ALGEBRA 1

Students identify and use the arithmetic properties of subsets of integers, rational , irrational, and real numbers, and this includes closure properties for the four basic arithmetic operations where applicable. 

Skills: 

1.1 Students use properties of numbers to demonstrate that assertions are true or false 

Students understand and use operations such as taking the opposite, reciprocal, raising to a power, and taking a root, and this includes the understanding and use of the rules of exponents 

Students solve equations and inequalities involving absolute value

Students simplify expressions prior to solving linear equations and inequalities in one variable, such as 3(2x - 5) + 4(x - 2) = 12. 

Students solve multi-step problems, including word problems involving linear equations and linear inequalities in one variable, with justification. 

Students graph a linear equation and compute the x- and y-intercepts, and they are also able to sketch the region defined by a linear inequality .

Students verify that a point on a line, given an equation of the line, and they are able to derive linear equations using the point-slope formula. 

Students understand the concepts of parallel and perpendicular lines and how their slopes are related, and they are able to find the equation of a line perpendicular to a given line that passes through a given point. 

Students solve a system of two linear equations in two variables, algebraically, and are able to interpret the answer graphically, and they are able to use this to solve a system of two linear inequalities in two variables, and to sketch the solution sets. 

Students add, subtract, multiply and divide monomials and polynomials, and they solve multi-step problems, including word problems, using these techniques.

Students apply basic factoring techniques to second and simple third degree polynomials, and these techniques include finding a common factor to all of the terms in a polynomial and recognizing the difference of two squares, and recognizing perfect.

Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing to lowest terms. 

Students add, subtract, multiply, and divide rational expressions and functions, and they solve both computationally and conceptually challenging problems using these techniques. 

Students solve a quadratic equation by factoring or completing the square. 

Students apply algebraic techniques to rate problems, work problems, and percent mixture problems.

Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about relations and functions. 

Students determine the domain of independent variables, and range of dependent variables defined by a graph, a set of ordered pairs, or symbolic expression.

Students determine whether a relation defined by a graph, a set of ordered pairs, or symbolic expression is a function and justify the conclusion. 

Students know the quadratic formula and are familiar with its proof by completing the square. 

Students use the quadratic formula to find the roots of a second degree polynomial and to solve quadratic equations. 

Students graph quadratic functions and know that their roots are the x-intercepts. 

Students use the quadratic formula and/or factoring techniques to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.

Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity. 

Students use the know simple aspects of a logical argument. 

Skills: 

24.1 Students explain the difference between inductive and deductive reasoning; and identify and provide examples of each. 

24.2 Students identify the hypothesis and conclusion in logical deduction.

24.3 Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.

Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements. 

Skills: 

25.1 Students use properties of numbers to construct simple valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions. 

25.2 Students judge the validity of an argument based on whether the properties of the real number system and order of operations have been applied correctly at each step. 

25.3 Given a specific algebraic statement involving linear, quadratic or absolute value expressions, equations or inequalities, students determine if the statement is true sometimes, always, or never.