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Glen Ridge Public Schools –Mathematics Curriculum
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Course Title: Advanced Algebra I
Subject: Mathematics
Grade Level: 8
Duration: 1 year
Prerequisite: Completion of Advanced Pre-Algebra with a grade of “B” or better, teacher recommendation, and completion of the summer assignment.
Elective or Required: Elective
Mathematics Mission Statement
Since Mathematical and Computational thinking are an integral part of our lives and 21st Century learning, students must be actively involved in their mathematics education with problem solving being an essential part of the curriculum. The mathematics and computer science curricula will emphasize thinking skills through a balance of computation, intuition, common sense, logic, analysis and technology.
Students will be engaged and challenged in a developmentally appropriate, student-centered learning environment. Students will communicate mathematical ideas effectively and apply those ideas by using manipulatives, computational skills, mathematical models and technology in order to solve practical problems.
To achieve these goals, students will be taught a standards-based curriculum that is aligned with the National Common Core Standards in Mathematics and the New Jersey Core Curriculum Content Standards in Technology and 21st Century Life and Careers.
Course Description:
Advanced Algebra I is an above-grade level advanced math course. Students are expected to enter this course fluent in their ability to complete operations with rational numbers (decimals, fractions, percents, integers) without a calculator. Algebra is a basic course for all college preparatory mathematics courses. Instructional emphasis will be placed on modeling real-life situations with expressions, equations, inequalities and systems of equations, and inequalities. In addition, students will explore functions as they represent real-world phenomena in the form of tables, equations and graphs through the use of technology.
The students entering eighth grade Advanced Algebra I have studied many of the topics in Units I, II, and X during the previous school year in the Advanced Pre-Algebra course. These topics are noted with an asterisk*. Teachers may choose to refer to the noted objectives and assign selected problems as a summer assignment, or they may choose to pretest, teach or skip according to students’ abilities. This strategy is strongly suggested as the Algebra I course content is very intense and time is at a premium.
Author: Kelsey Reed
Date Submitted: Summer 2012
Text: Burger, Edward B., David J. Chard, Paul A. Kennedy, Steven J. Leinwand, Freddie L. Renfro, Tom W. Roby, and Bert K. Waits. Algebra I. Holt McDougal. 2012.
Course Name: Advanced Algebra I
Topic/Unit: 1 - Equations
Approximate # of Weeks: 1-2
Essential Questions:
• How do you interpret and evaluate algebraic expressions that model real-world situations?
• How can you rewrite algebraic expressions?
• How do you write algebraic expressions to model quantities?
• How do you represent relationships algebraically?
• How can you use the properties of equality to support a solution to a linear equation?
• How do you solve literal equations?
• How do you rewrite formulas?
Common Core Standards:
• A.CED.1, 2, 4
• A.REI.1, 3
• A.SSE.1
• N.Q.1-3
Upon completion of this unit students will be able to:
• *Translate between words and algebra
• *Evaluate algebraic expressions
• *Solve one-step equations in one variable by using addition or subtraction.
• *Solve one-step equations in one variable by using multiplication or division
• *Solve equations in one variable that contain more than one operation
• *Solve equations in one variable that contain variable terms on both sides
• *Solve a formula for a given variable
• *Solve an equation in two or more variables for one of the variables
• Solve equations in one variable that contain absolute-value expressions.
• *Write and use ratios, rates, and unit rates
• *Write and solve proportions
• *Use proportions to solve problems involving geometric figures
• *Use proportions and similar figures to measure objects indirectly
• Analyze and compare measurements for precision and accuracy
• Choose an appropriate level of accuracy when reporting measurements
Interdisciplinary Standards ()
• Standard 5.1 – Science Practices
• Standard 6.3 – Active Citizenship in the 21st Century
• Standard 8.1 – Computer and Information Literacy
• Standard 8.2 – Technology Education
• Standard 9.1 – 21st - Century Life & Career Skills
Activities – include 21st Century Technologies:
• Video Tutors (Holt McDougal website)
• Interactivities (Holt McDougal website)
• PowerPoint Presentations (Holt McDougal)
• Selected online games and activities (see appendix)
• Modeling Activity – solving equations using algebra tiles (Holt McDougal)
• Modeling Activity – solving equations with variables on both sides using algebra tiles (Holt McDougal)
• TI-Calculator Activity – create a table to evaluate expressions (Holt and McDougal)
• TI-Calculator Activity – solving equations by graphing (Holt and McDougal)
• TI-Calculator Activity – solving systems of equations by graphing (Holt and McDougal)
• Map activity – use a map to determine the actual distance to travel to a number of cities. Explain how much more gas a vehicle that gets 12 mi/gal will need than a vehicle that gets 25 mi/gal. Students could also determine the total cost of gas for the trip for each vehicle (Holt and McDougal – Lesson Alternative Assessment)
• Equation Puzzle (Big Ideas)
• Precision and Accuracy Activity (Data Handbook – Holt McDougal)
• Solving Simple Equations Activities (Big Ideas)
• Solving Multi-Step Equations Activities (Big Ideas)
• Solving Equations with Variables on Both Sides Activities (Big Ideas)
• Rewriting Equations and Formulas Activities (Big Ideas)
• Selected online games and activities (see appendix)
Enrichment Activities:
• Practice C-level Worksheets (Holt McDougal)
• Challenge Worksheets (Holt McDougal)
• Problem Solving Worksheets (Holt McDougal)
• Taking Math Deeper Problems (Big Ideas)
Methods of Assessments/Evaluation:
• Entry Slips/Exit Slips
• Math Chat
• Notebook/Binder Quiz
• K-W-L
• EPR
• Journals/Open-ended Questions
• Homework
• Quizzes
• Chapter Test
• Unit Project
• Alternative Assessment
Resources/Including Online Resources
• Online Textbook Information: my.
