Algebra 1A - Greenways Academy
Syllabus
Algebra 1A Course Overview Algebra is a branch of mathematics that uses symbols in place of numbers to describe and generalize relationships. In Algebra 1A, you will explore relationships between mathematical quantities, how to reason with equations and inequalities, graphing, functions, and mathematical modeling. You will build on your knowledge of variables, exponents, expressions, and algebraic terminology by applying algebra to real-world situations.
Course Goals By the end of this course, you will be able to do the following:
Add, subtract, multiply, and divide monomials and binomials. Solve and graph linear equations and inequalities in one or more variables. Use and apply patterns, sequences, series and functions. Solve problems involving linear and quadratic functions. Apply rules for exponents and radicals. Interpret, build, and solve problems using quadratic functions and modeling.
Math Skills Middle school mathematics is a prerequisite for Algebra 1A. Before beginning this course, you should be able to do the following:
Solve problems involving operations with real numbers. Understand linear relationships through your work with ratios, proportions, and rates. Know the meaning of a line and be able to make predictions from linear relationships. Collect, analyze, and display data to solve problems.
General Skills To participate in this course, you should be able to do the following:
Complete basic operations with word processing software, such as Microsoft Word or Google Docs. Understand the basics of spreadsheet software, such as Microsoft Excel or Google Spreadsheets, but having prior computing experience is not necessary. Perform online research using various search engines and library databases. Communicate through email and participate in discussion boards. 1 © 2013 EDMENTUM, INC.
For a complete list of general skills that are required for participation in online courses, refer to the Prerequisites section of the Plato Student Orientation document, found at the beginning of this course.
Credit Value Algebra 1A is a 0.5-credit course.
Course Materials
Notebook Pencils Graphing calculator, recommend TI-83 or equivalent Computer with Internet connection and speakers or headphones Microsoft Word or equivalent Microsoft Excel or equivalent
Course Pacing Guide This course description and pacing guide is intended to help you keep on schedule with your work. Note that your course instructor may modify the schedule to meet the specific needs of your class.
Unit 1: Relationships Between Quantities and Reasoning with Equations Summary This unit focuses on expressions and equations. An equation is a statement of equality between two expressions. In this unit, you will create equations and inequalities in one variable and use them to solve problems. Day 1 day: 1
4 days: 2–5
Activity/Objective Syllabus and Plato Student Orientation Review the Plato Student Orientation and Course Syllabus at the beginning of this course. Adding Monomials Add monomials.
Type Course Orientation
Lessons
Subtracting Monomials Subtract monomials. Multiplying Monomials 2
Multiply monomials. Dividing Monomials Divide monomials. 4 days: 6–9
Adding Binomials and Monomials Add binomials.
Lessons
Subtracting Binomials and Monomials Subtract binomials. Multiplying Monomials and Binomials Multiply binomials. Dividing Binomials by Monomials Divide binomials. 11 days:
Linear Equations in 1 Variable: Isolating the Variable Solve more difficult linear equations by isolating the variable.
Lessons
10–20 Linear Inequalities in 1 Variable, Part 1 Solve linear inequalities using addition and subtraction. Linear Inequalities in 1 Variable, Part 2 Solve linear inequalities for which multiplication and division are required. More Difficult Linear Inequalities in 1 Variable Solve more difficult linear inequalities by isolating the variable. Literal Equations Write literal equations to solve math problems. Adapting and Using Formulas Rewrite formulas to solve problems with variables. Using Linear Equations to Solve Problems Use linear math sentences in one variable to solve practical problems. 12 days:
Ordered Pairs as Solutions of Linear Equations Determine whether an ordered pair is a solution of a linear equation. 3
Lessons
21–32 Graphing Linear Equations in 2 Variables Determine if a point is on the graph of a linear equation. Graphs, Slopes, and y-Intercepts Determine the slope and intercept of a linear relationship from its graph. Finding x- and y-Intercepts of a Linear Equation Find the intercepts of a linear equation. Equations, Graphs, Slopes, and y-Intercepts Use the slope and intercept of linear functions to write an equation from a graph, and draw a graph from an equation. Slope-Intercept Form Apply the slope-intercept form of the equation of a line. Point-Slope Form Apply the point-slope form of the equation of a line. 1 day: 33
1 day: 34
4 days:
Solving Problems with Systems of Linear Equations Solve practical problems with two variables.
