships (slope of a line and algebraic equations, expressions, and graphs).
  • Student demonstrates understanding of Algebra 1 concepts of algebraic reasoning (linear equations, inequalities, and algebraic equations, expressions, and graphs).
  • Student evaluates, analyzes, and solves mathematical situations using algebraic properties and symbols.
  • Student solves absolute values and compound inequalities of a single variable.
  • Student solves systems of equations and inequalities.
  • Student represents mathematical situations by determining when a relation is a function.
  • Student represents mathematical situations by determining the domain and range of relations.

Quarter Two Competency Measures:

  • Student simplifies algebraic expressions including those having integer exponents.
  • Student simplifies algebraic expressions, including those having integer exponents.
  • Student adds, subtracts, multiplies and divides simple rational expressions.
  • Student writes algebraic equations to generalize relations.
  • Student solves multi-step equations algebraically.

Quarter Three Competency Measures:

  • Student solves radical equations of a single variable, including those with extraneous roots.
  • Student solves absolute value and compound inequalities of a single variable.
  • Student adds, subtracts, multiplies and divides rational expressions and solves rational equations.
  • Student simplifies algebraic expressions involving negative and rational exponents.
  • Student simplifies numerical expressions, including those with rational exponents.
  • Student simplifies expressions involving complex numbers and expresses them in standard form, a + bi.
  • Approximate the real solutions of quadratic equations graphically.

Quarter Four Competency Measures:

  • Student evaluates, analyzes and solves mathematical situations using algebraic properties and symbols.
  • Student represents and computes fluently with complex numbers.
  • Student models and solves quadratic equations and inequalities.
  • Student defines and graphs exponential functions and uses them to model problems in mathematical and real-world contexts.