• Teacher Webpage
• Algebra I Textbook by Holt McDougal
• Big Ideas Algebra Textbook by Holt McDougal
• On Core Algebra workbook
• Selected Websites (see appendix)
Topic/Unit: II - Inequalities
Approximate # of Weeks: 1-2
Essential Questions:
• How do you solve inequalities that involve multiple operations?
• How do you justify the solution to an inequality?
• How do you use inequalities to analyze real-world situations?
Common Core Standards:
• A.CED.1, 2
• A.SSE.2
• A.REI.1, 3
• N.Q.1, 2
• F.BF.1
Upon completion of this unit students will be able to:
• *Identify solutions of inequalities in one variable
• *Write and graph inequalities in one variable
• *Solve one-step inequalities by using addition
• *Solve one-step inequalities by using subtraction
• *Solve one-step inequalities by using multiplication
• *Solve one-step inequalities by using division
• *Solve inequalities that contain more than one operation
• *Solve inequalities that contain variable terms on both sides
• Solve compound inequalities in one variable
• Graph solutions sets of compound inequalities in one variable
• Solve inequalities in one variable involving absolute-value expressions
Interdisciplinary Standards ()
• Standard 5.1 – Science Practices
• Standard 6.1 – U.S. History: America in the World
• Standard 6.3 – Active Citizenship in the 21st Century
• Standard 8.1 – Computer and Information Literacy
• Standard 8.2 – Technology Education
• Standard 9.1 – 21st - Century Life & Career Skills
Activities – include 21st Century Technologies:
• Video Tutors (Holt McDougal website)
• Interactivities (Holt McDougal website)
• PowerPoint Presentations (Holt McDougal)
• Selected online games and activities (see appendix)
• Truth Tables and Compound Statements Lab (Holt Mcdougal)
• Writing and Graphing Inequalities Activities (Big Ideas)
• Solving Inequalities Using Addition or Subtraction Activities (Big Ideas)
• Solving Inequalities Using Multiplication or Division Activities (Big Ideas)
• Solving Multi-Step Inequalities (Big Ideas)
Enrichment Activities:
• Practice C Worksheets (Holt McDougal)
• Challenge Worksheets (Holt McDougal)
• Problem Solving Worksheets (Holt McDougal)
• Taking Math Deeper Problems (Big Ideas)
Methods of Assessments/Evaluation:
• Entry Slips/Exit Slips
• Math Chat
• Notebook/Binder Quiz
• K-W-L
• EPR
• Journals/Open-ended Questions
• Homework
• Quizzes
• Chapter Test
• Unit Project
• Alternative Assessment
Resources/Including Online Resources
• Online Textbook Information: my.
• Teacher Webpage
• Algebra I Textbook by Holt McDougal
• Big Ideas Algebra Textbook by Holt McDougal
• On Core Algebra workbook
• Selected websites (see appendix)
Topic/Unit: III - Functions
Approximate # of Weeks: 4
Essential Questions:
• How do you represent functions?
• How can you model real-world situations using a function?
• How can you use functions to analyze a real world situation?
• How can you represent a function symbolically from a graph, a verbal description, or a table of values?
• How can you use operations to combine functions that model real-world situations?
• How can you find the domain and range of a function?
• How can you decide whether the domain of a function is discrete or continuous?
• How are piecewise functions and step functions different from other functions?
Common Core Standards:
• A.APR.1
• A.CED.1-3
• A.REI.10
• A.SSE.1
• N.Q.1, 2
• F.BF.1, 2
• F.IF.1, 2, 4-7
• F.LE.2
• S.ID.6
Upon completion of this unit students will be able to:
• Match simple graphs with situations
• Graph a relationship
• Identify functions
• Find the domain and range of relations and functions
• Identify independent and dependent variables
• Write an equation in function notation and evaluate a function for given input values
• Graph functions given a limited domain
• Graph functions given a domain of all real numbers
• *Create and interpret scatter plots
• *Use trend lines to make predictions
• Recognize and extend an arithmetic sequence
• Find a given term of an arithmetic sequence
Interdisciplinary Standards ()
• Standard 5.1 – Science Practices
• Standard 6.1 – U.S. History: America in the World
• Standard 6.3 – Active Citizenship in the 21st Century
• Standard 8.1 – Computer and Information Literacy
• Standard 8.2 – Technology Education
• Standard 9.1 – 21st - Century Life & Career Skills
Activities – include 21st Century Technologies:
• Video Tutors (Holt McDougal website)
• Interactivities (Holt McDougal website)
• PowerPoint Presentations (Holt McDougal)
• Selected online games and activities (see appendix)
• Story Activity – have students write and graph a situation described by a distinct graph and a situation described by a continuous graph (Holt McDougal Lesson Alternative Assessment)
• Vertical-Line Test Activity (Holt McDougal)
• Modeling Activity – variable relationships (Holt McDougal)
• TI-Calculator Activity – Connect Function Rules, Tables, and Graphs
• TI-Calculator Activity – Interpret Scatter Plots and Trend Lines
• The Domain and Range of a Function Activities 1 – 3 (Big Ideas)
• Finding Linear Patterns Activities 1 – 2 (Big Ideas)
• Matching Function with their Graphs (Big Ideas)
• Evaluating a Function Activity (Big Ideas)
• Comparing Graphs of Functions Activity (Big Ideas)
• Using a Pattern in Science to Predict Activity (Big Ideas)
• Writing a Story Activity (Big Ideas)
• Review Game Writing Linear Functions – Domain and Range (Big Ideas)
Enrichment Activities:
• Practice C Worksheets (Holt McDougal)
• Challenge Worksheets (Holt McDougal)
• Problem Solving Worksheets (Holt McDougal)
• Taking Math Deeper Problems (Big Ideas)
Methods of Assessments/Evaluation:
• Entry Slips/Exit Slips
• Math Chat
• Notebook/Binder Quiz
• K-W-L
• EPR
• Journals/Open-ended Questions
• Homework
• Quizzes
• Chapter Test
• Unit Project
• Alternative Assessment
Resources/Including Online Resources
• Online Textbook Information: my.
