Math Department

High School Resources

High School Math Performance Standards

Algebra 1

Each ASD mathematics course reflects the program statement and incorporates the general program goals. In addition, each course consists of a specific set of standards that determine the course content and a set of performance standards that delineate what a student should be able to do after successfully completing the course. After satisfactorily completing the ASD Algebra I curriculum, a student will be proficient in the seven strands of mathematics which comprise the Algebra I Math Content Standards. As evidence of proficiency, the student will be able to:

A1:1 Number Sense

.1 Classify numbers as Real, Irrational, Rational, Integer, Whole, Natural.
.2 Compare the differences and similarities among rational, irrational, whole, integral, and natural numbers and represent these relationships using Venn diagrams.
.3 Compare and order real numbers using <, <, >, >, _, and =.
.4 Compute a rational approximation for an irrational number.
.5 Use prime factors to find the greatest common factors (GCF) and least common multiple (LCM) of a set of monomials.

A1:2 Computation

.1 Add, subtract, multiply, and divide signed numbers and variables.
.2 Convert decimals, fractions, or percents to most useful form in various situations.
.3 Write radicals in simplest radical form.
.4 Use a calculator to evaluate a numeric expression involving roots and exponents.
.5 Evaluate formulas including the quadratic formula, distance formula, slope and midpoint formulas.
.6 Convert between scientific notation and standard decimal form.
.7 Multiply and divide numbers written in scientific notation.
.8 Identify the dimensions of a matrix.
.9 Add and subtract matrices.
.10 Multiply a matrix by a scalar.
.11 Use appropriate units to label solutions to application problems.
.12 Use unit analysis with standard and metric systems.
.13 Evaluate and simplify algebraic expressions using order of operations.

A1:3 Geometry/Graphs

.1 Compute area and perimeter or circumference of polygons and circles.
.2 Compute the surface area and volume of solid figures.
.3 Use the Pythagorean theorem to determine the length of a side of a right triangle.
.4 Determine if the coordinates of a point satisfy the equation of a graph.
.5 Find the distance between two points on a number line.
.6 Find the distance between two points on a coordinate plane.
.7 Determine the slope of a line given the graph or two points on the graph.
.8 Graph linear, quadratic, and absolute value equations and inequalities.
.9 Classify graphs that are linear, quadratic, and absolute value equations or functions.
.10 Explain how the graph of a line changes when the slope or y-intercept changes.

A1:4 Probability

.1 Create a sample space to illustrate all possible outcomes of a simple or compound event.
.2 Compute probability for simple and compound events.
.3 Solve probability problems represented as area models.

A1:5 Statistics

.1 Construct tables, charts, scatter plots, and graphs from given data.
.2 Make predictions based on data from a table, chart or graph.
.3 Compute mean, median, and mode for a set of data.
.4 Compute the range of a set of data.
.5 Represent data in a matrix.
.6 Estimate a line of best fit for a given set of data.

A1:6 Problem Solving

.1 Use various problem solving strategies including estimation, systematic lists, diagrams, patterns, guess and check, working backward, and solving a simpler problem.
.2 Check the reasonableness of answers using estimation.
.3 Write equations and inequalities to represent word problems.
.4 Graph and compare functions with and without a graphing calculator.
.5 Enter and run a simple program using a graphing calculator or computer.
.6 Create a spreadsheet (such as a table of function values) to display information.
.7 Select and use appropriate method for computing: estimation, mental math, pencil and paper, calculator, or computer.

P:7 Algebra

.1 Use correct algebraic vocabulary and notation in both written and oral communication.
.2 Write clear, step-by-step solutions to problems.
.3 Apply the properties of real numbers to simplify expressions.
.4 Solve linear equations and inequalities in one variable.
.5 Solve a literal equation or formula for a given variable.
.6 Convert a linear equation to slope-intercept form and graph it.
.7 Simplify expressions containing exponents and radicals.
.8 Add, subtract, multiply and divide polynomials.
.9 Classify polynomials by degree and by number of terms.
.10 Use a variety of techniques to factor polynomial expressions, including the greatest common factor, difference of two squares, perfect square trinomial, grouping, and trial and error.
.11 Simplify, add, subtract, multiply, and divide rational expressions.
.12 Simplify complex fractions.
.13 Solve problems using ratio and proportion.
.14 Solve systems of linear equations using the addition method, substitution method, and by graphing.
.15 Solve systems of inequalities by graphing.
.16 Solve absolute value equations and inequalities.
.17 Find the union and intersection of sets using methods that include Venn diagrams and number-line intervals.
.18 Solve problems containing "and" or "or" statements.
.19 Solve quadratic equations by factoring and using the Zero Product Property.
.20 Solve quadratic equations using the quadratic formula.
.21 Solve equations involving rational expressions and/or radicals.
.22 Write an equation for a line given its graph, a description of its graph, or a set of data.
.23 Determine the values of unknown variables given equal matrices.
.24 Determine whether a given relation is a function.
.25 Identify the domain and range from the graph of a function, relation, or a set of ordered pairs.
.26 Write an equation or rule from a set of paired data.
.27 Evaluate an equation expressed in function notation.
.28 Solve real world problems by applying the concepts and skills of algebra.