The Mathematics Program
Algebra 1
Competency Goal 1: The learner will simplify and perform operations on mathematical expressions
1.01 Perform operations on real numbers
• convert standard numbers to scientific notation and vice versa
• simplify expressions with absolute value
• compare and contrast number systems; counting, whole, integers, rational, irrational, and real numbers
1.02 perform operations on algebraic expressions/equations
• simplify variable expressions by collecting like terms
• simplify variable expressions by applying distributive to remove grouping symbols
• simplify mathematical expressions involving numbers, variables, or a combination of both by applying
order of operations
• use substitution of real numbers.
• represent real life-applications.
• translate into word phrases and vice versa.
• use addition or subtraction to simplify polynomial expressions
1.03 Apply definitions and properties of real numbers
• identify, explain, and apply real number properties including additive identity, multiplicative identity,
additive inverse, multiplicative inverse, multiplication property of -1 and 0, commutative, associative,
distributive, transitive, symmetric, and reflexive.
• identify errors while explaining his/her thinking process.
1.04 Perform operations with polynomial expressions to solve problems
• classify polynomials by degree and number of terms.
• use addition or subtraction to simplify polynomial expressions.
• use multiplication or division to simplify polynomial expressions with monomial and binomial terms.
• factor polynomial expressions using common factor method.
• factor polynomial expressions using difference of two squares method.
• factor polynomial expressions using quadratic trinomial method (“FOIL”).
1.05 Solve problems with radicals
• write square roots in simplified form
• estimate the decimal value of an irrational square root
• perform operations on square roots
1.06 Solve problems using exponents
• develop the laws of exponents and use them to simplify expressions
Competency Goal 2: The learner will solve algebraic equations and inequalities.
2.01 Use linear equations and inequalities to solve problems
• solve multi-step linear equations and inequalities in one variable using the addition, subtraction, and
multiplication properties of equality
• solve literal equations for a specified variable
• represent absolute value equations and inequalities on a number line.
• solve absolute value equations and inequalities
2.02 Use Quadratic equations to solve problems.
• solve quadratic equations using a variety of methods including the Quadratic formula
Competency Goal 3: The learner will use relations and functions to solve problems.
3.01 Foundations of functions
• describe independent and dependent variables in functional relationships
• model real-world phenomena with a variety of functions.
• apply direct variation in problem solving situations.
• identify and explain the definition of a function.
• identify a graph as a function and/or a relation using the vertical line test.
• identify the domain and range of a function from a set of data points.
• identify linear, quadratic, absolute value, and exponential functions from the graphs.
3.02 Linear functions
• develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic
equations in a real world context
• determine the reasonable domains and ranges in a context of real world problems
• graph and write equations of lines given characteristics such as two points, a point and a slope, or a
slope and y-intercept
• change between tables, graphs, verbal descriptions, and function
• interpret the slope and y-intercept of a graph in a real world context
• relate inverse and direct variation to linear functions and solve problems involving proportional change
• graph a linear inequality on a coordinate plane.
3.03 Use systems of linear equations to solve problems
• Interpret the meaning of the solution to a system of linear equations in a real world context
• solve systems of linear equations using concrete models, graphs, tables, and algebraic methods
3.04 Use Quadratic Functions to solve problems
• identify the vertex of the graph of a quadratic equation.
• identify the orientation of the graph of a quadratic equation
• identify the x-intercepts or zeros of the graphs of a quadratic equation and recognize them as solutions
• identify the y-intercept of the graph of a quadratic function.
• solve applications of quadratic functions involving projectile motion.
Competency Goal 4: The learner will understand and use properties and relationships in geometry.
• Understand types of angles created by parallel lines and transversals, and solve equations for missing
angle measures.
• Use scaling and proportional reasoning to solve problems related to similar and congruent polygons.
• Identify, define, and describe similar and congruent polygons with respect to angle measures, length of
sides, and proportionality of sides.
• Use the Pythagorean Theorem in problem solving.
Competency Goal 5: The student will work with probabilities
• distinguish between dependent and independent events.
• interpret data from charts, tables, graphs, and plots of data to predict outcomes.
• describe a set of data using the measures of range, mean, median, and mode..