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Essential Skills:Algebra II

1) Identify the graphs and equations of the Library of functions.Learning Goals

A. Students will understand and be able to recognize, interpret, and graph various types offunctions and relations (linear, quadratic, exponential, absolute value, piecewise, step).

B. Students will understand and find a linear equation of best fit and use it to makepredictions.

C. Students will understand and be able to solve and graph inequalities.

2. Do basic operations with functions including composition of functionsLearning Goals

A. Students will understand and use function notation. (Add, subtract, multiply anddivide pairs of functions)

B. Students will understand and use composition of functions and combine functionsby composition.

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3. Solve systems of equations with two or three variables.Learning Goals

A. Students will understand and use substitution, elimination, and determinants tosolve systems of two or three linear equations in two or three variables.

B. Students will understand and use systems of linear equations and inequalities.

4. Divide and factor polynomials and solve polynomial equations.Learning Goals

A. Students will understand and be able to divide polynomials by monomials.B. Students will understand and be able to divide polynomials by other polynomials

using long or synthetic division.C. Students will understand and be able to solve and factor polynomial equations.D. Students will understand and be able to use graphing technology to find

approximate solutions for polynomial equations.E. Students will understand and be able to use polynomial equations to solve word

problems.F. Students will understand and be able to write a polynomial given its solutionsG. Students will understand and be able to describe the relationships among the

solutions of an equation, the zeros of a function, the x-intercepts of a graph, andthe factors of a polynomial expression.

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5. Do basic operations with rational expressions.Learning Goals

A. Students will understand and be able to add, subtract, multiply, divide andsimplify algebraic fractions.

B. Students will understand and be able to simplify complex fractionsC. Students will understand and be able to solve equations involving algebraic

fractionsD. Students will understand and be able to solve word problems involving fractional

equationsE. Students will understand and be able to solve problems of direct, inverse, and joint

variation.

6. Simplify radicals and solve radical equations and equations with radicals. Perform basicoperations of exponents including rational and negative exponents.

Learning GoalsA. Students will understand and be able to simplify radicalsB. Students will understand and be able to solve equations that contain radical

expressions.C. Students will understand and use negative and fractional exponents.

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7. Add, subtract, multiply, and divide complex numbers.Learning Goals

A. Student will understand and be able to define complex numbers and perform basicoperations with them.

8. Solve quadratic equations.Learning Goals

A. Students will understand and be able to factor quadratics.B. Students will understand and be able to complete the square.C. Students will understand and be able to use the quadratic formula to find various

types of solutions including complex.D. Students will understand and graph a quadratic equation.E. Students will be able to solve word problems using quadratic equations.F. Students will understand and be able to solve pairs of equations, one quadratic and

one linear or both quadratic.

9. Graph conic sections and identify their equations.Learning Goals

A. Students will understand and be able to write the equation of conic sections(circle, ellipse, parabola, and hyperbola.)

B. Students will understand and be able to graph and identify the parts of conicsections.

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10. Solve a logarithmic equation.Learning Goals

A. Students will understand and be able to use the inverse relationship betweenexponents and logarithms.

B. Students will understand and be able to solve logarithmic and exponentialequations and inequalities.

C. Students will understand and be able to use calculators to find decimalapproximations of natural and common logarithmic numeric expressions

11. Define and use arithmetic and geometric sequences and series.Learning Goals

A. Students will understand and be able to find terms in sequences.B. Students will understand and be able to find partial sums of arithmetic and

geometric series.

12. Use the counting principle to compute combinations, permutations, and probabilities.Learning Goals

A. Students will understand and be able to compute combinations and permutations.B. Students will understand and be able to use combinations and permutations to

compute probabilities.

