Alignment Report by Resource
California State Learning Standards
Algebra Upgrade On-Line Course
Published by Learning Upgrade LLC
Each Standard is listed, with matching levels (lesson) from the 60 Algebra Upgrade levels listed below.
1.0
Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable:
1.1 Students use properties of numbers to demonstrate whether assertions are true or false.
- Level 8 Numbers: natural, whole, integer, rational, irrational, real
Level 5 Distributive Property: of multiplication
Level 6 Commutative Property: and Associative Property of multiplication & addition
2.0
Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
- Level 3 Exponent Rules: multiply, divide, exponent of an exponent, negative exponent
Level 18 Reciprocal Inverse: find the reciprocal of a number, undefined fractions
Level 55 Radical Expressions: simplify radical expressions, square roots, fractional exponents
3.0
Students solve equations and inequalities involving absolute values.
- 25: Absolute Value Equations: solve equations and inequalities with absolute values
4.0
Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
- Level 12: Solve Equations: solve one equation one variable multiple steps
Level 22: Solve Inequalities: solve inequalities with one variable
Level 39: Distribute Polynomials: distribute polynomials
5.0
Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
- Level 12: Solve Equations: solve one equation one variable multiple steps
Level 26: Rate: solve word problems with distance, rate, and time
6.0
Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
- Level 13 Linear Equations: graph a linear equation in standard form
Level 14 Graph By Intercepts: graph by x- and y- intercepts
Level 17 Slope Intercept: slope intercept form of a line
Level 21 Graphing Calculator: enter and graph linear equations on a calculator
Level 23 Compound Inequalities: graph compound inequalities on a number line
Level 24 Graph Inequalities: graph inequalities on a coordinate graph
7.0
Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
- Level 15 Points on a Line: check whether a given point is on a line
Level 20 Point Slope: find linear equation from a point and slope or parallel line
8.0
Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.
- Level 19 Parallel Perpendicular: determine whether a line is parallel or perpendicular
Level 20 Point Slope: find linear equation from a point and slope or parallel line
9.0
Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
- Level 30 Systems Graphing: solve two equations two variables using graphing calc
Level 31 Systems Substitution: solve two equations using substitution
Level 32 Systems Add Eliminate: solve two equations using elimination
10.0
Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.
- Level 33 Polynomial Basics: term, monomial, binomial, trinomial, order
Level 34 Combine Like Terms: add like terms together
Level 35 Add Polynomials: add polynomials
Level 36 Subtract Polynomials: subtract polynomials
Level 37 Multiply Polynomials: multiply polynomials
Level 38 Divide Polynomials: divide polynomials
11.0
Students apply basic factoring techniques to second- and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.
- Level 41 Factoring GCF: factor out the greatest common factor from a polynomial
Level 42 Trinomial Factor 1: factor trinomials all positive coefficients, a=1
Level 43 Trinomial Factor 2: factor trinomials negative coefficients, a=1
Level 44 Trinomial Factor 3: factor trinomials, a > 1
Level 45 Factor Perfect Square: identify perfect square trinomials and factor
Level 46 Factor Difference of Squares: identify difference of squares and factor
12.0
Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.
- Level 47 Rational Expressions: simplify rational expressions: factor and cancel
13.0
Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.
- Level 48 Rational Multiply Add: multiply, divide, add rational expressions
14.0
Students solve a quadratic equation by factoring or completing the square.
- Level 50 Quadratic Factoring: solve quadratic equations by factoring
Level 52 Quadratic Complete Square: solve quadratics by completing the square
15.0
Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.
- Level 26 Rate: solve word problems with distance, rate, and time
Level 58 Mixture Ratio Problems: solve mixture problems: fluids, prices
16.0
Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.
- Level 27 Functions Relations: determine function or not a function
Level 28 Function Notation: calculate function output values given input values
17.0
Students determine the domain of independent variables and the range of dependent
variables defined by a graph, a set of ordered pairs, or a symbolic expression.
- Level 29 Domain Range: determine for mappings, ordered pairs, tables, graphs
18.0
Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.
- Level 27 Functions Relations: determine function or not a function
Level 28 Function Notation: calculate function output values given input values
19.0
Students know the quadratic formula and are familiar with its proof by completing the square.
- Level 53: Quadratic Formula: solve quadratic equations by the quadratic formula
20.0
Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.
- Level 53: Quadratic Formula: solve quadratic equations by the quadratic formula
21.0
Students graph quadratic functions and know that their roots are the x-intercepts.
- Level 49: Quadratic Graphing: solve quadratic equations by graphing
22.0
Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.
- Level 49: Quadratic Graphing: solve quadratic equations by graphing
Level 53: Quadratic Formula: solve quadratic equations by the quadratic formula
23.0
Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.
- Level 54: Quadratic Word Problems: solve word problems: projectile motion, geometry
24.0
Students use and know simple aspects of a logical argument:
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.
- Level 59: Logic & Validity: solve common problems: counterexamples, conclusions
24.3
Students use counterexamples to show that an assertion is false and
- Level 59: Logic & Validity: solve common problems: counterexamples, conclusions
25.0
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:
25.1
Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.
- Level 59: Logic & Validity: solve common problems: counterexamples, conclusions
25.2
Students judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly
at each step.
- Level 59: Logic & Validity: solve common problems: counterexamples, conclusions
25.3
Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement
is true sometimes, always, or never.
- Level 59: Logic & Validity: solve common problems: counterexamples, conclusions