The mathematics curriculum provides sequential and comprehensive K-12 instruction in a collaborative, student-centered learning environment that fosters critical thinking, creativity, skillful problem-solving, and effective communication in order to enable all students to adapt to an ever-changing, global society and increase college and career readiness. An emphasis has been placed on conceptual understanding, higher-order thinking, and problem solving skills to prepare students for 21stcentury careers. This is further embedded through the integrated use of technology into daily lessons. Instruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with content as they build and expand their knowledge and understanding of mathematics. Students will experience mathematics as a coherent and useful subject within the context of real-life situations. In all, the curriculum aims to reach high standards while encouraging curiosity and building confidence in a collaborative atmosphere.
Algebra II Course Description
Algebra II begins with a basic review of many of the concepts from Algebra I which will be needed to pursue more advanced topics in Algebra. As the course progresses, several of the topics covered will include: factoring and polynomials, linear and non-linear functions, quadratics and complex numbers, radicals, and rational functions. Throughout this course, students will gain experience working through many problem-solving situations. Students will also be encouraged to make connections between math concepts and real-world applications.
Algebra IIUnits:
- Unit 1: Equations and Inequalities
- Unit 2: Linear Relations and Functions
- Unit 3: Systems of Equations and Inequalities
- Unit 4: Polynomial Functions
- Unit 5: Radical Functions
- Unit 6: Quadratics and Complex Numbers
- Unit 7: Rational Functions
- Unit 8: Probability and Statistics
Subject:
Mathematics / Course:
Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Equations and Inequalities
Unit Overview/Essential Understanding:
In Unit 1, students will use the properties of real numbers to evaluate expressions and formulas, as well as classify real numbers. They will use the properties of equality to solve many different types of equations. The students will also work with problems involving absolute value and inequalities.
Unit Objectives:
At the end of this unit, students will have a strong understanding of and be able to independently work with:
- Expressions and formulas
- Properties of real numbers
- Solving equations
- Solving absolute value equations
- Solving inequalities
- Solving compound and absolute value inequalities
Focus Standards Addressed in this Unit:
- CC.2.2.HS.D.1 – Interpret the structure of expressions to represent a quantity in terms of its context
- CC.2.2.HS.D.9 – Use reasoning to solve equations and justify the solution method
Important Standards Addressed in this Unit:
N/A
Misconceptions:
- Not following the correct order of operations
- General mistakes with arithmetic and fractions
- Confusion regarding “greater than” and “less than”
- Difficulty applying equations and inequalities to real-life situations
Concepts/Content:
- Variable
- Expression
- Order of operations
- Formula
- Real numbers
- Rational
- Irrational
- Integers
- Whole numbers
- Natural numbers
- Equation
- Solution
- Absolute value
- Empty set
- Extraneous
- Set-builder notation
- Interval notation
- Infinity
- Compound inequality
- Intersection
- Union
- Use the order of operations to evaluate expressions
- Use formulas
- Classify real numbers
- Use the properties of real numbers to evaluate expressions
- Translate verbal expressions into algebraic expressions and equations, and vice versa
- Solve equations using the properties of equality
- Evaluate expressions involving absolute value
- Solve absolute value equations
- Solve one-step inequalities
- Solve multi-step inequalities
- Solve compound inequalities
- Solve absolute value inequalities
- Direct teacher-led instruction
- Large group Q & A discussion
- Independent student work
- Small group collaboration
- Online remedial/enrichment videos
Assessments:
- informal questioning
- in-class formative assessments
- review of homework
- periodic quizzes
- unit test
Interdisciplinary Connections:
N/A / Additional Resources:
- Glencoe Algebra 2 textbook
- USA TestPrep
Subject:
Mathematics / Course:
Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Linear Relations and Functions
Unit Overview/Essential Understanding:
In Unit 2, students will use different forms to write and graph equations of lines (e.g. slope-intercept, point-slope, etc.), as well as use data to determine functional relationships between quantities. The students will also collect and organize data, make and interpret scatter plots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.