• Teacher Webpage
• Algebra I Textbook by Holt McDougal
• Big Ideas Algebra Textbook by Holt McDougal
• On Core Algebra workbook
• Selected websites (see appendix)
Topic/Unit: IV – Linear Functions
Approximate # of Weeks: 4
Essential Questions:
• How do you graph a linear function?
• How do you find a rate of change or a slope?
• What is the slope of a linear function and how can you use it to graph the function?
• How can you derive the slope-intercept form of a line?
• How do you write an equation for a function given a table, graph, or description?
• How can you use tables, graphs, and equations to compare functions?
• What is the inverse of a function, and how can you find the inverse of a linear function?
• How can you decide whether a correlation exists between numerical data?
• How do you find a linear model for a set of paired numerical data, and how do you evaluate the goodness of fit?
• How do you use a graphing calculator to perform linear regression on a set of paired numerical data?
• How can you use an absolute value function to model a real world situation?
• How do the values of m and b affect the graph of the function f(x) = mx + b?
• What are the effects of the constants h and k on the graph of y = (x - h( + k
• What is the effect of the constant a on the graph of g(x) = a(x(?
• What are the effects of the constants a, h, and k on the graph of g(x) = a(x - h( + k?
• How can you use graphing to solve equations involving absolute value?
Upon completion of this unit students will be able to:
• *Identify linear functions and linear equations
• Graph linear functions that represent real-world situations and give their domain and range
• Find x- and y-intercepts and interpret their meanings in real-world situations
• *Use x-and y-intercepts to graph lines
• Find rates of change an slopes
• Relate a constant rate of change to the slope of a line
• *Find slope by using the slope formula
• Identify, write, and graph direct variation
• *Write a linear equation in slope-intercept form
• *Graph a line using slope-intercept form
• Graph a line and write a linear equation using point-slope form
• Write a linear equation given two points
• Determine a line of best fit for a set of linear data
• Determine and interpret the correlation coefficient
• Describe how changing slope and y-intercept affect the graph of a linear function
• Graph absolute-value functions
Common Core Standards
• A.CED.1-3
• A.REI.10-11
• F.BF.1, 3-4
• F.IF.1, 2, 4-7
• F.LE.1, 2, 5
• G.GPE.5
• N.Q.1, 2
• S.ID.6-9
Interdisciplinary Standards ()
• Standard 5.1 – Science Practices
• Standard 6.1 – U.S. History: America in the World
• Standard 6.3 – Active Citizenship in the 21st Century
• Standard 8.1 – Computer and Information Literacy
• Standard 8.2 – Technology Education
• Standard 9.1 – 21st - Century Life & Career Skills
Activities – include 21st Century Technologies:
• Video Tutors (Holt McDougal website)
• Interactivities (Holt McDougal website)
• PowerPoint Presentations (Holt McDougal)
• Selected online games and activities (see appendix)
• Exploring Activity – constant changes (Holt McDougal text)
• TI-Calculator Activity – graph linear functions (Holt McDougal text)
• TI-Calculator Activity – The Family of Linear Functions (Holt McDougal text)
• Graphing Linear Equations Activities (Big Ideas)
• Slope of a Line Activities (Big Ideas)
• Graphing Linear Equations in Slope-Intercept Form Activities (Big Ideas)
• Writing Equations in Slope-Intercept Form Activities (Big Ideas)
• Writing Equations in Point-Slope Form Activities (Big Ideas)
• Solving Real-World Problems Activities (Big Ideas)
• Comparing Linear and Nonlinear Functions Activities (Big Ideas)
• Scatter Plots and Lines of Fit Activities (Big Ideas)
• Analyzing Lines of Fit Activities (Big Ideas)
Enrichment Activities:
• Practice C Worksheets (Holt McDougal)
• Challenge Worksheets (Holt McDougal)
• Problem Solving Worksheets (Holt McDougal)
• Taking Math Deeper Problems (Big Ideas)
Methods of Assessments/Evaluation:
• Entry Slips/Exit Slips
• Math Chat
• Notebook/Binder Quiz
• K-W-L
• EPR
• Journals/Open-ended Questions
• Homework
• Quizzes
• Chapter Test
• Unit Project
• Alternative Assessment
Resources/Including Online Resources
• Online Textbook Information: my.
