Algebra 1 Objectives
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Overall Objectives for Algebra 1:
Recognize and apply the unique vocabulary, properties, and symbolism of algebra.
Simplify and evaluate numerical and variable expressions (including linear, quadratic,
exponential, polynomial, square root, or rational expressions) using order of operations,
combining like terms, and exponent rules.
Apply problem solving techniques to worded problems and translate verbal phrases into
mathematical expressions, equations, or inequalities.
Solve linear, quadratic, polynomial, square root, and rational equations and inequalities
algebraically and graphically using various methods, including systems of linear
equations.
Recognize if an equation, table, or graph represents a function or specific type of function
such as linear, quadratic, exponential, square root, or rational function, and to create a
table or graph given an equation or write an equation given a table or graph.
Determine when a problem is complete and determine the reasonableness of solutions,
including sign, size, relative accuracy, and units of measurement.
Communicate mathematics and explain solutions to problems both orally and in well
written sentences.
Use the graphing calculator to evaluate expressions, set up tables, and graph equations.
Algebra 1 Objectives
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Detailed Objectives for Algebra 1:
Expressions, Equations, & Functions (Chapter 1)
Main Objective:
To evaluate expressions by hand and using a graphing calculator, translate verbal phases
into expressions, equations, and inequalities, and identify and represent functions with
verbal rules, equations, tables, and graphs.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with expressions,
equations, and functions.
To simplify and evaluate expressions using order of operations by hand and using a
graphing calculator.
To translate verbal phases and sentences into expressions, equations, and inequalities.
To find a unit rate.
To determine if a given number is a solution to an equation or inequality.
To identify if a table or mapping diagram is a function and to find the domain and range
of a function given a table or graph.
To create a table or graph for a function given an equation by hand and on the graphing
calculator and to find an equation given the table or graph of a function.
Properties of Real Numbers (Chapter 2)
Main Objective:
To perform operations with real numbers, apply properties of real numbers, and classify
and compare real numbers.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with properties of real
numbers.
To identify number sets (real, irrational, rational, integers, and whole numbers) and to
give examples of numbers in each set.
To compare and graph real, irrational, rational, integer, and whole numbers on a number
line.
To find opposites and absolute values of numbers.
To add, subtract, multiply, and divide real, rational, integers, and whole numbers.
To identify algebraic properties in a given an equation.
To perform matrix addition, subtraction, and scalar multiplication.
To simplify expressions by combining like terms and using the distributive property.
To find square roots of perfect squares and approximate square roots of non-perfect
squares.
Algebra 1 Objectives
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Solving Linear Equations (Chapter 3)
Main Objective:
To solve equations in one variable and proportion and percent problems.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with solving linear
functions.
To solve single and multistep equations in one variable using the distributive property,
variable on one side, and variable on both sides.
To understand what a solution to an equation is and know how to check to see if an
answer is correct by hand and on a graphing calculator.
To create and solve an equation from a word problem.
To write and simply ratios.
To solve proportions.
To create and solve a proportion from a word problem.
To solve percent problems using proportions and the percent equation.
To rewrite equations and formulas for a given variable.
Graphing Linear Equations and Functions (Chapter 4)
Main Objective:
To recognize and graph linear equations and functions.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with graphing linear
equations and functions.
To plot and name points in a coordinate plane.
To graph linear equations by hand using a table of points and on the graphing calculator.
To identify discrete and continuous functions.
To find x and y intercepts given an equation or graph, and to create a graph using the x
and y intercepts.
To find the slope and rate of change given two points, a table or graph.
To graph linear equations and functions written in various forms including slope-
intercept form and standard form.
To recognize and graph direct variations.
To write an equation in function notation and evaluate the function.
To compare the graphs of linear functions and equations.
Algebra 1 Objectives
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Writing Linear Equations (Chapter 5)
Main Objective:
To write linear equations and functions in standard and slope-intercept form, use linear
models to solve problems, and model data with a line of best fit.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with writing linear
functions.
To write linear equations and functions in standard and slope-intercept form given two
points, the slope and a point, graph, or table.
To determine if two equations represent perpendicular or parallel lines and write
equations of perpendicular and parallel lines.