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MICHIGAN CITY HIGH SCHOOLAlgebra II

Ongoing/All Year 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter

Course Title

ALGEBRA II

Assessment

1A, 1B, 2, 3, 4A, QTR1

Assessment

4B, 4C, 5A, 5B, 6A, QTR2

Assessment

6B, 7, 8A, 8B, 9A, QTR3

Assessment

9B, 10, 11, 12, QTR 4

Bundle #

7 Relations & Functions5 Linear Systems10 Functions9 Polynomials

Standards1.1 1.2 1.3. 1.4. 1.51.6 1.7 1.8 2.1 2.22.3 5.2 5.3 5.4 5.55.6 5.7

Bundle #

9 Polynomials6 Algebraic Fractions2 Radicals

Standards3.6 5.2 5.3 5.4 5.55.6 5.7 6.1 6.2 6.36.4 6.5 6.6

Bundle #

3 Complex Numbers1 Quadratic Equations4 Conic Sections

Standards3.1 3.3 3.4 3.5 3.74.1 4.2 5.3

Bundle #

8 Logarithms11 Sequences & Series12 Probability

Standards7.3 7.4 7.5 7.6 7.78.1 8.2 8.3 9.1 9.2

Best Practice Methods

SummarizingHomework & PracticeFrequent FeedbackAdvance OrganizersGraphing TechnologyUse of CalculatorsReinforcing EffortSimilarities & Differences

Best Practice Methods

SummarizingHomework & PracticeFrequent FeedbackAdvance OrganizersGraphing TechnologyUse of CalculatorsReinforcing EffortSimilarities & Differences

Best Practice Methods

SummarizingHomework & PracticeFrequent FeedbackAdvance OrganizersGraphing TechnologyUse of CalculatorsReinforcing EffortSimilarities & Differences

Best Practice Methods

SummarizingHomework & PracticeFrequent FeedbackAdvance OrganizersGraphing TechnologyUse of CalculatorsReinforcing EffortSimilarities & Differences

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ALGEBRA II Benchmark #1 – Quadratic EquationsStandard Indicator: Standard 3: Quadratic Equations and Functions; Standard 5:Polynomials3.3, 3.4, 3.5, 5.3, 3.7Declarative Knowledge Procedural Knowledge

Concepts Various ways to solve quadraticequations.

OrganizingIdeas

Students will understand and be able to:1. factor quadratics2. complete square3. use quadratic formula4. graph quadratic equation5. solve word problems6. systems involving quadratics

Processes Factor out perfect squaresPowers of i.Using substitutionCompleting the squareFOILSolving systems of equations

Details Methods of factoringComplete the squareFind the vertex, axis of symmetry,minimum/maximum valuesQuadratic formula

Vocabulary Roots , zeros, solutions, quadratic, vertex,axis of symmetry, minimum, maximum,complex numbers, imaginary numbers,rational & irrational, real numbers,discriminant, conjugate,

Skills Simplify radicalsSimplify complex numbersCreating T-chart

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ALGEBRA II Benchmark #2 - RadicalsStandard Indicator: Standard 3: Quadratic Equations and Functions; Standard 6: AlgebraicFractions3.6, 6.1Declarative Knowledge Procedural Knowledge

Concepts There are rules used forsimplifying radicals, solvingradical equations and equationswith radicals.

OrganizingIdeas

Students will understand:1. the laws of exponents2. simplifying radicals3. methods for solving

radical equations4. methods for solving

equations with radicals

Processes 1. Rules for adding, subtracting, multiplying, and dividingterms with exponents.

2. Rules for multiplying and dividing radicals.

Details Identify parts of rationalexponent(numerator/denominator =power/root)Rules for negative exponents

Vocabulary Square root, cube root, power,exponent, index number, radicals,radicand, fraction, rationalnumber, irrational number

Skills Prime factorizationRecognition of perfect squares, cubes, powers…

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ALGEBRA II Benchmark #3 – Complex NumbersStandard Indicator: Standard 3: Quadratic Equations and Functions

3.1

Declarative Knowledge Procedural KnowledgeConcepts There are rules for adding,

subtracting, multiplying, anddividing complex numbers.

OrganizingIdeas

Students will understand:1. powers of i2. perform operations with

complex numbers

Processes Distributive propertyFOIL

Details Powers of iUsing conjugatesCombining like terms

Vocabulary Conjugates, i, imaginarynumber(s), complex number(s),like terms

Skills Apply rules to simplify complex numbers.

