Scope and Sequence Report...Geometry - Unit #2 This chapter focuses on the role of reasoning in geometry. Students compare and contrast inductive and deductive reasoning and learn

Scope and Sequence Report

District: Susquenita School District, School: Susquenita High School, Year: 2019-2020, Grade Level: 12, Subject: Mathematics,

Unit Name Start/End Unit Description / Overview Stage 1: Desired Results:Understandings: (Big Ideas)

Stage 1: Desired Results: EssentialQuestions

Standards

Mathematics - ACGeometry - Unit#1

In plane geometry, all definitions are basedupon three basic terms and measurementsare used to classify angles and segments.

Geometry is logically built upon a few basicaxioms and undefined terms.

1. What are the 3 basic terms in Geometry?2. How do you use segment postulates todetermine congruent segments? 3. How doyou find the distance and midpoint between2 points in the coordinate plane? 4. How doyou name, measure, and classify angles? 5.How are pairs of angles classified? 6. Howcan polygons be classified by their sides andangles?

G.1.2.1.4. Identify and/or use properties ofregular polygons.G.2.1.2.1. Calculate the distance and/ormidpoint between two points on a numberline or on a coordinate plane.G.2.1.2.3. Use slope, distance, and/ormidpoint between two points on a coordinateplane to establish properties of atwo-dimensional shape.G.2.2.1.1. Use properties of angles formedby intersecting lines to find the measures ofmissing angles.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.3.HS.A.4. Apply the concept ofcongruence to create geometricconstructions.


This chapter focuses on the role of reasoningin geometry. Students compare and contrastinductive and deductive reasoning and learnthe importance of counterexamples indisproving statements. They analyzeconditional statements, learning to identifythe hypothesis and conclusion of a statementand write the converse, inverse, andcontrapositive. Reasoning using propertiesfrom algebra serves as a starting point forreasoning using theorems and postulatesfrom geometry. Students write two-columnproofs about segments and angles, aboutangles formed by intersecting lines, andabout important angle pair relationships.

Use of inductive and deductive reasoning toprovide proof and reasoning to an argument.

1. What is inductive reasoning? How do youuse inductive reasoning to complete apattern? 2. How do you write the converse,inverse, and contrapositive of a conditionalstatement? How do you write a biconditionalstatement? 3. What is deductive reasoning?How do we use deductive reasoning to forma logical argument? 4. What postulatesdescribe the relationships between points,lines, and planes? 5. How can you usealgebraic properties to prove statements ingeometry? 6. What are the steps in creating aformal 2-column proof? 7. How can youidentify and prove relationships betweenpairs of angles?

A1.1.2.1.2. Use and/or identify an algebraicproperty to justify any step in anequation-solving process.G.1.3.2.1. Write, analyze, complete, oridentify formal proofs (e.g., direct and/orindirect proofs/proofs by contradiction).CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.


Correctly id 1. How do we classify A

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This unit focuses on identifying both paralleland perpendicular lines in order to classifynew angle relationships formed from boththose line pairs and transversals while alsoproving that lines are parallel orperpendicular using the proof forms fromUnit 02. The final half of the unit ties inconcepts of linear equations and slope fromAlgebra I into the Geometry space.

entify angle relationships and theircharacteristics to prove parallel orperpendicular lines.

pairs of angles formed by two lines and atransversal? 2. Given parallel orperpendicular lines, what properties aboutangle pairs can be proven? 3. How can linesbe proven parallel or perpendicular? 4. Howcan slope be used to determine if lines areparallel or perpendicular? 5. How do youcreate, graph, and interpret the equation of aline? 6. What are the relationships betweensets of parallel and/or perpendicular lines?How do you find the distance between twoparallel lines?

1.2.2.1.3. Write or identify a linear equationwhen givenA1.2.2.1.4. Determine the slope and/ory-intercept represented by a linear equationor graph.G.2.2.1.1. Use properties of angles formedby intersecting lines to find the measures ofmissing angles.G.2.2.1.2. Use properties of angles formedwhen two parallel lines are cut by atransversal to find the measures of missingangles.


The focus of this unit is congruent triangles.Students will identify the types of trianglesby angle and side and how to properly writecongruence statements of triangles. Once thefoundational knowledge is laid out, studentswill learn to prove triangles congruent to oneanother using the various trianglecongruence theorems and postulates.Students will utilize proofs in this unit andcontinue to build upon their logic andreasoning skills from previous units.Students will also use rigid transformationsto explain congruence between triangles.

Understand and identify properties oftriangles in order to prove them congruent.

1. How do you classify triangles by sidesand angles? 2 How do you determine ifshapes are identical? 3. How do you use thesides of a triangle to determine congruency? 4. How do you use SAS and HL to provethat two triangles are congruent? 5. How doyou use ASA and AAS to prove that twotriangles are congruent? 6. What is CPCTCand how is it used to prove that parts of twotriangles are congruent? 7. How do you usethe properties of isosceles and equilateraltriangles to find measures in a triangle? 8.How do you use transformations to createcongruent figures?

G.1.2.1.1. Identify and/or use properties oftriangles.G.1.3.1.1. Identify and/or use properties ofcongruent and similar polygons or solids.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.3.HS.A.2. Apply rigid transformationsto determine and explain congruence.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.CC.2.3.HS.A.4. Apply the concept ofcongruence to create geometricconstructions.


This unit focuses on relationships withintriangles using special segments. Studentswill use these various special segments toidentify special characteristics of trianglesand to find angle and side lengths. Studentswill also use properties of opposite anglesand sides to identify types of triangles.

Use special segments to identify propertieswithin triangles.

1. What properties exist for the midsegmentof a triangle? 2. What are the perpendicularbisectors of a triangle and how can they beused to solve problems? 3. What are theangle bisectors of a triangle and how canthey be used to solve problems? 4. What arethe medians and altitudes of a triangle? 5.How can you determine if a triangle ispossible from 3 given sides? 6. How do youuse inequalities to make comparisons in twotriangles?

G.1.2.1.1. Identify and/or use properties oftriangles.G.1.2.1.3. Identify and/or use properties ofisosceles and equilateral triangles.G.1.3.1.2. Identify and/or use proportionalrelationships in similar figures.G.1.3.2.1. Write, analyze, complete, oridentify formal proofs (e.g., direct and/orindirect proofs/proofs by contradiction).CC.2.3.HS.A.11. Apply coordinategeometry to prove simple geometrictheorems algebraically.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.


This unit focuses on similarity of polygons,specifically triangles. Students will lear

Understand how to use similarity theoremsto prove similar triangles and how toidentify similar polygons.

1. What makes polygons similar? 2. Howcan AA be used to prove triangles aresimilar? 3. How can SAS and SSS be usedto prove similar triangles? 4. What is thetriangle proportionality theorem? 5. How doyou use scale factors to perform dilations?

G.1.2.1.1. Identify and/or use properties oftriangles.G.1.3.1.1. Identify and/or use properties ofcongruent and similar polygons or solids.G.1.3.1.2. Identify and/or use proportionalrelationships in










n about how proportions can be used toidentify similar polygons. They'll alsoidentify similar triangles through similaritytheorems and show how polygons canbecome similar through transformations.

similar figures.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.CC.2.3.HS.A.5. Create justifications basedon transformations to establish similarity ofplane figures.CC.2.3.HS.A.6. Verify and apply theoremsinvolving similarity as they relate to planefigures.


This unit focuses on right triangles andtrigonometry. Students will find missing sidelengths of right triangles using thePythagorean Theorem. They will also solveright triangles of various sizes usingtrigonometric ratios and inversetrigonometric ratios.

Using the Pythagorean theorem andtrigonometric ratios to solve right trianglesand problems related to right triangles.