To describe the correlation of data.
To find the line of best fit by hand and using linear regression on the graphing calculator
and then use the line of best fit to make predictions.
Solving and Graphing Linear Inequalities (Chapter 6)
Main Objective:
To solve and graph linear, compound, and absolute inequalities.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with solving and graphing
linear inequalities.
To solve linear inequalities applying properties of inequalities and graph solutions on a
number line.
To solve compound inequalities and equations and graph solutions on a number line.
To solve absolute value inequalities and equations and graph solutions on a number line.
To graph linear inequalities in two variables on a coordinate plane.
Systems of Equations and Inequalities (Chapter 7)
Main Objective:
To solve linear systems by graphing and using algebra and to solve systems of linear
inequalities by graphing.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with systems of equations
and inequalities.
To solve systems of equations by graphing, substitution, and the elimination method.
To determine if a system is consistent, inconsistent, dependent, or independent.
To solve linear systems of inequalities by graphing.
To determine if an ordered pair is a solution to a linear system of equations or
inequalities.
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Exponents and Exponential Functions (Chapter 8)
Main Objective:
To apply properties of exponents to simplify expressions, convert numbers to and from
standard form and scientific notation, and write and graph exponential functions.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with exponents and
exponential functions.
To apply properties of exponents to simplify expressions involving exponent products
and quotients, and zero and negative exponents.
To convert numbers to and from standard form and scientific notation.
To evaluate expressions in scientific notation.
To recognize if an equation, graph, or table represents and exponential function and
determine the domain and range of the function.
To write and exponential function given a table or graph.
Polynomials and Factoring (Chapter 9)
Main Objective:
To add, subtract, multiply, and factor polynomials and to write and solve polynomial
equations.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with polynomials and
factoring.
To add and subtract polynomial expressions.
To multiply polynomial expressions.
To factor the greatest common factor from a polynomial expression
To factor polynomials using greatest common factor, recognizing factoring rules,
grouping, and the guess and check method.
To solve polynomial equations in factored form.
Algebra 1 Objectives
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Quadratic Equations and Functions (Chapter 10)
Main Objective:
To graph and solve quadratic equations and functions.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with quadratic equations
and functions.
To compare graphs of quadratic functions.
To find the vertex, axis of symmetry, direction, maximum or minimum value and
intercepts given a graph or equation of a quadratic function.
To create a table of points given a quadratic equation or function and to use it to create a
graph.
To determine the number of real solutions by graphing a quadratic function.
To solve quadratic equations and functions using square roots, complete the square,
quadratic formula and by graphing by hand and on the graphing calculator.
To find the value of the discriminant and use it to determine the number and type of
solutions for a quadratic equation or function.
Radicals and Geometry Connections (Chapter 11)
Main Objective:
To graph square root functions, use properties of radicals to simplify expressions and
solve equations.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with radicals.
To graph and compare square root functions.
To simplify radical expressions involving rational and irrational numbers.
To add, subtract, multiply, and divide radical expressions.
To solve radical equations and check for extraneous roots.
To apply the distance and midpoint formulas.
Algebra 1 Objectives
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Rational Equations and Functions (Chapter 12)
Main Objective:
To graph rational functions, perform operations on rational expressions, and solve
rational equations.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with rational equations and
functions.
To determine if an equation or graph is a direct variation, inverse variation or neither.
To graph inverse variations given and equation by hand and using the graphing
calculator.
To divide polynomials.
To graph rational functions and determine the equations of asymptotes by hand and using
the graphing calculator.
To simplify rational expressions and state the excluded values.
To add, subtract, multiply, and divide rational expressions.
To solve rational equations.
Probability and Data Analysis (Chapter 13)
Main Objective:
To find probability of simple and compound events, analyze sets of data, and make and
interpret data displays.
Detailed Objectives:
To understand, interpret, and apply the vocabulary associated with simple probability and
data analysis.
To find probability and odds of simple events.
To find probabilities using permutations and combinations.
To find probabilities of compound events. (if time allows)
To analyze samples and surveys.
To find and analyze the measures of central tendency (mean, median, and mode).
To recognize, interpret, analyze and create stem-leaf plots, histograms, and box and
whisker plots.
