Topics and Objectives
1. Unit 1 - Algebra Basics
— Know the real number system and under that every number has a decimal expansion
— Organize the real number system in a graphic organizer and determine whether it is closed under various operations
— Recognize the Properties of Equality and how it is applied in solving basic arithmetic
— Evaluate expressions as well as simplify expressions by collecting like terms and using distributive property
— Translate expressions, equations, and inequalities
— Solving one-variable equations using the one-step or two-step method
2. Unit 2 - Multi-Step Equations & Inequalities
— Solve for one-variable equations and inequalities by using multi-step method
— Recognize special equations such as no solution and infinite solutions
— Solve algebraic proportion, absolute value, and multi-variable equations and inequalities as well as graphing inequalities on a number line
3. Unit 3 - Relations & Functions
— Know the various terms of a functions and understand that a function is when one input only contains one output
— Recognize the domain, range, and function values on a graph, table, and list of ordered pairs
— Evaluate function notations when given the domain to find the range or when given the range to find the domain and using a graph, table or list of ordered pairs
— Recognize an arithmetic sequence and remembering the formula for arithmetic sequence to find the nth term
4. Unit 4 - Linear Equations
— Graph proportional relationships, interpreting the unit rate as the slope of the graph
— Derive the equation y=mx versus the equation y=mx+b
— Construct a function to model a linear relationship between two quantities
— Determine the rate of change and initial value of the function from a description of a relationship or from two ordered pair values, including reading these from a table of from a
graph
— Determine whether two lines are parallel or perpendicular to each other by identifying the slopes and solving whether they are the same or the negative reciprocal of each
other
5. Unit 5 - System of Equations
— Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously
— Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations
— Solve simple cases by inspection
— Solve real-world and mathematical problems leading to two linear equations in two variables
6. Unit 6 - Exponent Rules
— Remember the Properties of Exponents to simplify monomials with common bases
— Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used
— Compare the values of scientific notation and choose units of appropriate size for measurements of very large or very small quantities
— Recognize a geometric sequence and remembering the formula for geometric sequence to find the nth term
— Calculate the exponential growth or decay of a real-world math problem by connecting the formula of the geometry sequence to daily application
— Simplify radicals of monomials
7. Unit 7 - Polynomials & Factoring
— Classify and use math operations to simplify polynomials
— Introduce the FOIL/double distribute method when multiplying binomial with binomials and binomials with trinomials
— Factor polynomials through greatest common factor, differences of squares, trinomials with and with a, and grouping
— Show how factoring polynomials is the opposite of distributing or simplifying a polynomial
— Divide polynomials by binomials by using factoring to simplify the division problem
8. Unit 8 - Quadratic Equations
— Introduce the proper terms of a quadratic function when presented as a graph or in the standard form equation
— Graph quadratic equations and inequalities on a coordinate plane
— Solve quadratics by factoring and remember the quadratic formula when the none of the factoring methods can be used to simplify the function
— Solve real-world math problems that relate to projectile objects in motion
— Compare linear and quadratic models
9. Unit 9 - Rational Expressions & Equations
— Simplify, multiply, divide, add and subtract rational expressions
— Simplify rational expressions when applied in a real-world application
— Solve for one-variable of a rational equation
10. Unit 10 - Radical Expressions & Equations
— Simplify radicals of square and cube root values by recognizing the perfect squares and cubes that will best simplify each value
— Add, subtract, multiply, and divide radicals
— Divide radicals of binomials by recognizing the conjugate of the denominator and multiplying it to the entire fraction
— Solve radical equations include extraneous solutions and those resulting in a quadratic equation