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ALGEBRA II Benchmark #4 – Conic SectionsStandard Indicator: Standard 4: Conic Sections

4.1, 4.2

Declarative Knowledge Procedural KnowledgeConcepts There are unique, but similar,

equations for each conic section.OrganizingIdeas

Students will understand andrecognize the equations for:parabolas, circles, ellipses, andhyperbolas.

Processes Putting equations in standard form.Use the specific parts to graph the various conic sections

Details Various conic sections have specificparts: asymptotes, center, radius,axes, foci, vertices…

Vocabulary parabolas, circles, ellipses, andhyperbolas; asymptotes, center,radius, axes, foci, vertices, diameter,directrix, conjugate axis, transverseaxis, conic, major axis, minor axis,co-vertices,

Skills Completing the squareGraphing equation

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ALGEBRA II Benchmark #5 – Linear SystemsStandard Indicator: Standard 2: Linear and Absolute Value Equations and Inequalities;Standard 3: Quadratic Equations and functions2.2, 2.3Declarative Knowledge Procedural KnowledgeConcepts There are various ways of solving

systems of equations.OrganizingIdeas

Students will be able to use :1. substitution2. elimination3. multiplication4. Cramer’s rule5. graphing

Processes Setting up a determinant

Details Students will pick an appropriatemethod for solving systems of 2 or3 variables.

Vocabulary Coefficient, variable, matrix,opposites, determinants, Cartesiancoordinates, elimination,substitution, Standard Form ofLinear Equation, Slope-InterceptForm, inequality,

Skills Graphing linesCommon multiples (LCM}Evaluating a determinantSubstitution & distributive properties of equalitiesOther properties of equality/inequalitiesKnow symbols of inequality(<,>, not equal, …)Basic operations with matrices

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ALGEBRA II Benchmark # 6 Algebraic FractionsStandard Indicator: Standard 6: Algebraic Fractions

6.2, 6.3, 6.4, 6.5, 6.6Declarative Knowledge Procedural KnowledgeConcepts There are rules for simplifying and

solving equation with algebraicfractions.

OrganizingIdeas

Students will be able todifferentiate between direct,inverse, and joint variation.Students will be able to simplifyalgebraic fractions and solvealgebraic fraction equations.

Processes Operations with algebraic fractionsFinding the constant of variation and using it to solvevariation problems.

Details Rules for adding, subtracting,multiplying and dividing fractions.Rules for factoring

Vocabulary Complex fractions, numerator,denominator, variations(direct,joint, and inverse), means andextremes

Skills Operations with fractions.Solving proportions—means and extremes.Factoring.

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ALGEBRA II Benchmark # 7 – Relations and FunctionsStandard Indicator: Standard 1: Relations and Functions; Standard 2: Linear and AbsoluteValue Equations and Inequalities

1.1, 1.4, 1.5, 1.6, 1.7, 1.8, 2.1, 2.4Declarative Knowledge Procedural KnowledgeConcepts There are many kinds of functions

which can be represented by theirown unique equation and graph.

OrganizingIdeas

Students will identify and graphvarious functions.

Processes

Details Functions are to include:1. linear2. absolute value3. step4. quadratic5. exponential6. piece-wise

Vocabulary Function, step, absolute value,linear, line, quadratic, exponential,piece-wise, scatter plots, best fit,

Skills Recognizing various forms of the functionsAnalyzing graphs for their unique form.Draw and use line of best fit to make a predictionWrite an equation of a line given 2 points.

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ALGEBRA II Benchmark # 8 – Logarithmic FunctionsStandard Indicator: Standard 7: Logarithmic & Exponential Functions

7.3, 7.4, 7.5, 7.6, 7.7Declarative Knowledge Procedural KnowledgeConcepts There are rules used for solving

logarithmic and exponentialfunctions.