Lesson
Review: Equations and Inequalities Review how to solve equations and inequalities.
Lesson
Unit Activity and Discussion—Unit 1
35–38 1 day:
Unit Activity Discussion
Posttest—Unit 1
Assessment
39
4
Unit 2: Linear and Exponential Relationships Summary This unit focuses on solving and graphing equations and inequalities in two variables. In this unit, you will also describe patterns and sequences with functions and use linear and exponential functions to model real-world problems. Day 1 day: 40
2 days: 41–42 1 day: 43 2 days: 44–45 1 day: 46
1 day: 47
2 days: 48–49 1 day: 50
5 days: 51–55
Activity / Objective
Type
Interpreting Graphs to Solve Problems Solve problems or answer questions based on linear graphs that represent real-world situations.
Lesson
Graphing Linear Inequalities in Two Variables Graph linear inequalities in two variables.
Lesson
Solving and Graphing Systems of Equations Solve a system of linear equations.
Lesson
Solving Systems of Linear Inequalities by Graphing Solve a system of inequalities by graphing.
Lesson
Patterns and Sequences Study different types of patterns and predict future items in these patterns.
Lesson
Functions Study relationships called functions, the parts of a function (input, output, rule), and how they are related.
Lesson
Finding the Domain and Range of a Function Find the domain and range of a function.
Lesson
Describing Functions with Equations, Tables, and Graphs Study how equations, tables, and graphs can represent the same function.
Lesson
Integer Exponents and the Product Rule Simplify a product using the product rule for exponents.
Lessons
Integer Exponents and the Quotient Rule Divide exponential forms with the same base using the quotient rule for exponents. 5
Integer Exponents and the Power Rule, Part 1 Use the power rule for exponents to simplify an expression with exponents raised to a power. Integer Exponents and the Power Rule, Part 2 Use the power rule for exponents to simplify an expression with exponents raised to a power. 7 days: 56–62
Solving Linear Systems Using Substitution Solve linear equations using the substitution method.
Lessons
Solving Linear Systems Using Linear Combinations Solve systems of linear equations using the linear combinations method Solving Linear Systems of Equations: Addition Solve a system of equations by adding or subtracting. 1 day: 63
1 day: 64
1 day: 65 2 days: 66–67
Solving Problems with Linear Systems Solve word problems using a system of two linear equations or inequalities.
Lesson
Rationalizing the Denominator in Rational Expressions Rationalize the denominator in rational expressions using the rules for exponents.
Lesson
Defining a Function with Its Rule Determine whether a relation represents a function.
Lesson
Equations and Graphs of Functions, Part 1 Determine if a graph represents a function.
Lesson
Equations and Graphs of Functions, Part 2 Determine if a graph represents a function. 8 days: 68–75
Solving Problems with Linear Functions Describe real-world situations as linear functions. Solving Problems with Quadratic Functions Describe real-world situations as quadratic functions. Exponential Growth 6
Lesson
Solve problems that involve exponential growth. Exponential Decay Solve problems that involve exponential decay. 2 days: 76–77 4 days: 78–81
Introduction to Sequences and Series Use and write sequences and series and find the sum of a series.
Lesson
Arithmetic Sequences and Series Write rules for arithmetic sequences and find sums of arithmetic series.
Lessons
Geometric Sequences and Series Learn to write rules for geometric sequences and find sums of geometric series. 1 day: 82 5 days:
Translations and Transformations Alter a function by translating and transforming the graph. Unit Activity and Discussion—Unit 2
83–87 1 day:
Lesson
Unit Activity Discussion
Posttest—Unit 2
Assessment
88 1 day:
Semester Review
89 1 day:
End-of-Semester Exam
Assessment
90
7
Algebra 1A Course Overview Algebra is a branch of mathematics that uses symbols in place of numbers to describe and generalize relationships. In Algebra 1A, you will explore relationships between mathematical quantities, how to reason with equations and inequalities, graphing, functions, and mathematical modeling. You will build on your knowledge of variables, exponents, expressions, and algebraic terminology by applying algebra to real-world situations.