Unit Objectives:
At the end of this unit, students will have a strong understanding of and be able to independently work with:
- Relations and functions
- Linear relations and functions
- Rate of change and slope
- Writing linear equations
- Scatter plots and lines of regression
Focus Standards Addressed in this Unit:
- CC.2.2.HS.D.7 – Create and graph equations or inequalities to describe numbers or relationships
- CC.2.2.HS.C.2 – Graph and analyze functions and use their properties to make connections between different representations
Important Standards Addressed in this Unit:
N/A
Misconceptions:
- Confusion with some concepts relating to functions (e.g. discrete vs. continuous, relation vs. function, domain vs. range, etc.)
- Difficulties with graphing using various methods
- Inaccurate plotting to create scatter plots
Concepts/Content:
- One-to-one
- Onto
- Discrete
- Continuous
- Domain
- Range
- Standard form
- Intercept
- Rate of change
- Slope
- Slope-intercept
- Point-slope
- Parallel
- Perpendicular
- Scatter plot
- Correlation
- Line of fit
- Prediction equation
- Analyze relations and functions
- Use equations of relations and functions
- Identify linear relations and functions
- Write linear equations in standard form
- Find rate of change
- Determine the slope of a line
- Write the equation of a line given the slope and a point on the line
- Write an equation of a line parallel or perpendicular to a given line
- Use scatter plots and prediction equations
- Model data using lines of regression
- Direct teacher-led instruction
- Large group Q & A discussion
- Independent student work
- Small group collaboration
- Online remedial/enrichment videos
Assessments:
- informal questioning
- in-class formative assessments
- review of homework
- periodic quizzes
- unit test
Interdisciplinary Connections:
N/A / Additional Resources:
- Glencoe Algebra 2 textbook
- USA TestPrep
Subject:
Mathematics / Course:
Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Systems of Equations and Inequalities
Unit Overview/Essential Understanding:
In Unit 3, students will analyze situations and formulate systems of equations in two or more unknowns to solve problems. They will use algebraic methods, graphs, or tables to solve systems of equations or inequalities. The students will also interpret and determine the reasonableness of solutions to systems of equations for given contexts.
Unit Objectives:
At the end of this unit, students will have a strong understanding of and be able to independently work with:
- Solving systems of equations
- Solving systems of inequalities by graphing
- Systems of equations with three variables
Focus Standards Addressed in this Unit:
- CC.2.2.HS.D.10 – Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically
Important Standards Addressed in this Unit:
N/A
Misconceptions:
- Common mistakes with creating a graph from a linear equation
- Confusing “greater than” and “less than”
- Difficulty creating a math problem from the information in a real life situation
Concepts/Content:
- System of equations
- Break-even point
- Consistent
- Inconsistent
- Independent
- Dependent
- Substitution method
- Elimination method
- Ordered triple
- Solve systems of linear equations graphically
- Solve systems of linear equations algebraically
- Solve systems of inequalities by graphing
- Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities
- Solve systems of linear equations in three variables
- Solve real-world problems using systems of equations and inequalities
- Direct teacher-led instruction
- Large group Q & A discussion
- Independent student work
- Small group collaboration
- Online remedial/enrichment videos
Assessments:
- informal questioning
- in-class formative assessments
- review of homework
- periodic quizzes
- unit test
Interdisciplinary Connections:
N/A / Additional Resources:
- Glencoe Algebra 2 textbook
- USA TestPrep
Subject:
Mathematics / Course:
Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Polynomial Functions
Unit Overview/Essential Understanding:
In Unit 4, students will use tools including factoring and properties of exponents to simplify polynomial expressions and to transform and solve equations. They will also identify the mathematical domains and ranges of polynomial functions.