OrganizingIdeas

Students will understand:1. the inverse relationship

between exponents andlogarithms

2. How to solve exponentialequations

3. how to use a calculator tofind natural & commonlogs

Processes 1. Rules for converting from one form to another2. Rules for switching bases3. How to use their calculator to find solutions4. How to use a graphing calculator to graph thefunctions5. Rules for solving equations

Details Rules for:1. converting from log form

to exponent form2. converting from one base

to another3. using logarithms

Vocabulary Exponent, logarithm, base, power,inverse, natural log, common log,e,

Skills 1. Solving equations2. Using the Laws of exponents3. Graphing equations

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ALGEBRA II Benchmark # 9 - PolynomialsStandard Indicator: Standard 5: Polynomials5.2, 5.3, 5.4, 5.5, 5.6, 5.7Declarative Knowledge Procedural KnowledgeConcepts There are rules for performing operations with

polynomials. When solving polynomialequations, there are solutions (roots, zeros) tothe equation.

OrganizingIdeas

Students will understand:1. How to divide polynomials by other

polynomials.2. How to solve and factor polynomial

equations3. How to write a polynomial given the

solutions4. The relationship between: solutions, roots,

zeros, x-intercepts of the graph.

Processes Rules for exponentsFinding the GCFDividing by the GCFNaming coefficientsFinding the degree of a term and a polynomialDivide using long divisionDivide using synthetic divisionUsing the ZPP to find the zerosUsing the zeros to write the equations

Details GCFFOILSynthetic divisionLong divisionGraphing equationsZero Product PropertyWriting polynomial equations given solutions

Vocabulary Coefficients, descending order, ascendingorder, degree of a polynomial or term,monomial, polynomial, roots, zeros, trinomial,binomial, solutions, synthetic division

Skills Find the GCFDistributive PropertyFOILGraphing

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ALGEBRA II Benchmark #10 – Relations and FunctionsStandard Indicator: Standard 1: Relations & Functions1.2, 1.3Declarative Knowledge Procedural KnowledgeConcepts There are ways of performing

basic operations with functionsincluding the composition offunctions

OrganizingIdeas

Students will understand:How to add, subtract, multiply,and divide pairs of functions.How to find the composition offunctions

Processes Order of operations within compositions

Details Understand function notation: f(x)= yKnow f _ g = f(g(x))Know properties of equality(commutative, associative, etc.) donot hold for compositions offunctions

Vocabulary Function, commutative property,associative property, distributiveproperty, composition,

Skills Order of operationsEvaluating expressionsFOILRules of exponentsCombining Like Terms

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ALGEBRA II Benchmark #11 – Sequences and SeriesStandard Indicator: Standard 8: Sequences and Series8.1, 8.2, 8.3Declarative Knowledge Procedural KnowledgeConcepts There are formulas used to

determine terms of sequences andsums of series.

OrganizingIdeas

1. Students will understand and beable to find terms in sequences.2. Students will understand and beable to find partial sums ofarithmetic and geometric series

Processes Use the formulas correctly to find the solutions for variousmissing terms

Details Identify initial (first) term, type ofsequence/series, the commondifference or common ratio.Recognize summation notation.Know how to use the formulas.

Vocabulary Sequence, series, geometric,arithmetic, term, commondifference, common ratio,summation notation (epsilon),geometric means, arithmeticmeans

Skills How to use technology to assist in finding solutions.Use the laws (rules) of exponentsKnow the order of operationsSolving equations for a given variable (literal equations)

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ALGEBRA II Benchmark #12 – ProbabilityStandard Indicator: Standard 9: Counting Principles and Probability9.1, 9.2Declarative Knowledge Procedural KnowledgeConcepts There are ways to count the number

of possibilities of a given situation,and determining the probabilities ofa specific event occurring.

OrganizingIdeas

Students will understand and be ableto compute combinations andpermutations.Students will understand and be ableto use combinations andpermutations to computeprobabilities.

Processes Use formulas to correctly find the number of possibilities foran event and the probability that a specific event or series ofevents will occur.

Details 1. There are formulas fordetermining permutations andcombinations of n distinct objectstaken r at a time.2. There are formulas fordetermining the probability ofevents.

Vocabulary Permutation, combination, factorial,probability, event, odds

Skills Use factorial function.Use technology to assist in problem solving.Use formulas correctly.

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Algebra II Assessment Planning GuideEssential Outcome 1: Identify the graphs and equations of the Library of functions.

