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DRAFT Algebra I 1st Quarter Units of Study Tools of Algebra (Units I and II) Solving One-Variable Equations (Unit III) Student Targets I can analyze subsets of the Real Number System and how they relate to each other. I can describe, identify, and apply properties of the Real Number System. I can perform addition, subtraction, multiplication, and division with real numbers in problem-solving situations. I can operate on real numbers (such as opposite, reciprocal, absolute value, power, etc). I can use equivalence relations and order relations to solve problems using real numbers. I can understand the concepts of variables and constants in expressions and use these expressions to describe realworld situations. I can simplify expressions using order of operations in the real number system. I can write equations and use formulas that model realworld situations. (IF TIME- at teacher’s discretion) I can add and subtract matrices that model real-world situations. (IF TIME- at teacher’s discretion) I can perform scalar multiplication on matrices that model real-world situations. I can solve any one-variable equation. I can recognize application of real number properties when solving equations. I can write and solve equations that describe real-world situations. Vocabulary Real Number system Natural numbers Whole numbers Integers Rational numbers Irrational numbers Commutative Property Associative Property Identity Property Distributive Property Transitive Property Reflexive Property Symmetric Property Opposite Reciprocal Absolute value Power/Exponent Base Algebraic expression Evaluate an expression Simplify an expression Variable Order of operations Like Terms One-variable equation Opposite operations Consecutive Integers Solution Like Terms DRAFT Algebra I 2nd Quarter Units of Study Proportional Reasoning (Unit IV) Student Targets Introductions to Functions and Graphing (Unit V) Vocabulary I can write and solve proportion sentences. I can use proportional reasoning to solve real-world problems. I can use trig ratios to solve real-world problems. I can compare the different ways ratios and proportions are used in various mathematical contexts. I can solve percent problems using proportions. I can solve percent problems using the equation method. I can determine percent of change in real-world problems. (IF TIME- at teacher’s discretion) I can use and apply direct and inverse variation to solve real-world problems. Ratio Proportion Trig Ratio Sine Cosine Tangent Leg Hypotenuse Right Triangle Similar Figures Percent Percent Proportion Percent Equation Percent of Change (Increase/Decrease) I can identify properties of the coordinate plane (quadrants, axes, etc.) to write ordered pairs and plot points. I can understand the concept of a function and roles of independent and dependent variables. I can determine the domain and range of a function. I can show understanding of the three views of a function and how they relate to each other. I can identify families of functions from both graphs and equations (linear, quadratic, absolute value, and exponential). I can show how changes in parameters affect graphs of functions. Function Relation Domain Range Mapping Table Independent Variable Dependent Variable Coordinate Coordinate Plane Quadrant Ordered Pair X-axis Y-axis Origin Inverse Linear Function Quadratic Function Absolute Value Function Exponential Function Line DRAFT Linear Functions (Unit VI) I can determine the domain and range of a linear function. I can determine the slope and intercepts of a linear function (formula and graph). I can demonstrate how slope shows rate of change in linear functions arising from real-world situations. I can create tables of numerical values of linear functions that relate to real-world situations. I can graph the equation of a line. I can write the equation of a line from the graph or given information (three forms). I can understand how formulas, graphs, and equations relate to each other. I can show how equations and graphs are models of the relationship between two real-world quantities. I can write an equation for a line of best fit (scatterplots). I can write the equation of a line that is parallel or perpendicular to the given line. Domain Range Slope X-intercept Y-intercept Rate of change slope-Intercept Form Point-Slope Form Scatterplot Line of Best Fit Regression Equation Parallel Lines Perpendicular Lines DRAFT Algebra I 3rd Quarter Units of Study Student Targets Vocabulary Solving Inequalities (Unit VII) I can solve any one-variable inequality. I can solve any linear inequality. I can write and solve inequalities that describe real-world situations. Inequality One-variable Inequality Two-variable inequalities Boundary Line Test Point Open Half-Plane Closed Half-Plane Compound Inequality Disjunction Conjunction Intersection Union Absolute Value Equations and Inequalities (Unit VIII) I can solve any absolute value equation. I can solve any absolute value inequality. I can write and solve absolute value equations that model real-world situations. Systems of Equations and Inequalities (Unit IX) I can understand systems of linear equations (two equations in two variables) and representations of linear systems. I can use multiple strategies to solve a system of equations. I can write and solve systems of linear equations that arise from real-world situations. Absolute Value Compound Inequality Disjunction Conjunction Intersection Union System of linear equations System of linear inequalities Independent system Dependent system Consistent Inconsistent Substitution Elimination Solve by graphing Intersecting Lines Parallel Lines Coinciding Lines Boundary Line Test Point Open Half-Plane Closed Half-Plane DRAFT Exponents (Unit X) Radicals (Unit XI) I can recognize, give examples of, and apply the laws of exponents. I can convert between standard and scientific notation. I can multiply and divide numbers in scientific notation. I can find square roots of both rational and irrational numbers (including fractions). I can identify the subsets of the Real Number System to which numbers belong. I can determine between which two consecutive integers a square root lies. I can simplify radical expressions using the Product Property of Radicals. (IF TIME- at teacher’s discretion) I can rationalize the denominator of a radical expression. I can solve real-world problems using the Pythagorean Theorem. I can use the Distance Formula to find the distance between two points on the coordinate plane. Power/Exponent Base Monomial Standard Notation Scientific Notation Zero Exponent Negative Exponent Power of a Power Power of a Product Power of a Quotient Product of Powers Quotient of Powers Radical Radicand Square Root Irrational Number Rational Number Perfect Square Radical Expression Pythagorean Theorem Leg Hypotenuse Right Triangle Right Angle Distance formula Product Property of Square Roots Quotient property of Square Roots Principal Square Root Negative Square Root DRAFT Algebra I 4th Quarter Units of Study Polynomials and Factoring (Units XII and XIII) Student Targets Probability and Odds (Unit XIV) I can identify characteristics of and classify polynomials (including degrees). I can perform basic operations of addition, subtraction, and multiplication with polynomials and simplify. I can factor polynomial expressions (greatest common monomial factor, “a” = 1, and “a” ≠ 1). I can recognize special products and factors of these products (difference of squares, perfect square trinomials). I can use factoring to solve second degree polynomial equations. I can represent simple probabilities in multiple ways (fractions, decimals, percents). I can determine probabilities in situations involving replacement and non-replacement. I can understand distinguish differences between theoretical and experimental probability. I can compute problems involving factorials. I can use the Fundamental Counting Principle to determine the number of outcomes of a specific event. I can understand the differences (and calculate) combinations and permutations. I can calculate both odds in favor of and odds against an event. I can use theoretical probability to make predictions of the outcomes of an event. I can conduct probability simulations and interpret the results. Vocabulary Monomial Binomial Trinomial Polynomial Degree of a Monomial Degree of a Polynomial Ascending Order Descending Order Like Terms Constant FOIL method Factoring Greatest Common Factor Prime Factorization Difference of Squares Perfect Square Trinomial Grouping Prime Composite Zero Product Property Probability Event Outcome Sample Space Equally likely outcomes Replacement Non-replacement Dependent Events Independent Events Compound Probability Factorials Fundamental Counting Principle Permutations Combinations Expectation/Prediction Odds (in favor of) Odds (against) Theoretical Probability Experimental Probability DRAFT Probability simulation Certain event Impossible event