Course Goals By the end of this course, you will be able to do the following:
Add, subtract, multiply, and divide monomials and binomials. Solve and graph linear equations and inequalities in one or more variables. Use and apply patterns, sequences, series and functions. Solve problems involving linear and quadratic functions. Apply rules for exponents and radicals. Interpret, build, and solve problems using quadratic functions and modeling.
Math Skills Middle school mathematics is a prerequisite for Algebra 1A. Before beginning this course, you should be able to do the following:
Solve problems involving operations with real numbers. Understand linear relationships through your work with ratios, proportions, and rates. Know the meaning of a line and be able to make predictions from linear relationships. Collect, analyze, and display data to solve problems.
General Skills To participate in this course, you should be able to do the following:
Complete basic operations with word processing software, such as Microsoft Word or Google Docs. Understand the basics of spreadsheet software, such as Microsoft Excel or Google Spreadsheets, but having prior computing experience is not necessary. Perform online research using various search engines and library databases. Communicate through email and participate in discussion boards. 1 © 2013 EDMENTUM, INC.
For a complete list of general skills that are required for participation in online courses, refer to the Prerequisites section of the Plato Student Orientation document, found at the beginning of this course.
Credit Value Algebra 1A is a 0.5-credit course.
Course Materials
Notebook Pencils Graphing calculator, recommend TI-83 or equivalent Computer with Internet connection and speakers or headphones Microsoft Word or equivalent Microsoft Excel or equivalent
Course Pacing Guide This course description and pacing guide is intended to help you keep on schedule with your work. Note that your course instructor may modify the schedule to meet the specific needs of your class.
Unit 1: Relationships Between Quantities and Reasoning with Equations Summary This unit focuses on expressions and equations. An equation is a statement of equality between two expressions. In this unit, you will create equations and inequalities in one variable and use them to solve problems. Day 1 day: 1
4 days: 2–5
Activity/Objective Syllabus and Plato Student Orientation Review the Plato Student Orientation and Course Syllabus at the beginning of this course. Adding Monomials Add monomials.
Type Course Orientation
Lessons
Subtracting Monomials Subtract monomials. Multiplying Monomials 2
Multiply monomials. Dividing Monomials Divide monomials. 4 days: 6–9
Adding Binomials and Monomials Add binomials.
Lessons
Subtracting Binomials and Monomials Subtract binomials. Multiplying Monomials and Binomials Multiply binomials. Dividing Binomials by Monomials Divide binomials. 11 days:
Linear Equations in 1 Variable: Isolating the Variable Solve more difficult linear equations by isolating the variable.
Lessons
10–20 Linear Inequalities in 1 Variable, Part 1 Solve linear inequalities using addition and subtraction. Linear Inequalities in 1 Variable, Part 2 Solve linear inequalities for which multiplication and division are required. More Difficult Linear Inequalities in 1 Variable Solve more difficult linear inequalities by isolating the variable. Literal Equations Write literal equations to solve math problems. Adapting and Using Formulas Rewrite formulas to solve problems with variables. Using Linear Equations to Solve Problems Use linear math sentences in one variable to solve practical problems. 12 days:
Ordered Pairs as Solutions of Linear Equations Determine whether an ordered pair is a solution of a linear equation. 3
Lessons
21–32 Graphing Linear Equations in 2 Variables Determine if a point is on the graph of a linear equation. Graphs, Slopes, and y-Intercepts Determine the slope and intercept of a linear relationship from its graph. Finding x- and y-Intercepts of a Linear Equation Find the intercepts of a linear equation. Equations, Graphs, Slopes, and y-Intercepts Use the slope and intercept of linear functions to write an equation from a graph, and draw a graph from an equation. Slope-Intercept Form Apply the slope-intercept form of the equation of a line. Point-Slope Form Apply the point-slope form of the equation of a line. 1 day: 33
1 day: 34
4 days:
Solving Problems with Systems of Linear Equations Solve practical problems with two variables.