1. How do you write a square root insimplest radical form? 2. How can theconverse of the Pythagorean Theorem beused to identify a type of triangle? 3. Whatis the Geometric Mean and how is it used? 4. How do you use the ratios of the sides oftwo special right triangles to solve problemsmore efficiently? 5. How do you apply thetangent ratio to find a missing side in a righttriangle? 6. How do you use the sine andcosine ratios to solve problems? 7. How doyou use the inverse tangent, sine, and cosineratios to solve a right triangle?

G.1.2.1.1. Identify and/or use properties oftriangles.G.1.3.1.2. Identify and/or use proportionalrelationships in similar figures.G.2.1.1.1. Use the Pythagorean theorem towrite and/or solve problems involving righttriangles.G.2.1.1.2. Use trigonometric ratios to writeand/or solve problems involving righttriangles.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.CC.2.3.HS.A.7. Apply trigonometric ratiosto solve problems involving right triangles.


This unit focuses on quadrilaterals. Studentswill learn to classify the various types ofquadrilaterals by angle, side, and theirunique characteristics. They'll also use thesecharacteristics to solve problems.

Use properties of quadrilatrals to identifysuch polygons and solve problems related tothese quadrilaterals.

1. How do you find angle measures inpolygons? 2. What are the properties ofparallelograms? 3. How can you prove thata quadrilateral is a parallelogram? 4. Whatare the properties of rhombuses, rectangles,and squares? 5. What are the properties oftrapezoids and kites? 6. How can youidentify special quadrilaterals?

G.1.2.1.2. Identify and/or use properties ofquadrilaterals.G.1.2.1.4. Identify and/or use properties ofregular polygons.CC.2.3.HS.A.11. Apply coordinategeometry to prove simple geometrictheorems algebraically.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.


Relationships between segments, lines,angles, in circles

Many relationships exist between a circleand its segments.

How is the tangent of a circle related to thecircle’s radius at the point of tangency? How do you find the measure of an arc usinga central angle? How do you use therelationships of a

G.1.1.1.1. Identify, determine, and/or use theradius, diameter, segment, and/or tangent ofa circle.G.1.1.1.










rcs and chords in a circle to find missingparts of a circle? How is the measure of acentral angle and an inscribed angle relatedto the measure of the intercepted arc? Howdo you find measures of angles inside oroutside a circle? How do you find themeasure of the secant, tangent, and externalsegments related to circles? How do youwrite equations of circles in the coordinateplane?

2. Identify, determine, and/or use the arcs,semicircles, sectors, and/or angles of acircle.G.1.1.1.3. Use chords, tangents, and secantsto find missing arc measures or missingsegment measures.

Mathematics -Algebra 2 - Unit#1

01 - QUADRATIC FUNCTIONS &FACTORING - Graph and write quadraticfunctions, solve quadratic equations using avariety of methods, perform operations withsquare roots and complex numbers.

Factoring quadratics Solving quadraticsGraphing quadratics

How do you graph quadratic functions instandard form? How do you graph quadraticfunctions in vertex form & intercept form?How do you solve simple quadraticequations by factoring? How do you solvemore complex quadratic equations byfactoring? How do you solve quadraticequations by finding square roots? How doyou perform operations with complexnumbers? How do you solve quadraticequations by completing the square? How doyou use the quadratic formula & thediscriminant? How do you solve & graphquadratic inequalities?

A2.1.3.1.1. Write and/or solve quadraticequations (including factoring and using theQuadratic Formula).A2.2.1.1.4. Identify and/or determine thecharacteristics of an exponential, quadratic,or polynomial function (e.g., intervals ofincrease/decrease, intercepts, zeros, andasymptotes).A2.2.2.1.1. Create, interpret, and/or use theequation, graph, or table of a polynomialfunction (including quadratics).CC.2.1.HS.F.7. Apply concepts of complexnumbers in polynomial identities andquadratic equations to solve problems.CC.2.2.HS.C.5. Construct and comparelinear, quadratic, and exponential models tosolve problems.CC.2.2.HS.D.4. Understand the relationshipbetween zeros and factors of polynomials tomake generalizations about functions andtheir graphs.


02 - POLYNOMIALS & POLYNOMIALFUNCTIONS - Graph polynomial functions,perform operations with polynomials, solvepolynomial equations and find zeros.

Graph polynomials Polynomial operationsPolynomial equations Find zeros

How do you simplify algebraic expressionswith exponents? How do you evaluate andgraph polynomial functions? How do youadd, subtract & multiply polynomials? Howdo you factor & solve polynomial equations?If you know one zero of a polynomialfunction, how do you find the other one(s)?How do you find all the zeros of apolynomial function when the L.C. is 1?How do you determine the possible numberof positive, negative & imaginary zeros of apolynomial function? How do you determineif a graph has a local maximum or localminimum?

A1.1.1.3. Use exponents, roots, and/orabsolute values to solve problems.A1.1.1.5. Simplify expressions involvingpolynomials.A2.1.2.1. Use exponents, roots, and/orabsolute values to represent equivalentforms or to solve problems.A2.1.2.2. Simplify expressions involvingpolynomials.CC.2.2.HS.D.3. Extend the knowledge ofarithmetic operations and apply topolynomials.CC.2.2.HS.D.4. Understand the relationshipbetween zeros and factors of polynomials tomake generalizations about functions andtheir graphs.








03 - RATIONAL EXPONENTS &RADICAL FUNCTIONS - Use rationalexponents, perform function operations,finding inverse functions, graph & solveradical equations.

Solve radical functions Graph radicalfunctions Solve inverse functions Graphinverse functions

What is the relationship between nth roots &rational exponents? How are the propertiesof rational exponents related to theproperties of integer exponents? Whatoperations can be performed on a pair offunctions to obtain a third function? How doyou find the inverse relation of a givenfunction? What do the graphs of square root& cube root functions look like? Why is itnecessary to check every apparent solutionof a radical equation in the originalequation?

A2.2.1.1.3. Determine the domain, range, orinverse of a relation.M08.B-F.1.1. Define, evaluate, and comparefunctions displayed algebraically,graphically, or numerically in tables or byverbal descriptions.M08.B-F.1.1.2. Compare properties of twofunctions, each represented in a differentway (i.e., algebraically, graphically,numerically in tables, or by verbaldescriptions).CC.2.1.HS.F.1. Apply and extend theproperties of exponents to solve problemswith rational exponents.CC.2.2.HS.C.8. Choose trigonometricfunctions to model periodic phenomena anddescribe the properties of the graphs.CC.2.2.HS.D.4. Understand the relationshipbetween zeros and factors of polynomials tomake generalizations about functions andtheir graphs.CC.2.2.HS.D.6. Extend the knowledge ofrational functions to rewrite in equivalentforms.


04 - EXPONENTIAL & LOGARITHMICFUNCTIONS - Exponential & logarithmicfunctions being used to model real worldsituations.

Exponential functions & equationsLogarithmic functions & equations

What does the graph of an exponentialgrowth function look like? How do you useexponential growth functions? What doesthe graph of an exponential decay functionlook like? How do you use exponentialdecay functions? When is the natural base euseful? How do you evaluate logarithms?How do you graph logarithmic functions?How do you rewrite & solve logarithmicexpressions using the logarithmicproperties? How do you solve exponential &logarithmic equations? Why do logarithmicequations sometimes have extraneoussolutions? How do you determine whether aset of data fits an exponential pattern or apower pattern?

A2.2.2.1. Create, interpret, and/or usepolynomial, exponential, and/or logarithmicfunctions and their equations, graphs, ortables.A2.2.2.1.2. Create, interpret, and/or use theequation, graph, or table of an exponential orlogarithmic function (including common andnatural logarithms).A2.2.2.1.3. Determine, use, and/or interpretminimum and maximum values over aspecified interval of a graph of a polynomial,exponential, or logarithmic function.A2.2.2.1.4. Translate a polynomial,exponential, or logarithmic function fromone representation of a function to another(graph, table, and equation).


