Essential Skills: Algebra II - Michigan City Area Schools€¦ · 1 Essential Skills: Algebra II 1)...
Transcript of Essential Skills: Algebra II - Michigan City Area Schools€¦ · 1 Essential Skills: Algebra II 1)...
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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