Algebra+I+Benchmarks

__ **Algebra I Benchmarks** __ AlgI.1.1 Define and differentiate between discrete and continuous sets. AlgI.1.2 Describe an interval using the form a ± b. AlgI.1.3 Describe an interval using inequalities. AlgI.1.4 Find the range, endpoints and midpoint of an interval. AlgI.1.5 Graph open and closed intervals on a number line. AlgI.1.6 Classify a number as a whole number, an integer, and/or a real number. AlgI.1.7 Find the union and/or intersection of two or more sets. ***Benchmark AlgI.2:** The students will simplify and solve equations. AlgI.2.1 Convert word problems into algebraic expressions and equations. AlgI.2.2 Combine like terms, including negative numbers, decimals and fractions. AlgI.2.3 Solve equations in the form ax+b=c, including problems with a negative value of a. AlgI.2.4 Solve equations of the form ax+b=cx+d. AlgI.2.5 Solve equations using the distributive property. ***Benchmark AlgI.3:** The students will simplify and solve inequalities and solve problems using percents, rations, and proportions. AlgI.3.1 Convert word problems into inequalities. AlgI.3.2 Solve inequalities of a variety of forms, including ax < c and ax + b < cx + d. AlgI.3.3 Solve real-world problems using percents, ratios, and proportions. ***Benchmark AlgI.4:** The students will write and graph equations using slope and / or points. AlgI.4.1 Find the slope or rate of change of a line passing through two points. AlgI.4.2 Differentiate between lines with positive slope, negative slope, slope of zero, and undefined slope. AlgI.4.3 Graph and write equations for vertical and horizontal lines. AlgI.4.4 Graph inequalities in the coordinate plane. AlgI.4.5 Graph equations in slope-intercept form and standard form. AlgI.4.6 Convert linear equations between standard form and slope-intercept form. AlgI.4.7 Write the equation of a line given the slope and a point. AlgI.4.8 Write the equation of a line given two points. AlgI.4.9 Determine relationships between graphs, equations, and tables of linear data. AlgI.4.10 Draw a line to fit a set of data and find an equation for that line. ***Benchmark AlgI.5:** The students will solve systems of linear equations and inequalities. AlgI.5.1 Solve systems of linear equations by graphing. AlgI.5.2 Solve systems of linear equations using substitution. AlgI.5.3 Solve systems of linear equations by combining two equations. AlgI.5.4 Use systems of linear equations to solve real-world problems. AlgI.5.5 Solve and graph systems of linear inequalities. ***Benchmark AlgI.6:** The students will solve and graph exponential equations. AlgI.6.1 Solve exponential growth problems including compound interest. AlgI.6.2 Solve exponential decay problems. AlgI.6.3 Graph exponential growth and decay equations using a graphing calculator. AlgI.6.4 Distinguish between linear increase, linear decrease, exponential growth, and exponential decay data. ***Benchmark AlgI.7:** The students will apply properties of exponents to simplify and graph equations. AlgI.7.1 Simplify expressions using the Product of Powers property, Power of a Power property, and Power of a Product Property. AlgI.7.2 Simplify expressions using Powers of a Quotient and Quotient of Powers property. AlgI.7.3 Simplify expressions involving negative exponents. AlgI.7.4 Graph an exponential equation without a calculator. ***Benchmark AlgI.8:** The students will identify types of polynomials, perform operations on them and solve real-world problems involving polynomials. AlgI.8.1 Classify each polynomial as monomial, binomial, or trinomial. AlgI.8.2 Add and subtract polynomials. AlgI.8.3 Multiply a polynomial by a monomial. AlgI.8.4 Multiply two binomials and multiply polynomials using the Extended Distributive property. AlgI.8.5 Solve real-world problems using polynomials. ***Benchmark AlgI.9:** The students will demonstrate an understanding of factoring polynomials and use factoring to solve problems. AlgI.9.1 Factor the greatest common monomial out of a polynomial. AlgI.9.2 Factor using the difference of squares pattern. AlgI.9.3 Factor perfect square trinomials or trinomials with a leading coefficient of 1. AlgI.9.4 Determine whether or not a polynomial is factorable or prime. AlgI.9.5 Solve equations by factoring. AlgI.9.6 Solve real-world problems using factoring. ***Benchmark AlgI.10:** The students will graph and solve quadratic equations. AlgI.10.1 Solve quadratic equations by finding square roots. AlgI.10.2 Simplify square roots. AlgI.10.3 Solve quadratic equations using the quadratic formula. AlgI.10.4 Solve quadratic equations by factoring. AlgI.10.5 Graph parabolas (with and without a graphing calculator). AlgI.10.6 Use the discriminant to determine the number of real roots. ***Benchmark AlgI.11:** The student will solve problems using the Pythagorean Theorem, square roots, and absolute values. AlgI.11.1 Solve equations containing square roots. AlgI.11.2 Solve problems containing absolute values, including distance on a number line. AlgI.11.3 Solve problems using the Pythagorean theorem and the distance formula. AlgI.11.4 Solve real-life problems using Pythagorean Theorem, square roots, or absolute values.
 * *Benchmark AlgI.1: ** The students will analyze an interval or set of data and use their analysis to graph and classify the data.