05 - RATIONAL FUNCTIONS - Focus ison graphing rational functions, performingoperations with rational expressions, andsolving rational equations.

Direct, inverse, & joint variationDiscontinuous graphs Rational expressionsRational functions, graphs, & equations

What are the differences between direct,inverse & joint variatio

A2.1.2.1.1. Use exponential expressions torepresent rational numbers.A2.1.2.2.2. Simplify rational algebraicexpressions.A2.1.










n? How do you graph simple rationalfunctions? How do you find vertical &horizontal asymptotes of a rational function?How do you multiply & divide rationalexpressions? How do you add & subtractrational expressions with differentdenominators? How do you simplify acomplex fraction? What are the steps forsolving rational equations? How do youcompare functions represented in differentways?

3.1.2. Solve equations involving rationaland/or radical expressions (e.g., 10/(x + 3) +12/(x � 2) = 1 or ?((x^2) + 21x) = 14).A2.2.1.1.3. Determine the domain, range, orinverse of a relation.

Mathematics - APCalculus - Unit #1

Limits will be investigated graphically,numerically, and analytically. Techniques todetermine end behavior of graphs offunctions will be studied.

How can we use the concept of limits toinvestigate the continuity of functions?

How can you find a limit graphically andnumerically? How can you evaluate a limitalgebraically? How do you show that afunction is continuous? What informationdoes the Intermediate Value Theorem giveus about functions that are continuous on aclosed interval? How can you determinecontinuity at a point and on an openinterval? How do you find limits at Infinity?How do you find and sketch verticalasymptotes of the graph of a function?

CC.2.2.HS.D.3. Extend the knowledge ofarithmetic operations and apply topolynomials.CC.2.2.HS.D.5. Use polynomial identities tosolve problems.CC.2.2.HS.D.6. Extend the knowledge ofrational functions to rewrite in equivalentforms.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


There are various methods and techniquesfor finding derivatives of functions. Theserules can be applied to calculate quantitiessuch as velocity, acceleration, and the ratesof change of two or more variables.

How do you find derivatives of functions? How do you find the slope of a tangent lineto a curve at a point? How do you find thederivative of a function using the limitdefinition? What is the relationship betweendifferentiability and continuity? How do youfind the derivative of a function using thebasic differentiation rules? How do you findthe derivative of a function using theProduct Rule and the Quotie

CC.2.2.HS.D.2. Write expressions inequivalent forms to solve problems.CC.2.2.HS.D.3. Extend the knowledge ofarithmetic operations and apply topolynomials.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use of





nt Rule? How do you find the derivative of afunction using the Chain Rule? How do youfind the derivative of a function using theGeneral Power Rule? How do you find thederivative of a function using implicitdifferentiation? How do you find a relatedrate? How can we apply techniques ofimplicit differentiation to find the rates ofchange of two or more variables that arechanging over time?

structure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Calculus techniques will be used to analyzegraphs of functions. The derivative of afunction will be used to determine maximumand minimum values of a function.Differentiation techniques will be used tosolve applied maximum and minimumproblems.

How can we use techniques of integration tosolve applied maximum and minimumproblems?

What are Extrema and how do you findthem? Under what conditions are weguaranteed a maximum and a minimum?What conclusions can be drawn if the MeanValue Theorem can be applied to a functionover a certain interval? How is the firstderivative test used to find extrema of afunction? How do we determine intervals onwhich a function is increasing or decreasing?How is the second derivative test used tofind extrema of a function? How can thesecond derivative be used to determine theconcavity of a function? How can youdetermine limits at infinity? How can youuse the slope of a curve to help graph afunction? How do you use Calculus to solveapplied maximum and minimum problems?How do we find tangent lineapproximations?

CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.2.HS.D.3. Extend the knowledge ofarithmetic operations and apply topolynomials.CC.2.2.HS.D.4. Understand the relationshipbetween zeros and factors of polynomials tomake generalizations about functions andtheir graphs.CC.2.2.HS.D.6. Extend the knowledge ofrational functions to rewrite in equivalentforms.CC.2.2.HS.D.7. Create and graph equationsor inequalities to describe numbers orrelationships.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Technique How can we determine the area under acurve?

What are antiderivatives? How canintegration be used to fin

CC.2.2.HS.D.3. Extend the knowledge ofarithmetic operations and apply topolynomials.CC.2.2.HS.D.4. Understand the relationshipbetween zeros and





s for approximating and finding the exactvalue for the area under a curve will bestudied. Integration rules will be utilized todetermine the average value of a functionand the position function.

d the particular solution to a differentialequation? How can we use Riemann Sumsto estimate the area under a curve? How canwe use limits to evaluate a definite integral?What is the Fundamental Theorem ofCalculus? What are techniques ofintegration? What are the different ways toapproximate a definite integral? How can weuse substitution to find the antiderivatives ofcomposite functions?

factors of polynomials to makegeneralizations about functions and theirgraphs.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Properties, derivatives, and anti-derivativesof Logarithmic, Exponential, and OtherTranscendental Functions will be explored.

What are the Properties, Derivatives andAntiderivatives of TranscendentalFunctions?

How do you find derivatives of logarithmicfunctions? How do you find and evaluatedefinite integrals of logarithmic functions?How do you find derivatives and integrals ofexpressions with “e”? How do you findderivatives of inverse trig functions? Howdo you find integrals of inverse trigfunctions? How do you find the derivativesof inverse functions? How can you useL'Hopital's Rule to determine the limit of arational function?

CC.2.1.HS.F.1. Apply and extend theproperties of exponents to solve problemswith rational exponents.CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.2.HS.D.2. Write expressions inequivalent forms to solve problems.CC.2.2.HS.D.6. Extend the knowledge ofrational functions to rewrite in equivalentforms.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.


Integration has a wide variety ofapplications. The definite integral can beused to determine area between two curves,volume, work done, and additionalapplications.

How can Integration be used to solvevarious application problems?

How do you use a definite integral to findthe area of a region between two curves?How do you find the volume of a solid ofrevolution by the disk method? How do youfind the volume of a solid of revolution bythe washer method? How do you find thevolume of a solid with known crosssections?

CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.2.3.HS.A.12. Explain volume formulasand use them to solve problems.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.


Sketching slope fields to graphicallyvisualize

What are the Methods for SolvingDifferential Equations?

How do you sketch a slope field of adifferential equation? How do you use anexponential function to model growth anddecay? How do you use separation ofvariables to solve a differential equation?

CC.2.1.HS.F.1. Apply and extend theproperties of exponents to solv







the solutions of differential equations will beexplored. Exponential functions to modelgrowth and decay will be used. Usingseparation of variables to solve differentialequations will be studied.

e problems with rational exponents.CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.1.HS.F.3. Apply quantitative reasoningto choose and interpret units and scales informulas, graphs, and data displays.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.

Mathematics - APStatistics - Unit#1

1. Data Analysis Some questions can be answered bycollecting, representing, and analyzing data,and the question to be answered determinesthe data to be collected, how best to collectit, and how best to represent it.

What is the difference between categoricaland quantitative data? What methods can beused to display and analyze categorical data?What methods can be used to display andanalyze quantitative data with graphs? Whatmethods can be used to describe quantitativedata with numbers?

A1.2.1.1.1. Analyze a set of data for theexistence of a pattern and represent thepattern algebraically and/or graphically.A1.2.3.2.2. Analyze data, make predictions,and/or answer questions based on displayeddata (box-and-whisker plots, stem-and-leafplots, scatter plots, measures of centraltendency, or other representations).CC.2.1.HS.F.4. Use units as a way tounderstand problems and to guide thesolution of multi-step problems.CC.2.1.HS.F.5. Choose a level of accuracyappropriate to limitations on measurementwhen reporting quantities.CC.2.4.HS.B.1. Summarize, represent, andinterpret data on a single count ormeasurement variable.