Unit Objectives:
At the end of this unit, students will have a strong understanding of and be able to independently work with:
- Factoring polynomials
- Operations with polynomials
- Dividing polynomials
- Polynomial functions
- Analyzing graphs of polynomial functions
Focus Standards Addressed in this Unit:
- CC.2.2.HS.D.3 – Extend the knowledge of arithmetic operations and apply to polynomials
- CC.2.2.HS.D.4 – Understand the relationship between zeros and factors of polynomials to make generalizations about functions and their graphs
Important Standards Addressed in this Unit:
N/A
Misconceptions:
- Misinterpretations of the properties of exponents
- Difficulties using the various factoring methods
- Confusion when interpreting domain and range of polynomial functions
Concepts/Content:
- Simplify
- Degree
- Long division
- Synthetic division
- Polynomial
- Leading coefficient
- End behavior
- Relative maximum and minimum
- Extrema
- Turning points
- Multiply, divide, and simplify monomial expressions involving powers
- Add, subtract, and multiply polynomials
- Divide polynomials using long division
- Divide polynomials using synthetic division
- Evaluate polynomial functions
- Identify general shapes of graphs of polynomial functions
- Graph polynomial functions and locate their zeros
- Find the relative maxima and minima of polynomial functions
- Direct teacher-led instruction
- Large group Q & A discussion
- Independent student work
- Small group collaboration
- Online remedial/enrichment videos
Assessments:
- informal questioning
- in-class formative assessments
- review of homework
- periodic quizzes
- unit test
Interdisciplinary Connections:
N/A / Additional Resources:
- Glencoe Algebra 2 textbook
- USA TestPrep
Subject:
Mathematics / Course:
Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Radical Functions
Unit Overview/Essential Understanding:
In Unit 5, students will simplify various radical expressions as well as apply operations to radical expressions. They will also determine solutions of radical equations using algebraic methods.
Unit Objectives:
At the end of this unit, students will have a strong understanding of and be able to independently work with:
- Simplifying radicals
- nth roots
- Operations with radical expressions
- Rational exponents
- Solving radical equations
Focus Standards Addressed in this Unit:
- CC.2.2.HS.D.2 – Write expressions in equivalent forms to solve problems
- CC.2.1.HS.F.1 – Apply and extend the properties of exponents to solve problems with rational exponents
Important Standards Addressed in this Unit:
N/A
Misconceptions:
- Difficulty simplifying basic radical expressions
- Problems involving rationalizing the denominator tend to be troublesome at times
- Basic arithmetic errors when solving equations and simplifying expressions
Concepts/Content:
- nth root
- Radical sign
- Index
- Rationalizing the denominator
- Conjugate
- Radical equation
- Extraneous solution
- Simplify radicals
- Use a calculator to approximate radicals
- Simplify radical expressions
- Add, subtract, multiply, and divide radical expressions
- Write expressions with radical exponents in radical form and vice versa
- Solve equations containing radicals
- Direct teacher-led instruction
- Large group Q & A discussion
- Independent student work
- Small group collaboration
- Online remedial/enrichment videos
Assessments:
- informal questioning
- in-class formative assessments
- review of homework
- periodic quizzes
- unit test
Interdisciplinary Connections:
N/A / Additional Resources:
- Glencoe Algebra 2 textbook
- USA TestPrep
Subject:
Mathematics / Course:
Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Quadratic Functions and Complex Numbers
Unit Overview/Essential Understanding:
In Unit 6, students will create and analyze graphs of quadratic functions and draw conclusions. They will also analyze situations involving quadratic functions and formulate quadratic equations to solve problems. Students will solve quadratic equations using graphs, tables, and algebraic methods. Finally, the students will work with complex numbers, in particular to describe the solutions of quadratic equations.
Unit Objectives:
At the end of this unit, students will have a strong understanding of and be able to independently work with:
- Graphing quadratic functions
- Solving quadratic equations by graphing
- Solving quadratic equations by factoring
- Complex numbers
- Completing the square
- The quadratic formula and the discriminant
Focus Standards Addressed in this Unit:
- CC.2.2.HS.C.5 – Construct and compare linear, quadratic, and exponential models to solve problems
- CC.2.1.HS.F.7 – Apply concepts of complex numbers in polynomial identities and quadratic equations to solve problems
Important Standards Addressed in this Unit:
N/A
Misconceptions:
- Difficulties with graphing quadratic equations
- Confusion with choosing the correct factoring method when solving quadratic equations
- Basic arithmetic errors when using completing the square or the quadratic formula
Concepts/Content:
- Quadratic
- Parabola
- Axis of symmetry
- Vertex
- Standard form
- Root
- Zero
- Factored form
- FOIL
- Imaginary unit
- Complex number
- Complex conjugates
- Completing the square
- Quadratic formula
- Discriminant
- Graph quadratic functions
- Find and interpret the maximum and minimum values of a quadratic function
- Solve quadratic equations by graphing
- Estimate solutions of quadratic equations by graphing
- Solve quadratic equations by factoring
- Perform operations with pure imaginary numbers
- Perform operations with complex numbers
- Solve quadratic equations by using the square root property
- Solve quadratic equations by completing the square
- Solve quadratic equations by using the quadratic formula
- Use the discriminant to determine the number and type of roots of a quadratic equation
- Direct teacher-led instruction
- Large group Q & A discussion
- Independent student work
- Small group collaboration
- Online remedial/enrichment videos
Assessments:
- informal questioning
- in-class formative assessments
- review of homework
- periodic quizzes
- unit test
Interdisciplinary Connections:
N/A / Additional Resources:
- Glencoe Algebra 2 textbook
- USA TestPrep
Subject:
Mathematics / Course:
Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Rational Functions
Unit Overview/Essential Understanding:
In Unit 7, the students will apply there prior knowledge of fractions to rational expressions, in particular using addition, subtraction, multiplication, and division. They will also solve many different rational equations, especially when relating to real life situations.