• Teacher Webpage
• Algebra I Textbook by Holt McDougal
• Big Ideas Algebra Textbook by Holt McDougal
• On Core Algebra workbook
• Selected websites (see appendix)
Topic/Unit: V – Systems of Equations and Inequalities
Approximate # of Weeks: 4
Essential Questions:
• How do you approximate the solution of a system of linear equations by graphing?
• How do you use substitution to solve a system of linear equations?
• How do you solve a system of linear equations by adding or subtracting?
• How do you solve a system of linear equations by multiplying?
• How do you solve a system of linear inequalities?
• How can you use systems of linear equations or inequalities to model and solve contextual problems?
• How can a system of linear equations have no or many solutions?
Common Core Standards:
• A.CED.2, 3
• A.REI.3, 5, 6, 11, 12
• N.Q.1, 2
Upon completion of this unit students will be able to:
• Identify solutions of systems of linear equations in two variables
• Solve systems of linear equations in two variables by graphing
• Solve systems of linear equations in two variables by substitution
• Solve systems of linear equations in two variables by elimination
• Compare and choose an appropriate method for solving systems of linear equations
• Solve special systems of linear equations in two variables
• Classify systems of linear equations and determine the number of solutions
• Graph and solve linear inequalities in two variables
• Graph and solve systems of linear inequalities in two variables
• Use a graphing calculator to view solutions of a system of linear inequalities
• Apply solving systems of equations to number theory puzzles
Interdisciplinary Standards ()
• Standard 5.1 – Science Practices
• Standard 6.3 – Active Citizenship in the 21st Century
• Standard 8.1 – Computer and Information Literacy
• Standard 8.2 – Technology Education
• Standard 9.1 – 21st - Century Life & Career Skills
Activities – include 21st Century Technologies:
• Video Tutors (Holt McDougal website)
• Interactivities (Holt McDougal website)
• PowerPoint Presentations (Holt McDougal)
• Selected online games and activities (see appendix)
• Modeling Activity – solving systems of linear equations with algebra tiles (Holt McDougal)
• TI-Calculator Activity – solve system of linear inequalities activity (Holt McDougal)
• Solving Systems of Linear Equations and by Graphing Activities (Big Ideas)
• Solving Systems of Linear Equations by Substitution Activities (Big Ideas)
• Solving Systems of Linear Equations by Elimination Activities (Big Ideas)
• Solving Special Systems of Linear Equations Activities (Big Ideas)
• System of Linear Inequalities Activities (Big Ideas)
• Graphing Linear Inequalities in Two Variables Activities (Big Ideas)
• Battle-Ship Systems Review Game (Big Ideas)
Enrichment Activities:
• Practice C Worksheets (Holt McDougal)
• Challenge Worksheets (Holt McDougal)
• Problem Solving Worksheets (Holt McDougal)
• Taking Math Deeper Problems (Big Ideas)
Methods of Assessments/Evaluation:
• Entry Slips/Exit Slips
• Math Chat
• Notebook/Binder Quiz
• K-W-L
• EPR
• Journals/Open-ended Questions
• Homework
• Quizzes
• Chapter Test
• Unit Project
• Alternative Assessment
Resources/Including Online Resources
• Online Textbook Information: my.
• Teacher Webpage
• Algebra I Textbook by Holt McDougal
• Big Ideas Algebra Textbook by Holt McDougal
• On Core Algebra workbook
• Selected websites (see appendix)
Topic/Unit: VI – Exponents and Polynomials
Approximate # of Weeks: 4
Essential Questions:
• How do you develop and use the properties of integer exponents?
• How do you evaluate square root and cube roots?
• How can you use inductive reasoning to observe patterns and write general rules involving properties of exponents?
• How can you model and classify polynomials?
• How can you perform operations with polynomials?
• How can you use the distributive property to multiply binomials?
• What are the patterns in the special products of (a + b)(a – b), (a + b)2, and
(a – b)2?
• How can we model real-world situations using exponents?
Common Core Standards:
• A.APR.1
• A.SSE.1, 2
• N.RN.1-3
Upon completion of this unit students will be able to:
• *Evaluate expressions containing zero and integer exponents
• *Simplify expressions containing zero and integer exponents
• Evaluate and simplify expressions containing rational exponents
• Classify polynomials and write polynomials in standard form
• Evaluate polynomial expressions
• Add and subtract polynomials
• Apply polynomial operations to finding areas of geometric figures
• Identify sets and the operations under which they are closed
• Find special products of binomials
Interdisciplinary Standards ()
• Standard 5.1 – Science Practices
• Standard 6.3 – Active Citizenship in the 21st Century
• Standard 8.1 – Computer and Information Literacy
• Standard 8.2 – Technology Education
• Standard 9.1 – 21st - Century Life & Career Skills
Activities – include 21st Century Technologies:
• Video Tutors (Holt McDougal website)
• Interactivities (Holt McDougal website)
• PowerPoint Presentations (Holt McDougal)
• Selected online games and activities (see appendix)
• Modeling Activity – polynomial addition and subtraction using algebra tiles (Holt McDougal)
• Modeling Activity – polynomial multiplication using algebra tiles (Holt McDougal)
• Group Multiplying Monomials Activity – students create either a monomial, binomial, trinomial, or a quadric polynomial then break into groups and multiply each pair of polynomials in their group (Holt and McDougal – Lesson Alternative Assessment)
• Properties of Exponents Activities (Big Ideas)
• Polynomials Activities (Big Ideas)
• Adding and Subtracting Polynomials Activities (Big Ideas)
• Multiplying Polynomials Activities (Big Ideas)
• Special Products of Polynomials Activities (Big Ideas)
Enrichment Activities:
• Practice C Worksheets (Holt McDougal)
• Challenge Worksheets (Holt McDougal)
• Problem Solving Worksheets (Holt McDougal)
• Taking Math Deeper Problems (Big Ideas)
Methods of Assessments/Evaluation:
• Entry Slips/Exit Slips
• Math Chat
• Notebook/Binder Quiz
• K-W-L
• EPR
• Journals/Open-ended Questions
• Homework
• Quizzes
• Chapter Test
• Unit Project
• Alternative Assessment
Resources/Including Online Resources
• Online Textbook Information: my.
