Damien High School

Mathematics & Computer Science DepartmentCurriculum Map

Course Title / Algebra 1
Prerequisites / Average of 60 or higher on the Quantitative and Mathematics portions of the HSPT or Passage of Part I of the Algebra Qualifying Exam or a “B” or higher in Damien’s Summer School Pre-Algebra course
CSU/UC Approval / Yes – Category D
Length of Course / Year
Brief Course Description / This course is designed to provide an introduction to, development of, and study of the basic skills and concepts of elementary algebra concepts. Topics include: fundamental operations of real numbers, evaluating algebraic expressions, simple linear equations and inequalities, solving systems of linear equations and inequalities, operations on polynomials – including factoring, integer exponents, introduction to square roots, introduction to graphing, ratio and proportion, applications (word problems), introduction to algebraic rational expressions and equations, and solving quadratic equations by factoring, the quadratic formula, and completing the square.
Assigned Textbook(s) / Allan E. Bellman, Sadie Chavis Bragg, Randall I. Charles, Basia Hall, William G. Handlin, Sr., Dan Kennedy;
Algebra ; Pearson Prentice Hall; 2007
Supplemental Material(s) / Algebra 1 Workbook; Pearson
PHSchool.com
Common Assessments Utilized / Common Final each semester
In-Class Work
Homework
Quizzes
Tests
ISOs Addressed / Be academically prepared for a higher education …
Exhibit community and global awareness …

Overview of Course / Skill Outcomes

This section serves as a precursor to the Curriculum Map and, as such, should briefly describe the various units (major content chunks) that comprise the course as well as the skills / techniques necessaryto be successful in the course.