Unit Objectives:
At the end of this unit, students will have a strong understanding of and be able to independently work with:
- Multiplying and dividing rational expressions
- Adding and subtracting rational expressions
- Solving rational equations
Focus Standards Addressed in this Unit:
- CC.2.2.HS.D.6 – Extend the knowledge of rational functions to rewrite in equivalent forms
Important Standards Addressed in this Unit:
N/A
Misconceptions:
- Forgetting the proper rules to follow when performing arithmetic operations on fractions
- Difficulties finding the least common multiple of two or more numbers/expressions
- General mistakes with factoring and reducing rational expressions
Concepts/Content:
- Rational expression
- Complex fraction
- Least common multiple (LCM)
- Rational equation
- Distance problem
- Mixture problem
- Work problem
- Simplify rational expressions
- Multiply and divide rational expressions
- Simplify complex fractions
- Determine the LCM of polynomials
- Add and subtract rational expressions
- Solve rational equations
- Solve problems involving distance, work, and mixture
- Direct teacher-led instruction
- Large group Q & A discussion
- Independent student work
- Small group collaboration
- Online remedial/enrichment videos
Assessments:
- informal questioning
- in-class formative assessments
- review of homework
- periodic quizzes
- unit test
Interdisciplinary Connections:
N/A / Additional Resources:
- Glencoe Algebra 2 textbook
- USA TestPrep
Subject:
Mathematics / Course:
Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Probability and Statistics
Unit Overview/Essential Understanding:
In Unit 8, the students will learn to represent counting situations using permutations and combinations. They will describe the likelihood of single events using odds and probability, and they calculate probabilities for pairs of dependent or independent events, and mutually exclusive or inclusive events.
Unit Objectives:
At the end of this unit, students will have a strong understanding of and be able to independently work with:
- The counting principle
- Permutations and combinations
- Probability
Focus Standards Addressed in this Unit:
- CC.2.4.HS.B.6 – Use the concepts of independence and conditional probability to interpret data
- CC.2.4.HS.B.7 – Apply the rules of probability to compute probabilities of compound events in a uniform probability model
Important Standards Addressed in this Unit:
N/A
Misconceptions:
- Confusion distinguishing between permutations and combinations
- Difficulties knowing when to add and when to multiply probabilities together in compound events
- General mistakes with understanding how to create probability distributions
Concepts/Content:
- Outcomes
- Sample space
- Event
- Independence
- Fundamental counting principle
- Permutation
- Combination
- Probability
- Success
- Failure
- Random
- Odds
- Probability distribution
- Relative-frequency histogram
- Solve problems involving independent events
- Solve problems involving dependent events
- Solve problems involving permutations
- Solve problems involving combinations
- Find the probability and odds of events
- Create and use graphs of probability distributions
- Direct teacher-led instruction
- Large group Q & A discussion
- Independent student work
- Small group collaboration
- Online remedial/enrichment videos
Assessments:
- informal questioning
- in-class formative assessments
- review of homework
- periodic quizzes
- unit test
Interdisciplinary Connections:
N/A / Additional Resources:
- Glencoe Algebra 2 textbook
- USA TestPrep