2. Modeling Distributions of Data Patterns exhibit relationships that can beextended, described, and generalized.

What methods can we use to compareourselves to a population? How can weestimate, interpret, and manipulatedistributions of data? How can we use adensity curve and normal distributions tomodel quantitative data?

A1.2.1.1.1. Analyze a set of data for theexistence of a pattern and represent thepattern algebraically and/or graphically.A1.2.3.2.2. Analyze data, make predictions,and/or answer questions base







d on displayed data (box-and-whisker plots,stem-and-leaf plots, scatter plots, measuresof central tendency, or otherrepresentations).A2.2.2.1.2. Create, interpret, and/or use theequation, graph, or table of an exponential orlogarithmic function (including common andnatural logarithms).CC.2.4.HS.B.3. Analyze linear models tomake interpretations based on the data.CC.2.4.HS.B.4. Recognize and evaluaterandom processes underlying statisticalexperiments.CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.


3. Describing Relationships Two variable quantities are proportional iftheir values are in a constant ratio. Therelationship between proportional quantitiescan be represented as a linear function.

How can we describe a relationship betweentwo variables? How can we usescatterplots and correlation to determine therelationship between two quantitativevariables? How can we create and interpret alinear regression line?

A1.2.2.2.1. Draw, identify, find, and/or writean equation for a line of best fit for a scatterplot.A1.2.3.2.2. Analyze data, make predictions,and/or answer questions based on displayeddata (box-and-whisker plots, stem-and-leafplots, scatter plots, measures of centraltendency, or other representations).A1.2.3.2.3. Make predictions using theequations or graphs of best-fit lines ofscatter plots.CC.2.4.HS.B.1. Summarize, represent, andinterpret data on a single count ormeasurement variable.CC.2.4.HS.B.2. Summarize, represent, andinterpret data on two categorical andquantitative variables.CC.2.4.HS.B.3. Analyze linear models tomake interpretations based on the data.


4. Collecting Data Bivariate data can be modeled withmathematical functions that approximate thedata well and help us make predictionsbased on the data.

What are the characteristics of good and badsampling techniques? What are importantconsiderations when conducting anexperiment? What issues need to beconsidered when making inferences from astatistical study?

CC.2.4.HS.B.1. Summarize, represent, andinterpret data on a single count ormeasurement variable.CC.2.4.HS.B.2. Summarize, represent, andinterpret data on two categorical andquantitative variables.CC.2.4.HS.B.4. Recognize and evaluaterandom processes underlying statisticalexperiments.








5. Probability Mathematics can be used to understand theregular patterns of chance behavior when thesame chance process is repeated again andagain.

How can simulation be used to modelprobability? What methods can be used tocalculate probabilities? How do you solveconditional probabilities?

CC.2.4.HS.B.4. Recognize and evaluaterandom processes underlying statisticalexperiments.CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.CC.2.4.HS.B.6. Use the concepts ofindependence and conditional probability tointerpret data.CC.2.4.HS.B.7. Apply the rules ofprobability to compute probabilities ofcompound events in a uniform probabilitymodel.

Mathematics -Basic Geometry -Unit #1

Geometry is logically built upon a few basicaxioms and undefined terms.

Geometry is logically built upon a few basicpostulates and undefined terms.

How can you use measurements to comparesegments and classify angles? How do youuse pattern to make predictions? How caninductive reasoning be used to solve aproblem? What are some basic terms andtheir importance to geometry? How do yousketch simple figures and find theirintersections? How do you measuresegments? How do you measure angles andclassify angles by their measure?

G.1.2.1.2. Identify and/or use properties ofquadrilaterals.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Trigonometric ratios can be used to solvereal world problems

Trigonometric ratios can be used to solvereal world problems

What information is needed to determine theheight of a flag pole? How do you simplifya square root? What is the relationshipamong the sides of a 45-45-90 triangle? What is the relationship among the sides of a30-60-90 triangle? How do you find thetangent of an acute angle? How do you findthe sine and cosine of an acute angle? Howdo you solve for the missing values given aright triangle?

A1.1.1.1.2. Simplify square roots (e.g., ?(24)= 2?6).G.1.2.1.1. Identify and/or use properties oftriangles.G.2.1.1.1. Use the Pythagorean theorem towrite and/or solve problems involving righttriangles.G.2.1.1.2. Use trigonometric ratios to writeand/or solve problems involving righttriangles.CC.2.3.HS.A.14










. Apply geometric concepts to model andsolve real world problems.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.CC.2.3.HS.A.7. Apply trigonometric ratiosto solve problems involving right triangles.CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.




What relationships exist among tangents,secants, and chords of a circle? How do youidentify the different segments and lines in acircle? How do you find missing lengthsusing the tangent theorem? How do youfind missing arc and angle measures usingthe properties of arcs of a circle? How doyou find the measures of arcs and chordsusing the chord theorems? How do you findmissing angle measures using the inscribedangle theorems? How do you find themeasures of angles, arcs and chords usingthe chord theorems? How do you write andgraph an equation of a circle? How do youidentify rotations and rotational symmetry?

G.1.1.1.1. Identify, determine, and/or use theradius, diameter, segment, and/or tangent ofa circle.G.1.1.1.2. Identify, determine, and/or use thearcs, semicircles, sectors, and/or angles of acircle.G.1.1.1.3. Use chords, tangents, and secantsto find missing arc measures or missingsegment measures.CC.2.3.HS.A.1. Use geometric figures andtheir properties to represent transformationsin the plane.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.3.HS.A.5. Create justifications basedon transformations to establish similarity ofplane figures.CC.2.3.HS.A.8. Apply geometric theoremsto verify properties of circles.CC.2.3.HS.A.9. Extend the concept ofsimilarity to determine arc lengths and areasof sectors of circles.CC.MP.1. Make sense of proble




ms and persevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Comparing segments and Angles helps us tofind missing measures.

Comparing Segments and angles helps us tofind missing measures.

How can you use measurements to comparesegments and classify angles? How do youfind the coordinates of the midpoint of asegment? How do you find the measure ofthe missing angle when an angle bisector isinvolved? What is special aboutcomplementary and supplementary angles? How do you find the measure of anglesformed by intersecting lines? How do youuse deductive reasoning to make accurateconclusions? How do you use the propertiesof equality and congruence to explain whystatements are true?

CC.2.1.HS.F.4. Use units as a way tounderstand problems and to guide thesolution of multi-step problems.CC.2.2.HS.D.1. Interpret the structure ofexpressions to represent a quantity in termsof its context.CC.2.2.HS.D.2. Write expressions inequivalent forms to solve problems.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Properties of Parallel and perpendicular linescan be used to prove relationships betweenangle measures and to make connectionsbetween algebra and geometry.

Properties of parallel and perpendicular linescan be used to prove relationships betweenangles measures and make connectionsbetween algebra and geometry

What relationship exists between anglesformed by parallel lines and a transversal? How do you determine if two lines areparallel, perpendicular or skew? How doyou use the perpendicular line theorems tosolve

CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.1.HS.F.3. Apply quantitative reasoningto choose and interpret units and scales informulas, graphs, and data display







problems? How can you distinguish if twoangles are corresponding, alternate interior,alternate exterior, or same side interiorangles? How do you find the congruentangles formed when a transversal cuts twoparallel lines/ What are four ways to showthat two lines cut by a transversal areparallel? How do you use the properties ofparallel and perpendicular lines to solve formissing values? What is the relationshipbetween the slopes of two parallel linesverses two perpendicular lines? How do youperform a translation How do you describea translation using coordinate notation?

s.CC.2.2.HS.D.7. Create and graph equationsor inequalities to describe numbers orrelationships.CC.2.3.HS.A.1. Use geometric figures andtheir properties to represent transformationsin the plane.CC.2.3.HS.A.11. Apply coordinategeometry to prove simple geometrictheorems algebraically.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.CC.2.3.HS.A.4. Apply the concept ofcongruence to create geometricconstructions.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Segments associated with Triangles can beused to determine properties of triangles.