Summative Assessment: Selected Response

Describe assessment and timeline Method Knowledge Types ofReasoning

PerformanceSkills

Products

Formative: Students will understand and be able to recognize,interpret, and graph various types of functions andrelations (linear, quadratic, exponential, absolutevalue, piecewise, step).Students will understand and find a linear equationof best fit and use it to make predictions.

Timeline: Two weeks

5+ questionmultiple choicequiz

X X

Formative: Students will understand and be able to solve andgraph inequalities.

Timeline: One week

5 questionmultiple choicequiz

X X

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Algebra II Assessment Planning GuideEssential Outcome 2: Do basic operations with functions including composition of functions

Summative Assessment: Selected Response

Describe assessment and timeline Method Knowledge Types of Reasoning Performance Skills Products

Formative: Students willunderstand and use functionnotation. (Add, subtract, multiplyand divide pairs of functions)

Students will understand and usecomposition of functions.

Timeline: ten days

10 questionmultiplechoice quiz

X X

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Algebra II Assessment Planning GuideEssential Outcome 3: Solve systems of equations with two or three variables.Summative Assessment: Selected Response: Use substitution, elimination, and determinants to solve systems of two or three linearequations in two or three variables. Use systems of linear equations and inequalities. (after 3 weeks)Describe assessment and timeline Method Knowledge Types of

ReasoningPerformanceSkills

Products

Formative: Students will understand and usesubstitution, elimination, and determinants to solvesystems of two or three linear equations in two orthree variables.

Timeline: Two weeks

Short answer X X X

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Algebra II Assessment Planning GuideEssential Outcome 4: Divide and factor polynomials and solve polynomial equations.

Summative Assessment: divide polynomials by monomials, divide polynomials by other polynomials using long or syntheticdivision, solve and factor polynomial equations, use graphing technology to find approximate solutions for polynomial equations,use polynomial equations to solve word problems, write a polynomial given its solutions, describe the relationships among thesolutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression.Describe assessment and timeline Method Knowledge Types of

ReasoningPerformance Skills Products

Formative: Divide polynomials bymonomials, divide polynomials byother polynomials using long orsynthetic division.Timeline: Seven days

Short answer(5questions)

X X X

Formative: Solve and factorpolynomial equations, usepolynomial equations to solve wordproblems. Write a polynomial givenits solutions.Timeline: Two weeks

Short answer(10 questions)

X X X

Formative: Use graphingtechnology to find approximatesolutions for polynomial equations,Describe the relationships amongthe solutions of an equation, thezeros of a function, the x-interceptsof a graph, and the factors of apolynomial expression.Timeline: One week

Short answer, 3questions (table:zeros, x-intercepts,factors, etc.)

X X X

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Algebra II Assessment Planning GuideEssential Outcome 5: Do basic operations with rational expressionsSummative Assessment: Students will understand and be able to add, subtract, multiply, divide and simplify algebraic fractions.Students will understand and be able to simplify complex fractionsStudents will understand and be able to solve equations involving algebraic fractionsStudents will understand and be able to solve word problems involving fractional equationsStudents will understand and be able to solve problems of direct, inverse, and joint variation.(3 _ weeks total)Describe assessment and timeline Method Knowledge Types of

ReasoningPerformanceSkills

Products

Formative: Students will understand and beable to add, subtract, multiply, divide andsimplify algebraic fractions. Students willunderstand and be able to simplify complexfractions.Timeline: Two weeks

MultipleChoice

X X X

Formative: Students will understand and beable to solve equations involving algebraicfractions, and be able to solve word problemsinvolving fractional equations.Timeline: One week

Short Answer(Work andmixtureproblems)

X X X

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Algebra II Assessment Planning GuideEssential Outcome 6: Simplify radicals and solve radical equations and equations with radicals. Perform basic operations ofexponents including rational and negative exponents.Summative Assessment: Students will understand and be able to simplify radicalsStudents will understand and be able to solve equations that contain radical expressions.Students will understand and use negative and fractional exponentsDescribe assessment and timeline Method Knowledge Types of Reasoning Performance Skills Products