• Teacher Webpage
• Algebra I Textbook by Holt McDougal
• Big Ideas Algebra Textbook by Holt McDougal
• On Core Algebra workbook
• Selected websites (see appendix)
Topic/Unit: VII – Factoring Polynomials
Approximate # of Weeks: 4
Essential Questions:
• How can you use common factors to write a polynomial in factored form?
• How can you factor the trinomial x2 + bx + c into the product of two binomials?
• How can you factor the trinomial ax2 + bx + c into the product of two binomials?
• How can you recognize and factor special products?
Common Core Standards:
• A.SSE.2-3
Upon completion of this unit students will be able to:
• *Write the prime factorization of numbers
• Find the GCF of monomials
• Factor polynomials by using the greatest common factor.
• Factor quadratic trinomials of the form x2 + bx + c
• Factor quadratic trinomials of the form ax2 + bx + c
• Factor perfect-square trinomials
• Factor the difference of two squares
• Choose an appropriate method for factoring a polynomial
• Combine methods for factoring a polynomial
Interdisciplinary Standards ()
• Standard 5.1 – Science Practices
• Standard 6.3 – Active Citizenship in the 21st Century
• Standard 8.1 – Computer and Information Literacy
• Standard 8.2 – Technology Education
• Standard 9.1 – 21st - Century Life & Career Skills
Activities – include 21st Century Technologies:
• Video Tutors (Holt McDougal website)
• Interactivities (Holt McDougal website)
• PowerPoint Presentations (Holt McDougal)
• Selected online games and activities (see appendix)
• Modeling Activity – factoring using algebra tiles (Holt McDougal)
• Modeling Activity – factorization of trinomials using algebra tiles (Holt McDougal)
• TI-Calculator Activity – use a graph to factor polynomials (Holt McDougal)
• Factoring x2 + bx + c Activities (Big Ideas)
• Factoring ax2 + bx + c Activities (Big Ideas)
• Factoring Special Products Activities (Big Ideas)
• Factoring Polynomials Using the GCF Activities (Big Ideas)
Enrichment Activities:
• Practice C Worksheets (Holt McDougal)
• Challenge Worksheets (Holt McDougal)
• Problem Solving Worksheets (Holt McDougal)
• Taking Math Deeper Problems (Big Ideas)
Methods of Assessments/Evaluation:
• Entry Slips/Exit Slips
• Math Chat
• Notebook/Binder Quiz
• K-W-L
• EPR
• Journals/Open-ended Questions
• Homework
• Quizzes
• Chapter Test
• Unit Project
• Alternative Assessment
Resources/Including Online Resources
• Online Textbook Information: my.
• Teacher Webpage
• Algebra I Textbook by Holt McDougal
• Big Ideas Algebra Textbook by Holt McDougal
• On Core Algebra workbook
• Selected websites (see appendix)
Topic/Unit: VIII – Quadratic Functions
Approximate # of Weeks: 4
Essential Questions:
• What are the effects of h and k on the graph of g(x) = (x – h)2 + k?
• What is the effect of the constant a on the graph of g(x) = ax2?
• How can you obtain the graph of g(x) = a(x – h)2 + k from the graph f(x) = x2?
• How can you solve a quadratic equation by graphing?
• How can you solve a quadratic equation using square roots?
• How can you model a real-world situation using a quadratic function?
• How can you use factoring to solve quadratic equations in standard ax2 + bx + c = 0 when a = 1?
• How can you use factoring to solve quadratic equations in standard ax2 + bx + c = 0 when a ( 1?
• How can you solve x2 + bx + c = 0 by completing the square?
• How can you solve ax2 + bx + c = 0 by completing the square when a ( 1?
• What is the quadratic formula and how can you derive it from ax2 + bx + c = 0?
• How can you use the discriminant to determine the number of solutions of a quadratic equation?
• How do you solve quadratic equations using the quadratic formula?
• How can you describe key attributes of the graph of f(x) = ax2 + bx + c by analyzing its equation?
• How can you solve a system of equations when one equation is linear and the other is quadratic?
