Develop a mathematical vocabulary to communicate more effectively.
Use order of operation (associative, commutative, and distributive properties) to simplify math expressions.
Recognize and make connections within mathematics and its application.
Reinforce and understand place value system for whole numbers and decimals.
Develop proficiency with computation and estimation within the set of real numbers.
Develop an understanding of geometric terms and those concepts in problem-solving activities.
Develop measurement skills to in the U.S. and metric systems.
Collect, organize, present, and interpret data using measures of central tendencies and the laws of probability.
Develop an understanding of ratios, proportions and percents.
Graph numbers and ordered pairs using a number line and coordinate plane.
Grade 8
The student will be able to:
Develop and practice effective communication using the language of mathematics
Develop reasoning skills and apply them to problem-solving situations using appropriate technology.
Recognize connections within mathematics and between mathematics and its applications.
Renew proficiency with computation and estimation within the set of real numbers.
Develop an understanding of geometric terms and concepts and apply those concepts in problem-solving activities.
Convert measurement within the U.S. and metric systems.
Collect, organize, present, and interpret data using measures of central tendencies and the laws of probability.
Graph and interpret Cartesian relationships.
Develop an understanding of ratios, proportions, and percents using variables for problem solving.
Develop explorations of algebraic concepts and processes.
Grade 8: Pre-Algebra
The student will be able to:
Develop and practice effective communication using the language of mathematics.
Develop reasoning skills and apply them to algebraic problem-solving situations using appropriate technology.
Recognize connections within mathematics and between mathematics and its applications.
Develop proficiency with computation and algebraic expression.
Develop an understanding of ratios, proportions, and percents using variables form problem solving.
Develop and apply measurement skills to perimeter, area, surface area, and volume.
Solve algebraic expressions and formulas involving rational numbers.
Collect, organize, present, and interpret data using measures of central tendencies and the laws of probability.
Solve one variable equations and inequalities using transformations.
Graph linear equations and inequalities in two variables in the Cartesian plane.
Pre-Algebra - H.S.
The student will be able to:
Perform basic operations of addition, subtraction, multiplication and division using whole numbers, integers, decimals and fractions.
Use the order of operations and associative, commutative and distributive properties to algebraic problems.
Solve one variable equations and inequalities using addition, subtraction, multiplication or division with one or two steps.
Understand and apply problem-solving skills to practical applications.
Recognize, name, and draw basic two-dimensional geometric figures.
Measure and calculate perimeter, circumference, and area of basic two-dimensional geometric figures.
Use statistical measurements to display information in various graphs including bar line, circle graphs, stem and leaf plots, and scattergrams.
Use percents in a variety of applications (banking, discounts, sales and budgets).
Calculate the basic probability of simple events using ratio and proportion (calculators are used once basic skills are covered).
Graph numbers and ordered pairs using a number line and coordinate plane.
Algebra I - Intro I
The student will be able to:
Transform words into symbols to write algebraic expressions.
Use algebra tiles to model and solve simple and complex equations using the transformations of addition, subtraction, multiplication, and division.
Solve simple and complex equations from word problems.
Read, interpret, solve and graph simple inequality problems.
Use current technology (graphing calculators and/or computers) to aid in and reinforce problems-solving skills.
Perform the basic operations within the following sets of numbers: natural, whole, integer and real.
Use the order of operations for simplifying expressions involving the associative, closure, commutative, distributive, identity, inverse, substitution, and equality properties.
Identify and combine similar terms.
Add, subtract, multiply and divide polynomial expressions.
Use general and specific factoring methods for polynomial expressions.
Algebra I - Intro II
The student will be able to:
Combine like terms using properties of positive and negative numbers.
Demonstrate the ability to evaluate expressions and solve simple equations and inequalities by appropriately applying order of operations, transformations by addition, subtraction, multiplication, and division, incorporating modeling with algebra titles.
Compute the value of and simplify expressions involving exponents and square roots.
Solve quadratic equations by factoring, using the quadratic formula, or by completing the square.
Apply factoring and product laws of polynomials.
Plot points, determine slope and X and Y intercepts of functions in order to graph and recognize graphs of algebraic functions and their applications to real-life situations.
Write a linear equation and interpret the meaning of the variables within the equation given the appropriate information.
Add, subtract, and multiply matrices and use them for problem solving.