Segments associated with Triangles can beused to determine properties of triangles.

How can you use triangle relationships tofind and compare angle measures anddistances? How do you use the sides andangles of a triangle to classify it? How doyou use the triangle sum and the exteriorangle theorems to find angle measures? How do you find missing sides and angles ofisosceles and equilateral triangles? How canyou find the missing sides of a right triangleusing both the Pythagorean Theorem and thedistance formula? How can you determineif three given side lengths will form a right,acu

CC.2.2.HS.D.10. Represent, solve, andinterpret equations/inequalities and systemsof equations/inequalities algebraically andgraphically.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.CC.MP.1. Make sense of proble




te, or obtuse triangle? What is unique aboutthe intersection of the medians of a triangle? Given 3 side lengths, How do you use thetriangle inequality theorem to determine ifthey form a triangle?



Properties of quadrilaterals and otherpolygons can be used to find side lengthsand angle measures

Properties of quadrilaterals and otherpolygons can be used to find side length andangle measures.

How do you use properties of quadrilateralsand other polygons to find side lengths andangle measures? How do you classifypolygons? What is true of opposite sides,angles and diagonals in a parallelogram? What are four ways to prove that aquadrilateral is a parallelogram? How doyou determine if a parallelogram is arhombus, rectangle or square? What are thespecial properties of the diagonals of arhombus and rectangle? How are the baseangles of an isosceles trapezoid related? How is the mid-segment of a trapezoidrelated to its bases? How do you identifyspecial quadrilaterals based on limitedinformation?

G.1.2.1.2. Identify and/or use properties ofquadrilaterals.CC.2.3.HS.A.11. Apply coordinategeometry to prove simple geometrictheorems algebraically.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Similar figures can be used to model andsolve real life problems

Similar figures can be used to model realworld problems.

How can you use a scale drawing todetermine actual measurements of an object?How are ratio and proportions used to findmissing values? How are proportions usedto determine if two figures are similar? Howcan Angle Angle(AA) be used to provetriangles are similar? How can SAS andSSS be used to prove similar triangles? How do you find missin

G.1.3.1.1. Identify and/or use properties ofcongruent and similar polygons or solids.G.1.3.1.2. Identify and/or use proportionalrelationships in similar figures.G.1.3.2.1. Write, analyze, complete, oridentify formal proofs (e.g., direct and/orindirect proofs/proofs by contradiction).CC.2.3.HS.A.1. Use geometric







g side lengths using both the triangleproportionality theorem and themid-segment theorem? How do you usescale factors to perform dilations? How doyou create dilations using the coordinateplane?

figures and their properties to representtransformations in the plane.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.1.HS.F.4. Use units as a way tounderstand problems and to guide thesolution of multi-step problems.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.CC.2.3.HS.A.5. Create justifications basedon transformations to establish similarity ofplane figures.CC.2.3.HS.A.6. Verify and apply theoremsinvolving similarity as they relate to planefigures.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Length and area of Geometric figures can beused to solve real life problems.

Area of geometric figures are determined byproperties of the figures.

How is area used to solve real life problems?How do you identify regular polygons? How do you use the polygon interior andexterior angle theorems to find missinginterior and exterior angles? How do youfind the heights of squares and rectanglesgiven their areas? How do you find theheight of a triangle given its area? How doyou find the height of a parallelogram givenits area? How do you find the height of atrapezoid given its area? How do you findthe radius of a circle given thecircumference or area?

G.1.2.1.1. Identify and/or use properties oftriangles.G.1.2.1.4. Identify and/or use properties ofregular polygons.G.2.1.1.1. Use the Pythagorean theorem towrite and/or solve problems involving righttriangles.G.2.2.2.1. Estimate area, perimeter, orcircumference of an irregular figure.G.2.2.2.2. Find the measurement of amissing length, given the perimeter,circumference, or area.G.2.2.2.3. Find the side lengths of a polygonwith a given per




imeter to maximize the area of the polygon.G.2.2.2.4. Develop and/or use strategies toestimate the area of a compound/compositefigure.G.2.2.2.5. Find the area of a sector of acircle.G.2.2.3.1. Describe how a change in thelinear dimension of a figure affects itsperimeter, circumference, and area (e.g.,How does changing the length of the radiusof a circle affect the circumference of thecircle?).G.2.2.4.1. Use area models to findprobabilities.CC.2.1.HS.F.3. Apply quantitative reasoningto choose and interpret units and scales informulas, graphs, and data displays.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.2.3.HS.A.3. Verify and apply geometrictheorems as they relate to geometric figures.CC.2.3.HS.A.8. Apply geometric theoremsto verify properties of circles.CC.2.3.HS.A.9. Extend the concept ofsimilarity to determine arc lengths and areasof sectors of circles.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


The surface area and volume of solids aredetermined by their properties

The surface area and volume of solids aredetermined by their properties

What area formulas can be used to derivesurface areas and volumes of solids? Howdo you identify and name polyhedra? Howdo you find the surface area of prisms andcylinders? How do you find the surface areaof pyramids and cones? Ho

G.1.1.1.1. Identify, determine, and/or use theradius, diameter, segment, and/or tangent ofa circle.G.1.2.1.5. Identify and/or use properties ofpyrami




w do you find the volume of prisms andcylinders? How do you calculate thevolume of pyramids and cones? What is theonly dimension you need in order to find thesurface area and volume of a sphere?

ds and prisms.G.2.3.1.1. Calculate the surface area ofprisms, cylinders, cones, pyramids, and/orspheres. Formulas are provided on areference sheet.G.2.3.1.2. Calculate the volume of prisms,cylinders, cones, pyramids, and/or spheres.Formulas are provided on a reference sheet.G.2.3.1.3. Find the measurement of amissing length given the surface area orvolume.G.2.3.2.1. Describe how a change in thelinear dimension of a figure affects itssurface area or volume (e.g., How doeschanging the length of the edge of a cubeaffect the volume of the cube?).CC.2.1.HS.F.3. Apply quantitative reasoningto choose and interpret units and scales informulas, graphs, and data displays.CC.2.3.HS.A.12. Explain volume formulasand use them to solve problems.CC.2.3.HS.A.13. Analyze relationshipsbetween two-dimensional andthree-dimensional objects.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.

Mathematics -Calculus - Unit #1

Limits will be investigated graphically,numerically, and analytically. Techniques todetermine end behavior of graphs offunctions will be studied.

How can we use the concept of limits toinvestigate the continuity of functions?

How can you find a limit graphically andnumerically? How can you evaluate a limitalgebraically? How do you show that afunction is continuous? What informationdoes the Intermediate Value Theorem giveus about functions that are continuous o

CC.2.2.HS.D.3. Extend the knowledge ofarithmetic operations and apply to poly



n a closed interval? How can you determinecontinuity at a point and on an openinterval? How do you find limits at Infinity?How do you find and sketch verticalasymptotes of the graph of a function?

nomials.CC.2.2.HS.D.5. Use polynomial identities tosolve problems.CC.2.2.HS.D.6. Extend the knowledge ofrational functions to rewrite in equivalentforms.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


There are various methods and techniquesfor finding derivatives of functions. Theserules can be applied to calculate quantitiessuch as velocity, acceleration, and the ratesof change of two or more variables.