Common Core Standards:
• A.APR.3
• A.CED.1-3
• A.REI.1, 4, 7, 10, 11
• A.SSE.3
• F.IF.2, 4, 5, 7-9
• F.BF.1, 3
• N.Q.1, 2
• S.ID.6
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Upon completion of this unit students will be able to:
• Identify quadratic functions and determine whether they have a minimum or maximum
• Graph a quadratic function and give its domain and range
• Find the zeros of a quadratic function from its graph
• Find the axis of symmetry and the vertex of a parabola
• Graph a quadratic function in the form y = ax2 + bx + c
• Graph and transform quadratic functions
• Solve quadratic equations by graphing
• Solve quadratic equations by factoring
• Solve quadratic equations by completing the square
• Solve quadratic equations by using the Quadratic Formula
• Determine the number of solutions of a quadratic equations by using the discriminant
• Solve systems of equations in two variables in which one equation is linear and the other is quadratic
• Recognize and graph cubic functions
• Solve cubic equations
Interdisciplinary Standards ()
• Standard 5.1 – Science Practices
• Standard 6.3 – Active Citizenship in the 21st Century
• Standard 8.1 – Computer and Information Literacy
• Standard 8.2 – Technology Education
• Standard 9.1 – 21st - Century Life & Career Skills
Activities – include 21st Century Technologies:
• Video Tutors (Holt McDougal website)
• Interactivities (Holt McDougal website)
• PowerPoint Presentations (Holt McDougal)
• Selected online games and activities (see appendix)
• Exploring Activity – axis of symmetry using graphing (Holt McDougal)
• TI-Calculator Activity– The Family of Quadratic Functions (Holt McDougal)
• TI-Calculator Activity– Explore Roots, Zeros, and x-Intercepts (Holt McDougal)
• Modeling Activity – completing the square using algebra tiles (Holt McDougal)
• Graphing y = x2 Activities (Big Ideas)
• Focus of a Parabola Activities (Big Ideas)
• Graphing y = ax2 + bx + c Activities (Big Ideas)
• Solving Polynomial Equations in Factored Form Activities (Big Ideas)
• Solving Quadratic Equations by Graphing Activities (Big Ideas)
• Solving Quadratic Equations Using Square Roots Activities (Big Ideas)
• Solving Quadratic Equations by Completing the Square Activities (Big Ideas)
• Solving Quadratic Equations by Using the Quadratic Formula Activities (Big Ideas)
• Solving System of Linear and Quadratic Equations Activities (Big Ideas)
Enrichment Activities:
• Practice C Worksheets (Holt McDougal)
• Challenge Worksheets (Holt McDougal)
• Problem Solving Worksheets (Holt McDougal)
• Taking Math Deeper Problems (Big Ideas)
Methods of Assessments/Evaluation:
• Entry Slips/Exit Slips
• Math Chat
• Notebook/Binder Quiz
• K-W-L
• EPR
• Journals/Open-ended Questions
• Homework
• Quizzes
• Chapter Test
• Unit Project
• Alternative Assessment
Resources/Including Online Resources
• Online Textbook Information: my.
• Teacher Webpage
• Algebra I Textbook by Holt McDougal
• Big Ideas Algebra Textbook by Holt McDougal
• On Core Algebra workbook
• Selected websites (see appendix)
Topic/Unit: IX – Exponential Functions
Approximate # of Weeks: 4
Essential Questions:
• How are geometric sequences used to describe patterns?
• What are discrete exponential functions and how can you represent them?
• How do you write, graph, and interpret an exponential growth function?
• How do you write, graph, and interpret an exponential decay function?
• How does the graph of f(x) = abx change when a and b are changed?
• How can you solve problems modeled by equations involving variable exponents?
• How can you use exponential regression to model data?
• How can you recognize, describe, and compare linear, exponential, and quadratic functions?
• How can you model changes in population using exponential functions?
Common Core Standards:
• A.CED.1, 2
• A.REI.11
• F.BF.1-3
• F.IF.1-7, 9
• F.LE.1-3, 5, 6
Upon completion of this unit students will be able to:
• Recognize and extend geometric sequences
• Find the nth term of a geometric sequence
• Evaluate exponential functions
• Identify and graph exponential functions
• Solve problems involving exponential growth and decay
• Identify and extend patterns using recursion
• Compare linear, quadratic, and exponential models
• Given a set of data, decide which type of function models the data and write an equation to describe the functions
• Identify linear and nonlinear rates of change
• Compare rates of change
• Compare functions in different representations
• Estimate and compare rates of change
• Simplify radical expressions
• Simplify radical expressions using operations
Interdisciplinary Standards ()
• Standard 5.1 – Science Practices
• Standard 6.1 – U.S. History: America in the World
• Standard 6.3 – Active Citizenship in the 21st Century
• Standard 8.1 – Computer and Information Literacy
• Standard 8.2 – Technology Education
• Standard 9.1 – 21st - Century Life & Career Skills
Activities – include 21st Century Technologies:
• Video Tutors (Holt McDougal website)
• Interactivities (Holt McDougal website)
• PowerPoint Presentations (Holt McDougal)
• Selected online games and activities (see appendix)
• Modeling Activity – growth and decay activity using counters (Holt McDougal)
• Comparing Linear, Exponential, and Quadratic Function Activities (Big Ideas)
• Exponential Functions Activities (Big Ideas)
• Exponential Growth Activities (Big Ideas)
• Exponential Decay Activities (Big Ideas)
• Geometric Sequences Activities (Big Ideas)
• Simplifying Square Roots Activities (Big Ideas)
Enrichment Activities:
• Practice C Worksheets (Holt McDougal)
• Challenge Worksheets (Holt McDougal)
• Problem Solving Worksheets (Holt McDougal)
• Taking Math Deeper Problems (Big Ideas)
Methods of Assessments/Evaluation:
• Entry Slips/Exit Slips
• Math Chat
• Notebook/Binder Quiz
• K-W-L
• EPR
• Journals/Open-ended Questions
• Homework
• Quizzes
• Chapter Test
• Unit Project
• Alternative Assessment
Resources/Including Online Resources
• Online Textbook Information: my.