Solve systems of equations containing two variables using the following methods: substitution, elimination, and graphing on both paper and the graphing calculator.
Employ manipulative and diagrams to translate word problems into mathematical relationships, solve, and be able to interpret results and estimate the reasonableness of the answer.
Algebra I
The student will be able to:
Apply properties of real numbers and order of operations to simplify numerical and algebraic equations.
Apply algebraic transformations in solving linear and quadratic equations and inequalities.
Solve systems of algebraic equations by graphing, substitution, or elimination methods.
Use fractions, ratios, and percents in simplifying expressions and solving equations and inequalities.
Perform addition, subtraction, multiplication, and division with polynomials.
Factor polynomials by using common factors, special products, grouping, and trial/error methods.
Translate word phrases or sentences into algebraic expressions and equations and estimate reasonableness of answers.
Compute the values of and simplify expressions involving exponents and square roots.
Graph and explore linear, quadratic, and absolute value equations both manually and with graphing calculators.
Recognize and do basic work with functions and relations.
Algebra II
The student will be able to:
Use the language of algebra to communicate mathematics through written expression and perform operations with real numbers.
Demonstrate an understanding of relations and functions.
Graph, solve, and use linear equations, inequalities, and systems of linear equations and inequalities incorporating the use of graphing devices to verify results.
Perform operations and solve problems with polynomials and include use of diagrams and tables.
Work with ratios, proportions, and percents and apply direct variations and proportions to solve problems.
Explore, graph, and interpret nonlinear equations on paper and on graphing devices.
Do basic operations with matrices.
Use rational algebraic equations and inequalities.
Solve problems with quadratic equations and inequalities.
Write equations of circles and parabola's and draw their graphs.
Algebra II-Applied
The student will be able to:
Use the properties of integers to combine like terms.
Evaluate expressions and solve equations using order of operations, as well as transformations by addition, subtraction, multiplication, and division.
Solve system of equations by graphing devices and substitution/elimination methods.
Calculate problems involving the properties of exponents and square roots.
Solve quadratic equations by factoring or by using the quadratic formula.
Apply the factoring and product laws of polynomials.
Use the Cartesian coordinate system to plot points, determine the slope, and X and Y intercepts.
Write a linear equation given the appropriate information.
Solve practical applications using problem-solving techniques.
Use graphing calculators to model and reinforce problem-solving techniques.
Geometry-Applied
The student will be able to:
Use basic terms, definitions, and notation to identify lines, segments, angles, perpendiculars, and parallel lines.
Use degrees and rotations to study angles, pairs of angles, and angle bisectors.
Determine the properties of polygons and polyhedrons.
Calculate the perimeter and area for various shapes and the volume of various solids.
Use translations, rotations, and reflections to study congruent figures as well as show the congruence of triangles by SSS, SAS, ASA, AAS, and HL methods.
Use parallel lines to study various types of angles and do constructions.
Apply the properties of quadrilaterals to parallelograms, rectangles, rhombi, squares, and trapezoids.
Apply the properties of equality and inequality to triangles as well as the Pythagorean
Theorem to right triangles.
Use ratios and proportions to study similar triangles and scale drawings.
Use parts of circles to calculate angles and the length of segments.
Use basic trigonometric ratios to find missing parts of the triangle.
Geometry
The student will be able to:
Apply the definitions and special relationships using points, lines, planes, angles, and parallel lines, including the relationship to coordinate geometry involving graphs with slope and use of distance formula.
Write deductive proofs using points, lines, planes, angles, parallel and perpendicular lines, congruent triangles, using SSS, SAS, ASA, AAS, HL, and quadrilaterals.
Identify and compare the properties of parallelograms, rectangles, rhombi, squares, and trapezoids.
Write proofs using the indirect method.
Solve problems using ratios and proportions and apply these to similar triangles and polygons.
Apply the Pythagorean Theorem to right triangles, including the special cases of 45-45 and 30-60 right triangles.
Use a circle and its related parts to solve problems involving radius, diameter, central and inscribed angles, chords, tangents, arcs, secants, and inscribed/circumscribed polygons using postulates and theorems.
Construct congruent segments and angles, parallel and perpendicular lines, special angles, triangles, circles, and proportional segments using a compass and straight edge.