How do you find derivatives of functions? How do you find the slope of a tangent lineto a curve at a point? How do you find thederivative of a function using the limitdefinition? What is the relationship betweendifferentiability and continuity? How do youfind the derivative of a function using thebasic differentiation rules? How do you findthe derivative of a function using theProduct Rule and the Quotient Rule? Howdo you find the derivative of a functionusing the Chain Rule? How do you find thederivative of a function using the GeneralPower Rule? How do you find the derivativeof a function using implicit differentiation?How do you find a related rate? How can weapply techniques of implicit differentiationto find the rates of change of two or morevariables that are changing over time?

CC.2.2.HS.D.2. Write expressions inequivalent forms to solve problems.CC.2.2.HS.D.3. Extend the knowledge ofarithmetic operations and apply topolynomials.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Calculus techniques will be used to analyzegraphs of functions. The derivative of afunction will be used to determine maximumand minimum values of a function.Differentiation techniques will be used tosolve applied maximum and minimumproblems.

How can we use techniques of integration tosolve applied maximum and minimumproblems?

What are Extrema and how do you findthem? Under what conditions are weguaranteed a maximum and a minimum?What conclusions can be drawn i

CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.2.HS.D.3. Extend the knowledge ofarithmetic operations and apply topolynomials.CC.2.2.HS.D.4. Understand the relationshipbetween zer





f the Mean Value Theorem can be applied toa function over a certain interval? How is thefirst derivative test used to find extrema of afunction? How do we determine intervals onwhich a function is increasing or decreasing?How is the second derivative test used tofind extrema of a function? How can thesecond derivative be used to determine theconcavity of a function? How can youdetermine limits at infinity? How can youuse the slope of a curve to help graph afunction? How do you use Calculus to solveapplied maximum and minimum problems?How do we find tangent lineapproximations?

os and factors of polynomials to makegeneralizations about functions and theirgraphs.CC.2.2.HS.D.6. Extend the knowledge ofrational functions to rewrite in equivalentforms.CC.2.2.HS.D.7. Create and graph equationsor inequalities to describe numbers orrelationships.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Techniques for approximating and findingthe exact value for the area under a curvewill be studied. Integration rules will beutilized to determine the average value of afunction and the position function.

How can we determine the area under acurve?

What are antiderivatives? How canintegration be used to find the particularsolution to a differential equation? How canwe use Riemann Sums to estimate the areaunder a curve? How can we use limits toevaluate a definite integral? What is theFundamental Theorem of Calculus? Whatare techniques of integration? What are thedifferent ways to approximate a definiteintegral? How can we use substitution tofind the antiderivatives of compositefunctions?

CC.2.2.HS.D.3. Extend the knowledge ofarithmetic operations and apply topolynomials.CC.2.2.HS.D.4. Understand the relationshipbetween zeros and factors of polynomials tomake generalizations about functions andtheir graphs.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.




Properties, derivatives, and antiderivativesof Logarithmic, Exponential, and OtherTranscendental Functions will be explored.

What are the Properties, Derivatives andAntiderivatives of TranscendentalFunctions?

How do you find derivatives of logarithmicfunctions? How do you find and evaluatedefinite integrals of logarithmic functions?How do you find derivatives and integrals ofexpressions with “e”? How do you findderivatives of inverse trig functions? Howdo you find integrals of inverse trigfunctions? How do you find the derivativesof inverse functions? How can you useL'Hopital's Rule to determine the limit of arational function?

CC.2.1.HS.F.1. Apply and extend theproperties of exponents to solve problemswith rational exponents.CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.2.HS.D.2. Write expressions inequivalent forms to solve problems.CC.2.2.HS.D.6. Extend the knowledge ofrational functions to rewrite in equivalentforms.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.


Integration has a wide variety ofapplications. The definite integral can beused to determine area between two curves,volume, work done, and additionalapplications.

How can Integration be used to solvevarious application problems?

How do you use a definite integral to findthe area of a region between two curves?How do you find the volume of a solid ofrevolution by the disk method? How do youfind the volume of a solid of revolution bythe washer method? How do you find thevolume of a solid with known crosssections?

CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.2.3.HS.A.12. Explain volume formulasand use them to solve problems.CC.2.3.HS.A.14. Apply geometric conceptsto model and solve real world problems.


Sketching slope fields to graphicallyvisualize the solutions of differentialequations will be explored. Exponentialfunctions to model growth and decay will beused. Using separation of variables to solvedifferential equations will be studied.

What are the Methods for SolvingDifferential Equations?

How do you sketch a slope field of adifferential equation? How do you use anexponential function to model growth anddecay? How do you use separation ofvariables to solve a differential equation?

CC.2.1.HS.F.1. Apply and extend theproperties of exponents to solve problemswith rational exponents.CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.1.HS.F.3. Apply quantitative reasoningto choose and interpret units and scales informulas, graphs, and data displays.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.







Mathematics -Calculus 2 - Unit#5

Curves represented by parametric equationswill be sketched. Using a set of parametricequations to find the slope of a tangent lineto a curve and the arc length of a curve willbe explored.

How do we write and graph parametricequations?

How can the graph of a curve given by a setof parametric equations be sketched? Howcan we eliminate the parameter in a set ofparametric equations? How can we find a setof parametric equations to represent a curve?How can we find the slope of a tangent lineto a curve given by a set of parametricequations? How can we find the arc lengthof a curve given by a set of parametricequations?

CC.2.1.HS.F.4.b. Solve real world problemsinvolving units of measurementCC.2.2.HS.C.2. Graph and analyze functionsand use their properties to make connectionsbetween the different representations.CC.2.2.HS.C.3.a. Given a table or graph,describe the relationship between twoquantitiesCC.2.2.HS.D.2. Write expressions inequivalent forms to solve problems.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Methods for approximating solutions toordinary differential equations will bestudied. Techniques for solving logisticdifferential equations will be explored.

How can we use techniques from Calculusand Analytical Geometry to generate andexplain solutions of differential equations?

How can differential equations be used tomodel growth and decay rates? How canEuler’s Method be used to approximate theparticular solution of a DEQ? How do youuse separation of variables to solve adifferential equation? How can we usecalculus to solve and analyze LogisticDEQs?

CC.2.1.HS.F.1. Apply and extend theproperties of exponents to solve problemswith rational exponents.CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.1.HS.F.3. Apply quantitative reasoningto choose and interpret units and scales informulas, graphs, and data displays.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.








Applications of integration, including workdone by a variable force will be explored.

How can we apply techniques of Integrationto solve real world problems?

How can we find the work done by avariable force? How can we determine fluidpressure and fluid force?

CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.1.HS.F.3. Apply quantitative reasoningto choose and interpret units and scales informulas, graphs, and data displays.CC.2.1.HS.F.4.a. Determine the necessaryunit(s) to use to solve real world problemsCC.2.1.HS.F.4.b. Solve real world problemsinvolving units of measurementCC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Integration techniques to evaluate morecomplicated integrals will be studied.Improper integrals will be evaluated.

What techniques can we use to evaluatecomplicated integrals?

How can the basic integration rules be usedto evaluate integrals? How do we usesubstitution to evaluate integrals? How dowe find antiderivatives using integration byparts? How can we use partial fractiondecomposition with linear factors tointegrate rational functions? How can weevaluate an improper integral that has aninfinite limit of integration? How can weevaluate an improper integral that has aninfinite discontinuity?

CC.2.2.HS.C.1. Use the concept andnotation of functions to interpret and applythem in terms of their context.CC.2.2.HS.C.8. Choose trigonometricfunctions to model periodic phenomena anddescribe the properties of the graphs.CC.2.2.HS.D.2. Write expressions inequivalent forms to solve problems.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.








Techniques will be applied to determinewhether an infinite series converges ordiverges. Taylor and Maclaurin polynomialsand power series will be explored.