Major Content Outcomes / Major Skill Outcomes (include Labs???)
I. Variables, Functions, Patterns, and Graphs
  1. Using Variables
  2. Exponents and Order of Operations
  3. Exploring Real Numbers
  4. Patterns and Functions
II. Rational Numbers
  1. Adding, Subtracting, Multiplying and Dividing Rational Numbers
  2. The Distributive Property
  3. Properties of Numbers
III. Solving Equations
  1. Solving Two-Step and Multi-Step Equations
  2. Equations With Variables on Both Sides
  3. Ratio and Proportion
  4. Equations and Problem Solving
  5. Percent of Change
IV. Solving Inequalities
  1. Inequalities and Their Graphs
  2. Solving Inequalities Using Addition, Subtraction, Multiplication and Division
  3. Solving Multi-Step Inequalities
  4. Compound Inequalities
  5. Absolute Value Equations and Inequalities
V. Graphs and Functions
  1. Relations and Functions
  2. Function Rules, Tables, and Graphs
  3. Writing a Function Rule
  4. Direct Variation and Inverse Variation
VI. Linear Equations and Their Graphs
  1. Rate of Change and Slope
  2. Slope-Intercept Form and Standard Form
  3. Point-Slope Form and Writing Linear Functions
  4. Parallel and Perpendicular Lines
VII. Systems of Equations and Inequalities
  1. Solving Systems by Graphing, Using Substitution, and Using Elimination
  2. Applications of Linear Systems
  3. Linear Inequalities
  4. Systems of Linear Inequalities
VIII. Exponents and Exponential Functions
  1. Zero and Negative Exponents
  2. Scientific Notation
  3. Multiplication and Division Properties of Exponents
  4. Exponential Functions
IX. Polynomials and Factoring
  1. Adding and Subtracting Polynomials
  2. Multiplying and Factoring
  3. Multiplying Binomials and Special Cases
  4. Factoring Trinomials and Special Cases
  5. Factoring by Grouping
X. Quadratic Equations and Functions
  1. Exploring Quadratic Graphs
  2. Quadratic Functions
  3. Solving Quadratic Equations by Factoring, Completing the Square, and Using the Quadratic Formula
  4. Using the Discriminant
XI. Radical Expressions and Equations
  1. Simplifying Radicals
  2. Operations With Radical Expressions
  3. Solving Radical Equations
  4. Graphing Square Root Functions
XI. Optional
  1. Trigonometric Ratios
  2. Angles of Elevation and Depression
XII. Rational Expressions and Functions
  1. Graphing Rational Functions
  2. Simplifying, Multiplying, Dividing, Adding, and Subtracting Rational Expressions
  3. Dividing Polynomials
  4. Solving Rational Equations
/ Upon completion of this course the student should be able to:
  1. Perform calculations on real numbers and use order of operations.
  2. Simplify and evaluate expressions using multiple algebraic expressions.
  3. Solve linear equations and simple quadratic equations.
  4. Solve application problems (word problems) using linear equations.
  5. Graph linear equations in two variables by using x- and y-intercepts.
  6. Add, subtract, multiply and factor polynomials.
  7. Use the rules/properties of exponents.
Unit 1
Students should be able to define variables and write an equation to model the relationship in a table.
Students should be able to simplify and evaluate an expression.
Students should be able to name the set(s) of numbers to which a number belongs.
Students should be able to identify the independent and dependent variables and write a function rule to describe the situation.
Unit 2
Students should be able to simplify an expression.
Students should be able to find each sum or difference of rational numbers.
Students should be able to evaluate an expression.
Students should be able to decide which property the equation illustrates.
Unit 3
Students should be able to solve an equation.
Students should be able to define a variable, write an equation, and then solve.
Students should be able to solve a proportion.
Unit 4
Students should be able to determine whether a number is a solution of the given inequality.
Students should be able to define a variable and write an inequality to model a situation.
Students should be able to solve an equation or inequality and then graph the solution.
Students should be able to solve a compound inequality and graph the solutions.
Unit 5
Students should be able to determine whether a relation is a function and if it is a function, state the domain and range.
Students should be able to find the range of a function given the domain.
Students should be able to model a rule with a table of values and a graph.
Students should be able to write a function rule to describe a statement.
Students should be able to write a function rule for a table of values.
Students should be able to write an equation of the direct variation that includes the given point.
Students should be able to determine whether a graph shows a direct variation.
Students should be able to find the constant of variation for an inverse function.
Unit 6
Students should be able to find the slope of a line that passes through a pair of points.
Students should be able to graph a linear equation.
Students should be able to write the equation of a line in standard form and in slope-intercept form.
Students should be able to find the x- and y-intercepts of a line.
Students should be able to write the equation of a line in point-slope form given slope and through a given point.
Students should be able to write an equation in point-slope form through the given points.
Students should be able to write an equation in slope-intercept form for a line the passes through the given point and is parallel or perpendicular to the given line.
Unit 7
Students should be able to solve a system by graphing, using substitution, and using elimination.
Students should be able to define variables, write an equation, and solve.
Students should be able to graph a linear inequality.
Students should be able to solve a system of inequalities by graphing.
Unit 8
Students should be able to simplify the expression.
Students should be able to evaluate exponential expressions andfunctions.
Students should be able to write a number in scientific notation.
Students should be able to graph exponential functions.
Unit 9
Students should be able to write a polynomial in standard form and name the polynomial based on its degree and number of terms.
Students should be able to simply and write the answer in standard form.
Students should be able to simplify each product and write in standard form.
Students should be able to find the GCF of the terms of the polynomial.
Students should be able to factor an expression.
Students should be able to factor completely.
Unit 10
Students should be able to find the equation of the axis of symmetry and the coordinates of the vertex of the graph of a function.
Students should be able to graph a quadratic function, label the axis of symmetry and the vertex.
Students should be able to graph a quadratic inequality.
Students should be able to find the number of x-intercepts of each function.
Students should be able to solve quadratic equations.
Students should be able to find the number of solutions of a quadratic equation using the discriminant.
Students should be able to solve the quadratic equation using the quadratic formula.
Students should be able to write a quadratic equation in standard form and then solve by factoring.
Students should be able to solve a quadratic equation by completing the square.
Unit 11
Students should be able to simplify a radical expression.
Students should be able to solve a radical equation.
Students should be able to make a table and graph a radical function.
Students should be able to find the domain of a radical function and then graph.
Unit 11 - Optional
Students should be able to find the measure of the other sides of a right triangle given the length of a side and the measure of an angle.
Students should be able to use the distance formula to find the distance between two points.
Students should be able to use the midpoint formula to find the midpoint between two points.
Unit 12
Students should be able to simplify, multiply, divide, add, and subtract rational expressions.
Students should be able to solve a rational equation.

