Unit 1: Expressions, Equations, Relations, and Functions

Unit 1: Expressions, Equations, Relations, and Functions

District Overview
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.
Honors Algebra II Course Description
Honors Algebra II is a highly academic mathematics course which contains an in-depth study of various applications of functions, patterns and relations, linear & non-linear expressions, linear & non-linear equations, operations with complex numbers, and data analysis. 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.
Honors Algebra IIUnits:
  • Unit 1: Expressions, Equations, Relations, and Functions
  • Unit 2: Linear Equations and Graphing Functions
  • Unit 3: Polynomial Functions
  • Unit 4: Radical Functions
  • Unit 5: Quadratic Functions and Complex Numbers
  • Unit 6: Exponential and Logarithmic Functions
  • Unit 7: Rational Functions
  • Unit 8: Probability and Statistics

Subject:
Mathematics / Course:
Honors Algebra II / Suggested Timeline:
4 to 5 weeks
UnitTitle:
Expressions, Equations, Relations, and Functions
Unit Overview/Essential Understanding:
In Unit 1, students will use the properties of real numbers to evaluate expressions and formulas, as well as use the properties of equality to solve equations. Students will also identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations.
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
  • Solving equations
  • Relations and functions
  • Linear relations and functions
  • Rate of change and slope

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
  • CC.2.2.HS.C.1 – Use the concept and notation of functions to interpret and apply them in terms of their context

Important Standards Addressed in this Unit:
N/A
Misconceptions:
  • Not following the correct order of operations
  • General mistakes with arithmetic and fractions
  • Confusion regarding domain and range
  • Difficulty applying formulas and slope to real-life situations

Concepts/Content:
  • Variable
  • Expression
  • Order of operations
  • Formula
  • Equation
  • Solution
  • One-to-one
  • Onto
  • Discrete
  • Continuous
  • Domain
  • Range
  • Standard form
  • Intercept
  • Rate of change
  • Slope
/ Competencies/Skills:
  • Use the order of operations to evaluate expressions
  • Use formulas
  • Translate verbal expressions into algebraic expressions and equations, and vice versa
  • Solve equations using the properties of equality
  • 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
/ Description of Activities:
  • 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:
Honors Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Linear Equations and Graphing 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 identify and sketch graphs of parent functions. 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:
  • Writing linear equations
  • Scatter plots and lines of regression
  • Special functions
  • Parent functions and transformations
  • Inverse functions and relations

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:
  • Difficulties with graphing using various methods
  • Inaccurate plotting to create scatter plots
  • Confusion when applying different transformations to functions

Concepts/Content:
  • Slope-intercept
  • Point-slope
  • Parallel
  • Perpendicular
  • Scatter plot
  • Correlation
  • Line of fit
  • Prediction equation
  • Piecewise function
  • Step function
  • Absolute value function
  • Parent function
  • Translation
  • Reflection
  • Dilation
  • Inverse
/ Competencies/Skills:
  • 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
  • Write and graph piecewise-defined functions
  • Write and graph absolute value functions
  • Identify and use parent functions
  • Describe transformations of functions
  • Find the inverse of a function or relation
  • Determine whether two functions or relations are inverses
/ Description of Activities:
  • 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:
Honors Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Polynomial Functions
Unit Overview/Essential Understanding:
In Unit 3, 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
/ Competencies/Skills:
  • 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
/ Description of Activities:
  • 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:
Honors Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Radical Functions
Unit Overview/Essential Understanding:
In Unit 4, 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
/ Competencies/Skills:
  • 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
/ Description of Activities:
  • 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:
Honors Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Quadratic Functions and Complex Numbers
Unit Overview/Essential Understanding:
In Unit 5, 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
/ Competencies/Skills:
  • 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
/ Description of Activities:
  • 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:
Honors Algebra II / Suggested Timeline:
4 to 5 weeks
Unit Title:
Exponential and Logarithmic Functions
Unit Overview/Essential Understanding:
In Unit 6, the students will analyze situations modeled by exponential and logarithmic functions, formulate an equation or inequality, and solve the problem. They will also determine solutions of exponential and logarithmic equations using algebraic methods and graphs.
Unit Objectives:
At the end of this unit, students will have a strong understanding of and be able to independently work with:
  • Solving exponential equations
  • Logarithms and logarithmic functions
  • Solving logarithmic equations and inequalities
  • Properties of logarithms

Focus Standards Addressed in this Unit:
  • CC.2.2.HS.C.5 – Construct and compare linear, quadratic, and exponential models to solve problems
  • CC.2.2.HS.C.6 – Interpret functions in terms of the situations they model

Important Standards Addressed in this Unit:
N/A
Misconceptions:
  • Confusion with converting between exponential and logarithmic forms
  • Forgetting the appropriate ways to apply the properties of exponents
  • Difficulty with how to properly check logarithmic solutions

Concepts/Content:
  • Exponential equation
  • Compound interest
  • Logarithm
  • Logarithmic equation
  • Logarithmic inequality
  • Common logarithm
  • Natural logarithm
/ Competencies/Skills:
  • Solve exponential equations
  • Evaluate logarithmic expressions
  • Graph logarithmic functions
  • Solve logarithmic equations
  • Solve logarithmic inequalities
  • Simplify and evaluate expressions using the properties of logarithms
  • Solve logarithmic equations using the properties of logarithms
/ Description of Activities:
  • 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:
Honors 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
/ Competencies/Skills:
  • 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
/ Description of Activities:
  • 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:
Honors 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
/ Competencies/Skills:
  • 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
/ Description of Activities:
  • 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

Top View