How can we determine the convergence ordivergence of infinite series?

How can we determine whether a sequenceconverges or diverges? What are theproperties of infinite geometric series? Howand when can we use the nth-Term test?How and when can we apply the IntegralTest? What are the properties of p-series andharmonic series? How and when can we usethe Direct Comparison Test? How and whencan we use the Limit Comparison Test?How and when can we use the AlternatingSeries Test? When can the Ratio and RootTests be used? How can we find Taylor andMaclaurin polynomial approximations ofelementary functions? What are theproperties of a Power Series? How can werepresent functions by Power Series? Howcan we find a Taylor or Maclaurin series fora function?

CC.2.2.HS.C.1. Use the concept andnotation of functions to interpret and applythem in terms of their context.CC.2.2.HS.D.2. Write expressions inequivalent forms to solve problems.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Vectors and the three-dimensionalcoordinate system will be investigated.Mathematical operations involving vectorswill be studied.

How can we use vectors to analyze thegeometry of space?

How do we perform basic vector operationsand represent vectors graphically? How canwe plot points in a three-dimensionalcoordinate system? How do we compute thedot product of two vectors? How do wecompute the the cross product of two vectorsin space?

CC.2.1.HS.F.4.b. Solve real world problemsinvolving units of measurementCC.2.2.HS.C.1. Use the concept andnotation of functions to interpret and applythem in terms of their context.CC.2.2.HS.C.2. Graph and analyze functionsand use their properties to make connectionsbetween the different representations.CC.2.3.HS.A.13. Analyze relationshipsbetween two-dimensional andthree-dimensional objects.CC.2.3.HS.A.13.a. Match the shape ofreal-world objects to two-dimensional andthree-dimensional shapes (e.g. the trunk of atree is cylindrical in shape; a car is cube inshape; the flower of a sunflower is circularin shape; a bookshelf is rectangular prism inshape).CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use of








Mathematics -Consumer Math -Unit #0

The students will be able to: read, round, andcompare numbers; perform arithmeticoperations(add, subtract, multiply anddivide) involving fractions, decimals andintegers; perform data analysis; and usevarious problem solving techniques to solveproblems.

The students are able to perform previouslycovered basic mathematical skills applied tothe world beyond the classroom.

What Skills(mathematical and otherwise) doyou need to possess and what skills do youneed to acquire? How do you write and readnumbers in standard form and in scientificnotation? How do you round and comparenumbers? How do you add, subtract,multiply and divide decimals? How domultiply, divide, add, and subtract andcompare fractions, mixed numbers andintegers? How do you convert from fractionto decimal to percent and back again pluscalculate the percent of a number? How doyou calculate mean and elapsed time? Howdo you use charts, graphs, and tables, toanalyze data? How do you use tables andcharts to analyze business data? How do youuse graphs to analyze business data? How doyou construct a line, bar, or pie chart forbusiness data? When would you need toconvert between units of measure orcurrency? How do you convert the basicunits of measure in both the U.S. and metricsystems? How do you convert units ofcurrency? When would you use each type ofestimation method discussed? How do youestimate a quantity using rounding? Howwould you estimate a quantity using frontend estimation? How do you change thenumbers in a problem to make it easier toestimate the answer? How do you estimateby clustering? How do yo determine whichone of the 14 methods use when solvingproblems? How do you use the four-stepmethod to solve a problem? What questionsshould you ask yourself when solving aproblem? When solving a problem, how doyou know what operations you need to useand in what order? When is estimation

CC.2.1.HS.F.5. Choose a level of accuracyappropriate to limitations on measurementwhen reporting quantities.CC.2.2.HS.D.8. Apply inverse operations tosolve equations or formulas for a givenvariable.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.




okay to use? When is it okay to guess andcheck? When can you use algebra to solve aproblem? When would it be appropriate todraw a picture? When could you useprobability to analyze business data?


In what ways can you manage your incomeeffectively?

The students will be able to calculate andmanage income effectively, compute taxesand payroll deductions, maintain checking'sand saving's accounts and budget/managetheir money in modern society.

How do you calculate gross income? Howdo you calculate straight time pay? What isthe difference between overtime over 40hours and overtime based on an 8 hour day?How do calculate the total hours on a weeklytime card? How do you compute the totalpay on a piecework basis? How do youdetermine your salary per pay period? Howdo you calculate straight commission anddetermine gross pay? How do you computegraduated commission? How do youcalculate net income? How do youdetermine the amount withheld for federalincome tax(FIT)? How do you calculatestate taxes(SIT)on a straight percent basis?How do you calculate state taxes on agraduated income tax basis? How do youcalculate the amount withheld for SocialSecurity(SS) and Medicare Taxes? How doyou calculate deductions for healthinsurance? How do you calculate your netpay per pay period? In what ways can youmanage your money to help with yourfuture? How do you compute the averagemonthly expenditure? What steps do youtake to create a budget? How do you create apie chart from a budget? How do you applyand analyze a budget? In what ways can youmanage your money to help you in thefuture? How do you maintain a checkingaccount? How do you fill out a checkingaccount deposit slip? How do you correctlyfill out a check? How do you calculate thebalance in a check register? How do youcalculate the current balance on a checkingaccount bank statement? How do youprepare a bank reconciliation? What stepswould you take to bank on-line? How doyou maintain a savings account? How doyou fill out a savings ac

CC.2.1.HS.F.5. Choose a level of accuracyappropriate to limitations on measurementwhen reporting quantities.CC.2.2.HS.D.8. Apply inverse operations tosolve equations or formulas for a givenvariable.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.




count deposit slip? How do you correctly fillout a savings account withdrawal slip? Howdo you calculate simple interest? How doyou calculate compound interest? How doescompound interest differ from simpleinterest? How do you calculate compoundinterest using a compound interest table?How do you calculate compound interest ona daily basis? How do you calculate thefuture value of an annuity?


The management of expenses is essential inmanaging your income because you do notwant your expenses to be more than youincome.

The real world is a difficult place becausechoices between goods things(purchases)need to be decided. We need to be able touse all product information to makeinformed decisions when making purchases.We also need to be able to understand anduse credit cards and loans effectively tocontrol our expenses.

Why is it important to use all productinformation, not just selling price, to makegood buying decisions? How do youcalculate sales tax? How do you calculatedtotal purchase price? How do you determinethe cost per unit? Why is it important tocomparison shop? How do you calculate theitem's final price after using a coupon orreceiving a rebate? How do you calculate thedollar amount of the markdown? How doyou calculate the sale price when themarkdown rate is known? What do youhave to do to take advantage of using credit?What is credit? What is the differencebetween a charge account and a credit card?What are some advantages anddisadvantages of using credit? How do youcalculate the new balance on a chargeaccount? How do you calculate the financecharge using the unpaid balance method?How do you calculate the finance chargeusing the average daily balance method? What are the different types of loanpayments and interest payments? How doyou calculate the maturity value of a singlepayment loan? How do you calculate theamount financed on an installment loan?How do you calculate the monthly paymentand finance charge of an installment loan?How do you allocate the payment of amonthly installment loan? How do youcalculate the final payment when paying offan installment loan? How do you determinethe Annual Percentage Rate(APR) of a loan?

CC.2.1.HS.F.5. Choose a level of accuracyappropriate to limitations on measurementwhen reporting quantities.CC.2.2.HS.D.8. Apply inverse operations tosolve equations or formulas for a givenvariable.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.

Mathematics -Consumer Math -Unit #3A

Major decisions concerning transportatio CC.2.1.HS.F.5. Choose a level of accuracyappropriat







n, housing costs, insurance and investmentswill affect how we spend our income.

