Mathematics Standards of Learning
Reprinted with permission from:

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Intro | Kindergarten | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | Grade 6 | Pre Algebra | Algebra I | Geometry

In the course of meeting these standards, students will demonstrate substantial growth in their ability to solve problems using multiple algebraic methods. This includes expansion in the kind and complexity of word sentences a student can translate into mathematical expressions; expansion of the kind and difficulty of expressions a student can manipulate and solve; use of some techniques of analytic geometry; recognition of the possible use of multiple different methods to generate precise or approximate solutions to problems; and a recognition of the relative strength and weaknesses of different strategies as applied to specific problems.

• A1-1 The student will translate between problem situations, verbal expressions, and mathematical expressions with variables, and extend this process to include problems involving exponents and simple radicals, polynomials, absolute values and inequalities. For expressions that are not written as equations, the student will evaluate these expressions for given replacement values of the variables. For equations or sets of equations, the student will determine the values of the variables that constitute the solution set of the equation or set of equations.
• A1-2 The student will solve linear equations and inequalities in one variable, solve literal equations (formulas) for a given variable and apply these skills to solve practical problems.
• A1-3 The student will extend the properties of real numbers into the context of algebraic equations with variables and be able to explain algebraic manipulations in terms of the properties of real numbers. In this way, the student will justify each step used in the process of simplifying expressions and solving equations and inequalities.
• A1-4 The student will translate freely among various representations of linear equations, including the slope of the line and a point on it; two points on a line; a point on the line and the condition that the line is parallel or perpendicular to another given line; a graph of the line or of points on it; a problem situation or word problem representing a line; and an equation for the line in slope-intercept form, standard form, or arbitrary form.
• A1-5 The student will translate an equation for a line in any form to an equation for either variable in terms of the other variable, and use the equation to find values for one variable given replacement values for the other variable. This includes using a linear equation in a problem situation to solve the problem, and recognizing when a linear equation cannot be used to solve a problem.
• A1-6 The student will determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line. The student will also describe the slope as a rate of change and identify slopes as positive, negative, zero, or undefined
• A1-7 The student will solve systems of two linear equations in two variables by graphical estimation and by algebraic techniques including substitution and the addition and subtraction of equations (with and without a multiplication step). These techniques will be applied to solve practical problems. Students will extend this work to graphing the solution set of two linear inequalities. Students will also solve systems of addition and subtraction equations in three variables with three unknowns by substitution.
• A1-8 The student will use the Pythagorean Theorem and its converse to find distance measures in the special case of right triangles, and use the representation of this theorem in the coordinate plane, the distance formula, to find the distance between any two points or the length of a specified line segment between two points. The student will also explain each step when given a proof of the Pythagorean Theorem.
• A1-9 The student will determine the domain and range of a relation given a set of ordered pairs, a graph, or a function rule, and will identify the relations that are and are not functions.
• A1-10 The student will draw mapping diagrams for ordered pairs and vice versa, graph functions and relations over finite domains in the coordinate plane, and, given a function rule, find the values of a function for elements in its domain and locate the zeros of the function algebraically.
• A1-11 The student will use matrices to organize and manipulate data, including matrix addition, subtraction, and scalar multiplication. Data will arise from business, industrial and consumer situations.
• A1-12 The student will factor completely binomials and trinomials, including quadratics and expressions having coefficients for the highest order term greater than one, in one or two variables when they are factorable over the rational numbers.
• A1-13 The student will factor special forms of (factorable) polynomials, including those requiring regrouping or repeated factorization and those having coefficients for the highest order term greater than one. This will include the extraction of monomial and binomial factors from expressions in the third or fourth degree.
• A1-14 The student will simplify expressions involving radicals, including the square roots of expressions involving constants and variables, and expressions involving the sum, difference, and products of radicals of both real numbers and monomial and binomial expressions, and use radical expressions to solve problems.
• A1-15 The student will add, subtract, and multiply polynomials and divide polynomials with monomial and binomial divisors. The student will also simplify rational algebraic expressions by combining like terms and by addition, subtraction, multiplication, and division of the polynomial components of these expressions.
• A1-16 The student will graph quadratic equations and inequalities. The student will estimate solutions to quadratic equations in one variable graphically and solve these equations algebraically by factoring and by using the quadratic formula. These techniques will be applied to the solution of problems involving quadratics.
• A1-17 The student will analyze a given set of data for the existence of a pattern, represent the pattern algebraically and graphically, if possible, and determine if the relation is a function.
• A1-18 The student will analyze a relation to determine whether a direct or inverse variation exists and represent it algebraically and graphically if possible.
• A1-19 The student will, given a set of data points, write an equation for a line of best fit, using the median fit method, and use the equation to make predictions.
• A1-20 The student will compare multiple one-variable data sets, using statistical techniques that include measures of central tendency, range, stem and leaf plots, and box and whisker graphs.