St. Lucie County Public Schools Mathematics Scope and Sequence ...

St. Lucie County Public Schools Mathematics Scope and Sequence 2012-13 SYCourse: Algebra II Course Code: 1200330 Quarter: 2.1Topic of Study: Quadratic Functions and EquationsIncluded Standards: MA.912.A.2.7, MA.912.A.2.10, MA.912.A.2.6, MA.912.A.10.3, MA.912.A.7.6,MA.912.A.7.3, MA.912.A.7.5, MA.912.A.7.4, MA.912.A.1.6Learning Goals: Students will understand quadratic functions and equations and be able tosolve quadratic functions and equations.Pacing Guide: 24 days/12 blocksCommon Core Standard Sheet Math Routine SyllabusNGSSSMathematical Practices(MACC.K12.MP)1. Make sense of problems andpersevere in solving them.2. Reason abstractly andquantitatively.3. Construct viable arguments andcritique the reasoning of others.4. Model with mathematics.5. Use appropriate toolsstrategically.6. Attend to precision.7. Look for and make use ofstructure.8. Look for and express regularity inrepeated reasoning.MA.912.A.2.7Perform operations (addition,subtraction, division, andmultiplication) of functionsalgebraically, numerically, andgraphically. (I,R)MA.912.A.2.10Describe and graph transformationsof functions. (I, R)INSTRUCTIONAL IMPLICATIONS(EXAMPLES/ SKILLS)Essential Vocabulary:coordinate plane, origin, y-axis, x-axis,ordered pair, quadrants, relation,domain, range, linear, expression,equation, inequalities, absolute value, nosolution, order of operations, literalequations, isolateRemarks/Examples:Example:Let f(x)=7x+2 and g(x)=x². Find f(x)*g(x)Depth of Knowledge:ModerateRemarks/Examples:Example: Describe how you would graphfrom the graph ofTargetsELA Standards (embedded)LACC.910.RST.2.4/LACC.1112.RST.2.4(Vocabulary Development)Determine the meaning of symbols, key terms,and other domain-specific words and phrases asthey are used in a specific scientific or technicalcontext relevant to grades 9-12 texts and topics.LACC.910.RST.3.7 (Multi-Media)Translate quantitative or technical informationexpressed in words in a text into visual form (e.g.,a table or chart) and translate informationexpressed visually or mathematically (e.g., in anequation into words).LACC.1112.RST.3.7 (Multi-Media)Integrate and evaluate multiple sources ofinformation presented in diverse formats andmedia (e.g., quantitative data, video, multimedia)in order to address a question or solve a problem.Use order of operations to combinefunctional equations.Use graphs to show the results ofoperations on the functions.Represent functions algebraically.Represent functions numerically.Represent functions graphically.Describe the transformations ofquadratic functions.Graph the transformations of functions.MA.912.A.2.6Identify and graph commonfunctions (including but not limitedto linear, rational, quadratic, cubic,radical, absolute value). (I, R).Depth of Knowledge:ModerateRemarks/Examples:Example 1:Graph , and.Depth of Knowledge:ModerateIdentify quadratic functions.Grade Algebra 2 Qtr. 2 Page 1 of 5