• Teacher Webpage
• Algebra I Textbook by Holt McDougal (2012)
• Algebra I Textbook by Holt McDougal (2007)
• Big Ideas Algebra Textbook by Holt McDougal
• Big Ideas Accelerated Textbook by Holt McDougal
• On Core Algebra workbook
• Selected websites (see appendix)
Topic/Unit: X – Data Analysis and Probability
Approximate # of Weeks: 1-2
Essential Questions:
• What statistics can you use to characterize and compare the center and spread of data sets?
• Which statistics are most affected by outliers, and what shapes can data distributions have?
• How can you estimate statistics from data displayed in a histogram?
• How can you compare data sets using box plots?
• How can categorical data be organized and analyzed?
• How do you find the experimental probability of an event?
• How do you find the probability of a compound event?
• How can you use simulations to estimate probabilities?
• What is the difference between independent and dependent events?
• How can you display data in a way that helps you make decisions?
Common Core Standards:
• S.CP.1-4, 7
• S.IC.1
• S.ID.1-3, 5
Upon completion of this unit students will be able to:
• *Use data presented in bar graphs and circle graphs to solve equations
• *Organize data in tables and graphs
• *Choose a table or graph to display data
• *Create stem-and-leaf plots
• *Describe the central tendency of a data set
• *Create and interpret box-and-whisker plots
• Create dot-plots
• Use a dot plot to describe the shape of a data distribution
• *Recognize misleading graphs
• *Recognize misleading statistics
• *Examine different sampling methods and sources of bias
• Use a number cube to simulate a probability experiment
• *Determine the experimental probability of an event
• *Use experimental probability to make predictions
• Use a graphing calculator to find experimental probabilities by generating random numbers
• *Determine the theoretical probability of an event
• *Find the probability of independent events
• *Find the probability of dependent events
• *Find the probability of compound events
Interdisciplinary Standards ()
• Standard 5.1 – Science Practices
• Standard 6.1 – U.S. History: America in the World
• Standard 6.3 – Active Citizenship in the 21st Century
• Standard 8.1 – Computer and Information Literacy
• Standard 8.2 – Technology Education
• Standard 9.1 – 21st - Century Life & Career Skills
Activities – include 21st Century Technologies:
• Video Tutors (Holt McDougal website)
• Interactivities (Holt McDougal website)
• PowerPoint Presentations (Holt McDougal)
• Selected online games and activities (see appendix)
• Exploring Activity – use a number cube to simulate a probability experiment (Holt McDougal)
• Dice Rolling Activity – students use dice rolls to determine experimental probability of rolling a “5” and use it to make a prediction about how many times they would roll a 5 in 100 times (Holt McDougal – Alternative Assessment)
• TI-Calculator Activity – use random numbers to find experimental probability (Holt McDougal)
• Exploring Activity – use dice rolls to determine compound events (Holt McDougal)
• Measures of Central Tendency Activities (Big Ideas)
• Box-and-Whisker Activities (Big Ideas)
• Shapes of Distributions Activities (Big Ideas)
• Choosing a Data Display Activity (Big Ideas)
• Independent and Dependent Events Activity (Data Handbook – Holt McDougal)
• Data Displays Activity (Data Handbook – Holt McDougal)
• Appropriate Data Displays Activity (Data Handbook – Holt McDougal)
• Measures of Central Tendency Activity (Data Handbook – Holt McDougal)
Enrichment Activities:
• Practice C Worksheets (Holt McDougal)
• Challenge Worksheets (Holt McDougal)
• Problem Solving Worksheets (Holt McDougal)
• Taking Math Deeper Problems (Big Ideas)
Methods of Assessments/Evaluation:
• Entry Slips/Exit Slips
• Math Chat
• Notebook/Binder Quiz
• K-W-L
• EPR
• Journals/Open-ended Questions
• Homework
• Quizzes
• Chapter Test
• Unit Project
• Alternative Assessment
Resources/Including Online Resources
• Online Textbook Information: my.