Algebra 1

Unit 1 – Variables, Function Patterns, and Graphs

Content Outcomes / Essential Questions / Key Concepts / Standards Addressed
Students will understand the use of variables. / How are phrases in English written as algebraic expressions?
How are situations modeled with equations? / Modeling relationships with variables.
Modeling relationships with equations. / California: CA 17
Common Core: 6.EE-2
Students will learn about exponents and order of operations. / How is order of operations used to simplify expressions?
How is substitution used to evaluate expressions? / Simplifying expressions using order of operations PEMDAS:
Parentheses, Exponents, Multiplication or Division, Addition or Subtraction.
Evaluating expressions using substitution. / California: CA 17
Common Core:
Students will learn about real numbers. / How are real numbers classified?
How are real numbers compared? / Classifying real numbers. / California: CA 17
Common Core: 8.NS-1
Students will learn about patterns and functions. / How are dependent and independent quantities identified?
How are relationships written as functions? / Writing Function Rules.
Understanding dependent and independent quantities. / California: CA 17
Common Core: 6.EE-9

Algebra 1

Unit 2 – Rational Numbers

Content Outcomes / Essential Questions / Key Concepts / Standards Addressed
Students will understand how to add rational numbers. / What are real numbers?
How are real numbers added? / Adding numbers with the same sign.
Adding numbers with different signs. / California: CA 1
Common Core: 7.NS-1
Students will understand how to subtract rational numbers. / What are rational numbers?
How are rational numbers subtracted? / Subtracting numbers. / California: CA 1
Common Core: 7.NS-1c
Students will understand how to multiply and divide rational numbers. / How are real numbers multiplied?
How are real numbers divided? / Multiplying and dividing numbers with the same sign.
Multiplying and dividing numbers with different signs. / California: CA 1
Common Core: 7.NS-2
Students will understand the Distributive Property. / What is the Distributive Property?
How is the Distributive Property used to simplify expressions? / The Distributive Property. / California: CA 1
Common Core: 7.NS-2a
Students will learn about the properties of numbers. / What are the properties of real numbers?
How are the properties of real numbers identified? / Properties of real numbers. / California: CA 1
Common Core: 7.NS-1d, 7.NS-2c

Algebra 1

Unit 3 – Solving [Simple] Equations

Content Outcomes / Essential Questions / Key Concepts / Standards Addressed
Students will understand how to solve two-step equations. / What are inverse operations?
How are inverse operations used to solve two-step-equations? / Solving two-step-equations using inverse operations. / California: CA 4,5
Common Core: A-REI-3
Students will understand how to solve multi-step equations. / How is Distributive Property used to combine like terms?
How is Distributive Property used to solve equations? / Using Distributive Property to combine like terms.
Using Distributive Property to solve equations. / California: CA 4,5
Common Core: A-REI-3
Students will understand how to solve equations with variables on both sides. / How are equations with variables on both sides solved?
How are equations that are identities or have no solution identified? / Solving equations with variables on both sides.
Identifying equations that are identities and have no solution. / California: CA 4,5
Common Core: A-REI-3
Students will learn about ratios and proportions. / What are proportions?
How are algebraic proportions solved? / Solving algebraic proportions. / California: CA 4,5
Common Core: A-REI-3
Students will understand how to solve real-world problems. / How is a variable defined in terms of another variable?
How are distance-rate-time problems solved?
How are consecutive integer problems solved? / Defining a variable in terms of another variable.
Solving distance-rate-time problems.
Solving consecutive integer problems. / California: CA 4,5
Common Core: A-REI-3