St. Lucie County Public Schools Mathematics Scope and Sequence 2012-13 SYMA.912.A.10.3Decide whether a given statementis always, sometimes, or never true(statements involving linear orquadratic expressions, equations, orinequalities, rational or radicalexpressions, or logarithmic orexponential functions). (I, R)MA.912.A.7.6Identify the axis of symmetry,vertex, domain, range, andintercept(s) for a given parabola.(I, R, M)MA.912.A.7.3Solve quadratic equations over thereal numbers by completing thesquare. (I, R, M)MA.912.A.7.4Use the discriminate to determinethe nature of the roots of aquadratic equation. (I, R, M)MA.912.A.7.5Solve quadratic equations over thecomplex number system.(I, R, M)MA.912.A.1.6Identify the real and imaginary partsof complex numbers and performbasic operations. (I, R)Remarks/Examples:Example 1:Is the statement true for all x,for some x, or for no x?Depth of Knowledge:HighRemarks/Examples:Example 1:Identify the axis of symmetry, vertex, domain,range, and intercepts for the graph ofDepth of Knowledge:LowRemarks/Examples:Example 1:Solve the following equation for x:Depth of Knowledge:ModerateRemarks/Examples:Example 1:Use the discriminant to determine whetherhas distinct real roots.Depth of Knowledge:LowRemarks/Examples:Example 1:Solve the following equation for x over the set ofcomplex numbers:Depth of Knowledge:ModerateRemarks/Examples:Example 1:Multiply (7-4i)(10+6i).Depth of Knowledge:ModerateTest mathematical statements by usingsubstitution.Test mathematical statements by usinglogic.Test mathematical statements by usingmathematical principles.Test to see if statements are true undersome conditions, never true, or alwaystrue.Identify the axis of symmetry of aparabola.Identify the vertex of a parabola.Identify the domain of a parabola.Identify the intercepts for aparabola.Solve quadratic equations usingcompleting the square.Solve for the discriminate.Use the discriminate to determinethe nature of the roots of thequadratic.Solve quadratic equations over thecomplex number system.Understand when imaginary numbersoccur.NOTE: Operations with imaginary numberswill not be taught in the quarter. Just theunderstanding of when discriminates arenegative, then they create imaginarynumbers.Grade Algebra 2 Qtr. 2 Page 2 of 5

St. Lucie County Public Schools Mathematics Scope and Sequence 2012-13 SYCourse: Algebra II Course Code: 1200330 Quarter: 2.2Topic of Study: Polynomials and Polynomial FunctionsIncluded Standards: MA.912.A.2.6, MA.912.A.4.5, MA.912.A.4.8, MA.912.A.4.3, MA.912.A.4.7,MA.912.A.4.9, MA.912.A.4.10, MA.912.A.4.4, MA.912.A.4.6Learning Goals: Students will understand polynomials and be able to solve polynomials andpolynomial functions.Pacing Guide: 21 days/10 blocksNGSSSMathematical Practices(MACC.K12.MP)1. Make sense of problems andpersevere in solving them.2. Reason abstractly andquantitatively.3. Construct viable arguments andcritique the reasoning of others.4. Model with mathematics.5. Use appropriate toolsstrategically.6. Attend to precision.7. Look for and make use ofstructure.8. Look for and express regularity inrepeated reasoning.MA.912.A.2.10Describe and graph transformationsof functions. (I, R)MA.912.A.2.6Identify and graph commonfunctions (including but not limitedto linear, rational, quadratic, cubic,radical, absolute value). (I, R)MA.912.A.10.3Decide whether a given statementis always, sometimes, or never true(statements involving linear orquadratic expressions, equations, orinequalities, rational or radicalexpressions, or logarithmic orexponential functions). (I, R)INSTRUCTIONAL IMPLICATIONS(EXAMPLES/ SKILLS)Essential Vocabulary:Polynomial functions, end behaviors,domain, range, roots, intercepts, factors,polynomials, expressions, complex roots,synthetic division, Rational RootTheorem, Conjugate Root Theorem,zeros, Fundamental Theorem of AlgebraRemarks/Examples:Example: Describe how you would graphfrom the graph of .Depth of Knowledge:ModerateRemarks/Examples:Example 1:Graph , and.Depth of Knowledge:ModerateRemarks/Examples:Example 1:Is the statement true for all x,for some x, or for no x?Depth of Knowledge:HighTargetsELA Standards (embedded)LACC.910.RST.2.4/LACC.1112.RST.2.4(Vocabulary Development)Determine the meaning of symbols, key terms,and other domain-specific words and phrases asthey are used in a specific scientific or technicalcontext relevant to grades 9-12 texts and topics.LACC.910.RST.3.7 (Multi-Media)Translate quantitative or technical informationexpressed in words in a text into visual form (e.g.,a table or chart) and translate informationexpressed visually or mathematically (e.g., in anequation into words).LACC.1112.RST.3.7 (Multi-Media)Integrate and evaluate multiple sources ofinformation presented in diverse formats andmedia (e.g., quantitative data, video, multimedia)in order to address a question or solve a problem.Describe the transformations ofquadratic functions.Graph the transformations of functions.Identify cubic functions.Test mathematical statements by usingsubstitution.Test mathematical statements by usinglogic.Test mathematical statements by usingmathematical principles.Test to see if statements are true undersome conditions, never true, or alwaystrue.Grade Algebra 2 Qtr. 2 Page 3 of 5