Lesson
Review: Equations and Inequalities Review how to solve equations and inequalities.
Lesson
Unit Activity and Discussion—Unit 1
35–38 1 day:
Unit Activity Discussion
Posttest—Unit 1
Assessment
39
4
Unit 2: Linear and Exponential Relationships Summary This unit focuses on solving and graphing equations and inequalities in two variables. In this unit, you will also describe patterns and sequences with functions and use linear and exponential functions to model real-world problems. Day 1 day: 40
2 days: 41–42 1 day: 43 2 days: 44–45 1 day: 46
1 day: 47
2 days: 48–49 1 day: 50
5 days: 51–55
Activity / Objective
Type
Interpreting Graphs to Solve Problems Solve problems or answer questions based on linear graphs that represent real-world situations.
Lesson
Graphing Linear Inequalities in Two Variables Graph linear inequalities in two variables.
Lesson
Solving and Graphing Systems of Equations Solve a system of linear equations.
Lesson
Solving Systems of Linear Inequalities by Graphing Solve a system of inequalities by graphing.
Lesson
Patterns and Sequences Study different types of patterns and predict future items in these patterns.
Lesson
Functions Study relationships called functions, the parts of a function (input, output, rule), and how they are related.
Lesson
Finding the Domain and Range of a Function Find the domain and range of a function.
Lesson
Describing Functions with Equations, Tables, and Graphs Study how equations, tables, and graphs can represent the same function.
Lesson
Integer Exponents and the Product Rule Simplify a product using the product rule for exponents.
Lessons
Integer Exponents and the Quotient Rule Divide exponential forms with the same base using the quotient rule for exponents. 5
Integer Exponents and the Power Rule, Part 1 Use the power rule for exponents to simplify an expression with exponents raised to a power. Integer Exponents and the Power Rule, Part 2 Use the power rule for exponents to simplify an expression with exponents raised to a power. 7 days: 56–62
Solving Linear Systems Using Substitution Solve linear equations using the substitution method.
Lessons
Solving Linear Systems Using Linear Combinations Solve systems of linear equations using the linear combinations method Solving Linear Systems of Equations: Addition Solve a system of equations by adding or subtracting. 1 day: 63
1 day: 64
1 day: 65 2 days: 66–67
Solving Problems with Linear Systems Solve word problems using a system of two linear equations or inequalities.
Lesson
Rationalizing the Denominator in Rational Expressions Rationalize the denominator in rational expressions using the rules for exponents.
Lesson
Defining a Function with Its Rule Determine whether a relation represents a function.
Lesson
Equations and Graphs of Functions, Part 1 Determine if a graph represents a function.
Lesson
Equations and Graphs of Functions, Part 2 Determine if a graph represents a function. 8 days: 68–75
Solving Problems with Linear Functions Describe real-world situations as linear functions. Solving Problems with Quadratic Functions Describe real-world situations as quadratic functions. Exponential Growth 6
Lesson
Solve problems that involve exponential growth. Exponential Decay Solve problems that involve exponential decay. 2 days: 76–77 4 days: 78–81
Introduction to Sequences and Series Use and write sequences and series and find the sum of a series.
Lesson
Arithmetic Sequences and Series Write rules for arithmetic sequences and find sums of arithmetic series.
Lessons
Geometric Sequences and Series Learn to write rules for geometric sequences and find sums of geometric series. 1 day: 82 5 days:
Translations and Transformations Alter a function by translating and transforming the graph. Unit Activity and Discussion—Unit 2
83–87 1 day:
Lesson
Unit Activity Discussion
Posttest—Unit 2
Assessment
88 1 day:
Semester Review
89 1 day:
End-of-Semester Exam
Assessment
90
7