Calculate area and perimeter of triangles, parallelograms, rectangles, squares, trapezoids, circles, hexagons, and polygons, including development of these formulas using postulates, theorems, and proofs.
Calculate volumes and surface area of three-dimensional figures including spheres, cones, cylinders, prisms, pyramids, and rectangular solids.
Pre-Calculus
The student will be able to:
Solve linear equations, quadratic equations, and inequalities using factoring, quadratic formula, and completing the square, as well as higher degree equations using the factor and remainder theorems, including equations with complex solutions.
Relate solutions and graphs to absolute value problems, inequalities, greatest integer, and piece-wise defined functions.
Identify various functions, domains, and ranges including algebraic, trigonometric, logarithmic, and exponential functions, and graph them employing graphing calculators.
Analyze the properties of conic sections.
Define the six trigonometric functions and use them with angles measured in degrees and radians and convert between radians and degrees.
Use the six trigonometric definitions and the Pythagorean relations to prove identities, solve trig equations, and solve right triangles including applications to real-world problems.
Manipulate the graphs of the trigonometric functions by analysis of changes in period, amplitude, phase shifts, and line shifts.
Use the law of Sines, the law of Cosines, and area formulas for oblique triangles.
Solve systems of linear and quadratic equations, including the use of Cramer's Rule.
Calculus
The student will be able to:
Analyze graphs using graphing technology.
Understand the concept of a limit, calculate limits, and estimate limits from graphs.
Identify continuity as a property of functions, understand continuity in terms of limits, and interpret continuity in functions geometrically.
Understanding asymptotic and unbounded behavior and describe asymptotic behavior in terms of the limit.
Understand the concept of a derivative and its application to functions. Define the derivative as the limit of the difference quotient and understand the relationship between differentiability and continuity. Find the derivative at a point, and find the tangent and normal lines to the curve at a point.
Find the derivative of a function. State the relationship between increasing and decreasing behavior of the function and the sign of the derivative. Find the critical points of a function. Apply the Mean Value Theorem.
Find second derivatives and corresponding characteristics of the graphs of f, f', and f''.
Identify the relationship between the concavity of and the sign of f''. Identify points of inflection and concavity changes.
Apply derivatives to optimize finding both local and absolute maxima and minima. Use implicit differentiation to find the derivative of an inverse function. Interpret the derivative as a rate of change.
Demonstrate proficiency in the application of derivatives. Find the derivatives of sums, products, and quotients of functions. Apply the Chain Rule and implicit differentiation.
Use the Fundamental Theorem of Calculus. Understand and apply techniques of anti-differentiation. Find specific antiderivatives using initial conditions. Solve separable differential equations.
Find numerical approximations to definite integrals using Reimann sums, the Trapezoid
Rule, and approximate definite integrals of functions. Find the area between two curves.
Calculus - A.P.
The student will be able to:
Analyze graphs using graphing technology.
Understand the concept of a limit, calculate limits, and estimate limits from graphs.
Identify continuity as a property of functions, understand continuity in terms of limits, and interpret continuity in functions geometrically.
Understanding asymptotic and unbounded behavior and describe asymptotic behavior in terms of the limit.
Understand the concept of a derivative and its application to functions. Define the derivative as the limit of the difference quotient and understand the relationship between differentiability and continuity. Find the derivative at a point, and find the tangent and normal lines to the curve at a point.
Find the derivative of a function. State the relationship between increasing and decreasing behavior of the function and the sign of the derivative. Find the critical points of a function. Apply the Mean Value Theorem.
Find second derivatives and corresponding characteristics of the graphs of f, f', and f''.
Identify the relationship between the concavity of and the sign of f''. Identify points of inflection and concavity changes.
Apply derivatives to optimize finding both local and absolute maxima and minima. Use implicit differentiation to find the derivative of an inverse function. Interpret the derivative as a rate of change.
Demonstrate proficiency in the application of derivatives. Find the derivatives of sums, products, and quotients of functions. Apply the Chain Rule and implicit differentiation.
Use the Fundamental Theorem of Calculus. Understand and apply techniques of anti-differentiation. Find specific anti-derivatives using initial conditions. Solve separable differential equations.
Find numerical approximations to definite integrals using Reimann sums, the Trapezoid Rule, and approximate definite integrals of functions. Find area between two curves and the volume of a solid of revolution.