St. Lucie County Public Schools Mathematics Scope and Sequence 2012-13 SYMA.912.A.4.3Factor polynomial expressions.(I, R, M)MA.912.A.4.4Divide polynomials by monomialsand polynomials with varioustechniques, including syntheticdivision. (I, R, M)Remarks/Examples:Example 1:Example 2:Example 3:Depth of Knowledge:ModerateRemarks/Examples:Example 1: SimplifyExample 2:Use Greatest Common Factor to factorpolynomial expressions.Use grouping to factor polynomialexpressions.Use difference of squares to factorpolynomial expressions.Use the roots to factor polynomialexpressions.Divide polynomials by monomials.Divide polynomials by polynomials.Use synthetic division to divide.Use long division to divide.Factor polynomials to divide.Example 3: Use synthetic division toMA.912.A.4.5Graph polynomial functions withand without technology anddescribe end behavior. (I, R, M)divideby x+3.Depth of Knowledge:ModerateRemarks/Examples:End behavior may be interpreted asbehavior of the function for very largepositive or negative(absolutely)independent variables.Example 1:Graph the following equation:Graph polynomial functions.Describe end behavior.Example 2:Describe the end behavior for the graphof the following equationMA.912.A.4.6Use theorems of polynomialbehavior (including but not limitedto the Fundamental Theorem ofAlgebra, Remainder Theorem, theRational Root Theorem, Descartes'Rule of Signs, and the ConjugateRoot Theorem) to find the zeros of apolynomial function. (I, R, M)Depth of Knowledge:ModerateRemarks/Examples:Example 1:Given that 4 is a zero of the polynomial, use syntheticdivision to find the remaining zeros of thepolynomial.Example 2:Use the Remainder Theorem to evaluateat x=3.Explain your solution method.Example 3:Use the Rational Root Theorem todetermine the possible rational roots ofthe equation .Example 4:Use Descartes' Rule of Signs todetermine the possible number of positivereal zeros and negative real zeros of thefollowing polynomial function:Use theorems of polynomial behavior tofind zeroes of a polynomial function.Use Fundamental theorem of Algebra tofind roots.Use Remainder Theorem to find zeros ofa function.Use Rational Root Theorem to find zerosof a function.Use Descartes’ Rules of Signs to findzeros of a function.Use Conjugate Root Theorem to findzeros of a function.Depth of Knowledge:ModerateGrade Algebra 2 Qtr. 2 Page 4 of 5

St. Lucie County Public Schools Mathematics Scope and Sequence 2012-13 SYMA.912.A.4.8Describe the relationships amongthe solutions of an equation, thezeros of a function, the x-interceptsof a graph, and the factors of apolynomial expression with andwithout technology. (I, R, M)MA.912.A.4.9Use graphing technology to findapproximate solutions forpolynomial equations. (I, R, M)MA.912.A.4.10Use polynomial equations to solvereal-world problems. (I, R, M)Remarks/Examples:Example 1:Use technology to find the solutions ofthe following equation:Relate your results to the graph of thefunctionDepth of Knowledge:ModerateRemarks/Examples: Example:Approximate the solution(s) ofto thenearest thousandth.Depth of Knowledge: LowRemarks/Examples: Example: Youwant to make an open-top box with avolume of 500 square inches from apiece of cardboard that is 25 inches by 15inches by cutting squares from thecorners and folding up the sides. Find thepossible dimensions of the box.Depth of Knowledge: LowDescribe the relationship betweensolutions, zeros, intercepts, and factorsof an equation.Understand how to use technology tograph functions.Use technology to find solutions ofpolynomials.Solve real world problems involvingpolynomials.Grade Algebra 2 Qtr. 2 Page 5 of 5