· Web viewInstruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with

District OverviewThe 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 21st century 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 DescriptionHonors 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 II Units: 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

Unit Title: Expressions, Equations, Relations, and FunctionsUnit 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/AMisconceptions:

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

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

Description of Activities: Direct teacher-led instruction Large group Q & A discussion Independent student work Small group collaboration Online remedial/enrichment videos

Onto Discrete Continuous Domain Range Standard form Intercept Rate of change Slope

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

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




Unit Title: Linear Equations and Graphing FunctionsUnit 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


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

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


Parent function Translation Reflection Dilation Inverse

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 inversesAssessments:

informal questioning in-class formative assessments review of homework periodic quizzes unit test






Unit Title: Polynomial FunctionsUnit 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

graphsImportant Standards Addressed in this Unit:N/AMisconceptions:

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







Unit Title: Radical FunctionsUnit 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


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


Assessments: informal questioning in-class formative assessments review of homework periodic quizzes

unit testInterdisciplinary Connections:N/A





Unit Title: Quadratic Functions and Complex NumbersUnit 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


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







Unit Title: Exponential and Logarithmic FunctionsUnit 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


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








Unit Title: Rational FunctionsUnit 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


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








Unit Title: Probability and StatisticsUnit 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 modelImportant Standards Addressed in this Unit:N/AMisconceptions:

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





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· Web viewInstruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with