Formative: Students will understandand be able to simplify radicals;students will understand and usenegative and fractional exponents.Timeline: Two weeks

10 question,short answer

X X X

Formative: Students will understandand be able to solve equations thatcontain radical expressions.Timeline: One week

5 questions,short answer

X X X

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Algebra II Assessment Planning GuideEssential Outcome 7: Add, subtract, multiply, and divide complex numbersSummative Assessment: Student will understand and be able to define complex numbers and perform basic operations with themDescribe assessment and timeline Method Knowledge Types of

ReasoningPerformanceSkills

Products

Formative: Student will understand and beable to define complex numbers and performbasic operations with them.Timeline: One week

MultipleChoice

X X X

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Algebra II Assessment Planning GuideEssential Outcome 8: Solve quadratic equationsSummative Assessment: Factor quadratics, complete the square, use the quadratic formula to find various types of solutionsincluding complex, graph a quadratic equation, solve word problems using quadratic equations, and solve pairs of equations, onequadratic and one linear or both quadratic.Describe assessment and timeline Method Knowledge Types of

ReasoningPerformanceSkills

Products

Formative: Students will understand and be ableto factor quadratics, complete the square, and usethe quadratic formula to find various types ofsolutions including complex.Timeline: Two weeks

X X X

Formative: Students will understand and grapha quadratic equation, solve word problems usingquadratic equations, and solve pairs of equations,one quadratic and one linear or both quadratic.Timeline: Two weeks

X X X

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Algebra II Assessment Planning GuideEssential Outcome 9: Graph conic sections and identify their partsSummative Assessment: Students will understand and be able to write the equation of conic sections (circle, ellipse, parabola, andhyperbola.). Students will understand and be able to graph and identify the parts of conic sections.Describe assessment and timeline Method Knowledge Types of

ReasoningPerformanceSkills

Products

Formative: Students will understand and be able to writethe equation of parabolas. Students will understand and beable to graph and identify the parts of a parabola.Timeline: 7 days

Given anequation,put in thecorrectform, findthe partsand graph.

X X X X

Formative: Students will understand and be able to writethe equation of circles, ellipses, & hyperbolas. Studentswill understand and be able to graph and identify the partsof these conic sections. Decide the conic type.Timeline: 7 days

Given anequation,put in thecorrectform, findthe partsand graph.

X X X X

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Algebra II Assessment Planning GuideEssential Outcome 10: Solve logarithmic equationsSummative Assessment: Students will understand and be able to use the inverse relationship between exponents and logarithms.Students will understand and be able to solve logarithmic and exponential equations and inequalities.Students will understand and be able to use calculators to find decimal approximations of natural and common logarithmic numericexpressionsDescribe assessment and timeline Method Knowledge Types of

ReasoningPerformanceSkills

Products

Formative: Students will understand andbe able to use the inverse relationshipbetween exponents and logarithms, solvelogarithmic and exponential equations andinequalities and be able to use calculatorsto find decimal approximations of naturaland common logarithmic numericexpressionsTimeline: 10 days

Short answer X X X

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Algebra II Assessment Planning GuideEssential Outcome 11: Define and use arithmetic and geometric sequences and series.Summative Assessment: Students will understand and be able to find terms in sequences. Students will understand and be able tofind partial sums of arithmetic and geometric series.Describe assessment and timeline Method Knowledge Types of

ReasoningPerformanceSkills

Products

Formative: Students will understand and be ableto find terms in sequences. Students willunderstand and be able to find partial sums ofarithmetic and geometric series.Timeline: 10 days

Short Answer X X X

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Algebra II Assessment Planning GuideEssential Outcome 12: Use the counting principle to compute combinations, permutations, and probabilities.Summative Assessment: Students will understand and be able to compute combinations and permutations. Students will understandand be able to use combinations and permutations to compute probabilities.Describe assessment and timeline Method Knowledge Types of

ReasoningPerformanceSkills

Products

Formative: Students will understand and be ableto compute combinations and permutations.Students will understand and be able to usecombinations and permutations to computeprobabilities.Timeline: 10 days

Short Answer X X X

July 2009