• Teacher Webpage
• Algebra I Textbook by Holt McDougal (2012)
• Algebra I Textbook by Holt McDougal (2007)
• Big Ideas Algebra Textbook by Holt McDougal
• Big Ideas Accelerated Textbook by Holt McDougal
• On Core Algebra workbook
• Selected websites (see appendix)
Appendix:
|Website |Description |
|Unit I |
| |Solving equations with addition and subtraction. Each time an|
| |answer is correct the player gets a chance to score a basket. |
| solving absolute-value equations in a “Who wants to |
|s.html |be a billionaire?” type online game. |
| |Solve equations with various parameters (1-step equations, |
| |2-step equations, equations with variables on both sides, and |
| |distributive property). Each time an answer is selected |
| |correctly the player gets to place a piece in the “Connect |
| |Four” type game. |
| |Jeopardy game on equations. Topics include: basic equations, |
| |two step equations, equations with variables on both sides, |
| |pot luck mixture of equations, and literal equations. This |
| |can be played with one or two players/teams. |
|Unit II |
| |Multiple choice practice game with a genie who offers hints |
| |when a problem is incorrect |
| |Rags to riches on graphing and solving inequalities |
| jeopardy on solving inequalities. Topics include: |
|ile=1294159199 |add/subtract inequalities, multiply/divide inequalities, solve|
| |two-step inequalities, compound inequalities, and mixed |
| |practice. |
| game where you are given an inequality (make sure to |
|/inequalitiesAdvanced.html |click the jump to double inequalities) then shoot down the |
| |objects that fall on parts of the inequality that is not a |
| |solution. |
|Unit III |
| jeopardy game on functions. Topics include: |
|420673.php |function or not?, evaluating, difference quotient, domain, and|
| |range. |
| |In this activity, evaluate each function at the given value |
| |using function notation. |
| |Rags to riches game on functions/relations. |
| |Given a set of ordered pairs identify 1) the domain, 2) the |
| |range, or 3) determine if the relation is a function. BEAWARE |
| |- a card may have more than one correct answer, however, only |
| |one will create a match. |
| |Multiple choice practice on correlation of scatter plots. |
|Unit IV |
| |Graph functions with various slopes to help save the zogs in |
| |this interactive game. |
| |Graph functions with various slopes and intercepts to zap the |
| |cockroaches. |
| |Rags to riches. Given the standard form of a linear equation,|
| |find the intercepts. |
| |Matching. Match the slope with the corresponding ordered |
| |pair. |
| |Matching. Match equations of the same line: point-slope form |
| |and slope-intercept form. |
| |This activity allows the user to enter a set of data, plot the|
| |data on a coordinate grid, and determine the equation for a |
| |line of best fit. |
|Unit V |
| |Inequality surf worksheet. Students graph an inequality in |
| |the coordinate plane and then see if the surfer is “splashed |
| |over” by the graph of the inequality. |
| |Hoop shoot game. This two-step equation game can be played |
| |alone or with another student. This game can also be played at|
| |school by dividing the classroom in two teams. Once a |
| |question is answered correctly you must make a basket to earn |
| |a point, trickier than it looks! |
| |Rags to riches. Solving systems of equations. |
| |Jeopardy on systems. Topics include: solve by graphing, solve|
| |by elimination, solve by substitution, solve systems of |
| |inequalities |
| jeopardy on systems. Topics include: solutions of |
|916458.php |ordered pairs, solve by graphing, solve by substitution and |
| |elimination, solve special cases, solve word problems. |
| worksheet on solving systems of equations. |
|UIA.pdf | |
|Unit VI |
| |Matching. Exponents – negatives, zeros, and quotients |
| jeopardy on laws of exponents. |
|963.php | |
| |Rags to riches. Multiplying monomials. |
| |Fill-in-the-blank quiz. Multiplying polynomials. |
| |Matching. Multiplying binomials. |
| |Jeopardy. Operations with polynomials. |
|Unit VII |
| |Timed practice on factoring. |
| |Matching trinomials with the factored form. |
| |Rags to riches on factoring. |
| |Multiple-choice practice on factoring (including perfect |
| |square trinomials). |
|Unit VIII |
| |Jeopardy on the characteristics of a quadratic function. |
| |Topics include: identifying the form of equation, find the |
| |vertex, find the x-intercept, what does the graph look like, |
| |applications. |
| |Team game where various quadratic equations to solve using the|
| |quadratic formula. |
| |Chutes and ladder game (need actual chutes and ladder game to |
| |complete activity). Students work in groups and solve |
| |problems based on number rolls as they advance through the |
| |game. |
| |Quadratic formula song. Students love this! |
|Unit IX |
| |Multiple-choice practice on graphing exponential functions. |
| |Multiple-choice practice on number patterns. |
| |Practice with applied exponential growth and decay |
| |Multi-team jeopardy on exponential functions. Topics include:|
| |geometric sequences, exponential functions, graphing |
| |exponential functions, exponential growth and decay, and |
| |linear/quadratic/exponential models |
| |M&M-toss experiment on exponential growth and decay. |
| |Directions on how to do this hands-on experiment. |
| |Penny-toss experiment. Directions on how to do this hands-on |
| |experiment. Counters can be used in place of pennies. |
| |Matching worksheet on simplifying radicals. |
|Unit X |
| |The game of SKUNK. Students practice decision-making skills |
| |leading to a better understanding of choice versus chance and |
| |building the foundation of mathematical probability. |
| |Multiple-choice practice on probability. A parrot offers |
| |hints when answers are incorrect. |
| |Box-and-whisker plot maker. |
| with multiple in-class probability games. |
| |Multiple-choice questions on practicing with data (frequency |
| |tables, cumulative frequency tables, circle graphs, |
| |box-and-whiskers, histograms) |
| |Fruit loop activity. Students use fruit loops to explore |
| |measures of central tendency. |
| |Sample population and bias activity. Students will utilize |
| |pre-existing data pertaining to the color of backpacks used by|
| |high school freshmen for a statistical study. |
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