Algebra 1

Unit 4 – Solving Inequalities

Content Outcomes / Essential Questions / Key Concepts / Standards Addressed
Students will learn about inequalities and their graphs. / How are solutions of inequalities identified?
How are solutions of inequalities graphed? / Identifying solutions of inequalities using substitution.
Graphing inequalities. / California: CA 3 - 5
Common Core:
Students will understand how to solve inequalities using addition and subtraction. / How are inequalities solved using addition?
How are inequalities solved using subtraction? / Using addition to solve inequalities.
Using subtraction to solve inequalities. / California: CA 3 - 5
Common Core: A-REI-3
Students will understand how to solve inequalities using multiplication and division. / How are inequalities solved using multiplication?
How are inequalities solved using division? / Using multiplication to solve inequalities.
Using division to solve inequalities. / California: CA 3 - 5
Common Core: A-REI-3
Students will understand how to solve multi-step inequalities. / How are multi-step inequalities with variables on one side solved?
How are multi-step inequalities with variables on both sides solved? / Solving multi-step inequalities with variables on one side.
Solving multi-step inequalities with variables on both sides. / California: CA 3 - 5
Common Core: A-REI-3
Students will understand how to solve compound inequalities. / How are inequalities containing “and” solved and graphed?
How are inequalities containing “or” solved and graphed? / Solving and graphing inequalities containing “and”.
Solving and graphing inequalities containing “or”. / California: CA 3 - 5
Common Core: A-REI-3
Students will understand how to solve absolute value equations and inequalities. / How are equations that involve absolute value solved?
How are inequalities that involve absolute value solved? / Solving equations that involve absolute value.
Solving inequalities that involve absolute value. / California:
Common Core:

Algebra 1

Unit 5 – Solving Inequalities

Content Outcomes / Essential Questions / Key Concepts / Standards Addressed
Students will learn about relations and functions. / What is a function?
How are relations and functions identified?
How are functions evaluated? / Identifying relations and functions.
Evaluating functions. / California: CA 16, 17
Common Core: F-IF-1
Students will understand how to use function rules, tables, and graphs. / How are functions modeled using rules, tables, and graphs? / Modeling functions using rules, tables, and graphs. / California: CA 16, 17
Common Core:
Students will understand how to write a function rule. / How is a function rule written given a table or real-world situation? / Writing a function rule given a table or real-world situation. / California: CA 16, 17
Common Core:
Students will learn about direct variation. / How is a direct variation equation written?
How are ratios and proportions used with direct variations? / Writing an equation of a direct variation.
Using ratios and proportions with direct variations. / California: CA 16, 17
Common Core:
Students will learn about inverse variation. / How are inverse variations solved?
How do direct variations and inverse variations compare? / Solving inverse variations.
Comparing direct and inverse variation. / California: CA 16, 17
Common Core:

Algebra 1

Unit 6 – Linear Equations and their Graphs

Content Outcomes / Essential Questions / Key Concepts / Standards Addressed
Students will learn about the rate of change and slope. / How are rates of change found from tables and graphs?
What is slope?
How is slope [of a line] found? / Finding rates of change from tables and graphs.
Finding slope using the slope formula: . / California: CA 6 -8
Common Core:
Students will learn about the slope-intercept form of a line. / What is slope-intercept form of a line?
What is a linear equation?
How are linear equations written in slope-intercept form?
How are linear equations graphed [using slope and y-intercept]? / Writing linear equations in slope-intercept form: y = mx + b.
Graphing linear equations in slope-intercept form. / California: CA 6 -8
Common Core: F-IF-7a
Students will learn about the standard form of a line. / What is an intercept?
How are linear equations graphed using x- and y-intercepts?
How are linear equations written in standard form? / Graphing equations using x- and y-intercepts.
Writing equations in standard form: Ax + By = C. / California: CA 6 -8
Common Core: F-IF-7a
Students will learn about the point-slope form of a line and how to write linear equations. / What is point-slope form?
How are linear equations graphed using point-slope form?
How are linear equations written using point-slope form? / Graphing and writing linear equations using point-slope form: y – y1 = m(x – x1). / California: CA 6 -8
Common Core:
Students will learn about parallel and perpendicular lines. / What are parallel lines?
What are perpendicular lines?
How are parallel lines determined?
How are perpendicular lines determined? / Determining whether the lines are parallel by comparing slopes.
Determining whether the lines are perpendicular by comparing slopes. / California: CA 6 -8
Common Core:

Algebra 1