How do you calculate the total cost ofoperating a car? How do you calculate thesticker price of a new vehicle? How do youcalculate the dealer's cost of a new vehicle?How do you calculate the average retailprice or wholesale price of a used vehicle?How do you use a table to compute theannual premium for vehicle insurance? Howdo you calculate the total cost per mile ofoperating and maintaining a vehicle? Howdo you calculate the total cost of leasing avehicle? How do you calculate the cost torent a vehicle? What are some of thecommon costs involved in home ownership?How do you calculate the mortgage loanamount? How do you use a table todetermine the monthly payment and totalinterest of a mortgage? How do youcalculate the closing costs? How do youallocate the monthly payment of amortgage? How do you calculate the realestate taxes for a home? How do youdetermine the amount of coverage forhomeowners insurance? How do youcalculate the annual homeowner's insurancepremium? How do you calculate the cost ofutilities? How do you decide whether to rentor own a home? What are the differenttypes of insurance you can obtain and howdo you know which ones you shouldpurchase? How do you calculate healthinsurance premiums? How do you calculatethe amount the patient pays for health cre?How can you use a table to calculate theannual premium for life insurance? What arethe different types of life insurance? In whatways can you invest to make your moneywork for you? How do you calculateinterest on certificates of deposit(CD)? Howdo you determine APR? How do youcalculate the total cost of a stockinvestment? How do you calculate the profitor loss from a stock sale? How do youcalculate the annual dividend of a stockinvestment? How do you calculate the profitor loss of a mutual fund? How do youcalculate the annual interest rate of a bondinvestment? How can Real Estate bebeneficial to you? In what ways can youinvest your retirement?

e to limitations on measurement whenreporting quantities.CC.2.2.HS.D.8. Apply inverse operations tosolve equations or formulas for a givenvariable.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.

Mathematics -Consumer Math -Unit #3B

Major decisions concerning personnel andthe various necessary expenses whenoperating a business will affect how weprice our services to ensure our businessremains viable.

What are major business financial decisionsthat need to be made to effectively operate abusiness?

What are some business personnel costs?How do businesses calculate the cost ofrecruiting new employees? How dobusinesses calculate the Cost-of-Living Payincrease? How do businesses calculate therate of employee benefits based on annualgross pay? What is disability insurance andwhy does one need it? How do businessescalculate the employer cost for workers'compensation insurance? How do businessescalculate total business travel expenses?How do businesses calculate total employeetraining cost? What factors do businesseshave to consider with purchasing andinventory? How does a business calculate atrade discount? How does a businesscalculate a trade discount using acomplement method? How does a businessdetermine the final net price after chaindiscounts? How do businesses calculate thecash price when the discount is based onordinary dating? How do businessescalculate the cash price when the discount isbased on the end-of-month dating? How dobusinesses calculate inventory? What are thedifferent ways that businesses calculate thevalue of inventory? How do businessescalculate the annual cost of carryinginventory? What are some sales factors thatbusiness must consider when determiningnet profit? How do businesses calculate thecost of markup in dollars? How dobusinesses calculate the markup rate? Howdo businesses determine the net profit indollars? How do businesses calculate the netprofit rate? How do businesses calculate theselling price of an item based on cost andmarkup rate based on selling price? How dobusinesses calculate the markup rate basedon cost? How do businesses calculate theselling price based on cost and markup rate?How do businesses calculate the markdownin dollars and as a percent of the regularselling price? Wha





t factors does a business have to make whenit makes a marketing decision? How dobusinesses calculate the rate of a particularresponse in an opinion survey? How canbusinesses determine the annual salespotential of a new product? How dobusinesses calculate market share of a newproduct? How can businesses use the factormethod or a graph to determine projectedsales? How do businesses calculate the costof advertising in a newspaper? How dobusinesses calculate the cost of advertisingon TV? How do businesses calculate theselling price that will result in the highestpossible net profit?


The management of business expenses isessential in managing your business becauseyou do not want your expenses to be morethan the income.

Understanding Business finances, it'smanagement and control of services,accounting and financial management.

In What ways does a business manage itsfinances? In What ways do businessesallocate funds for overhead expenses? Howdo businesses compute their monthly rentalcharges? How do businesses calculate thetotal building maintenance charges? How dobusinesses determine the total equipmentrental costs? How do businesses calculatethe monthly telephone costs? How dobusinesses calculate the monthly cost forelectricity? How do businesses calculate thetotal cost of professional services? How dobusinesses account for their employees,equipment, finances, inventory and otherbusiness expenses? How do businessescomplete a payroll register? How do youcalculate the percent of a particular businessexpense to the total expense? How dobusinesses calculate the cost ofmanufacturing an item and determine howmany units can be produced? How dobusinesses calculate the break-even point?How do businesses use the straight-linemethod to calculate the annual depreciationof an item? How do businesses calculate thebook value of an item used usingstraight-line depreciation? How do business





es use the Modified Accelerated CostRecovery System(MACRS) to calculate theannual depreciation and book value? Howdo businesses manage their taxes,investments and loans? How do businessescalculate taxable income? How dobusinesses calculate the selling expense andthe net proceeds from an issue of stocks orbonds? How do businesses determine thematurity value of a commercial loan? Howdo the businesses determine the cost andyield of a treasury bill? How do businessescalculate the cost of inflation? How do youexplain and compute the gross domesticproduct and consumer price index?

Mathematics -IntermediateAlgebra - Unit#10A

Students will analyze data using variousmethods and draw conclusions about thedata.

Students will analyze data using variousmethods and draw conclusions about thedata.

How do you analyze and interpret data fromvarious data displays? How do you comparemeasures of central tendency? How do youmake and interpret data in stem and leafplots? How do you make and interpret boxand whisker plots?

A1.2.3.1.1. Calculate and/or interpret therange, quartiles, and interquartile range ofdata.A1.2.3.2.1. Estimate or calculate to makepredictions based on a circle, line, bar graph,measure of central tendency, or otherrepresentation.A1.2.3.2.2. Analyze data, make predictions,and/or answer questions based on displayeddata (box-and-whisker plots, stem-and-leafplots, scatter plots, measures of centraltendency, or other representations).CC.2.1.HS.F.3. Apply quantitative reasoningto choose and interpret units and scales informulas, graphs, and data displays.CC.2.1.HS.F.5. Choose a level of accuracyappropriate to limitations on measurementwhen reporting quantities.CC.2.4.HS.B.1. Summarize, represent, andinterpret data on a single count ormeasurement variable.CC.2.4.HS.B.2. Summarize, represent, andinterpret data on two categorical andquantitative variables.CC.2.4.HS.B.3. Analyze linear models tomake interpretations based on the data.CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.CC.MP.1. Make sense of proble






Mathematics -IntermediateAlgebra - Unit#10B

Students will understand how to find theprobability of different situations in real lifesettings.

Students will understand how to find theprobability of different situations in real lifesettings.

How can you calculate probability in variouscontexts? How are probability and oddsrelated? How do you choose between usinga permutation or combination? How do youcalculate the probability of more than oneevent occuring?

A1.2.3.3.1. Find probabilities for compoundevents (e.g., find probability of red and blue,find probability of red or blue) and representas a fraction, decimal, or percent.CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.CC.2.4.HS.B.6. Use the concepts ofindependence and conditional probability tointerpret data.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.

Mathematics -IntermediateAlgebra - Unit#11

Students will be able to analyze sequencesand series and find the nth term.

Students will be able to analyze sequencesand series and find the nth term.

How do you analyze sequences and findsums of series? How do you write rules fornumber patterns? How can you tell that asequence is arithmetic? How can you findthe som of the terms of a geometric series?

A2.2.1.1.1. Analyze a set of data for theexistence of a pattern, and represent thepattern with a rule algebraically and/orgraphically.A2.2.1.1.2. Identify and/or extend a patternas either an arithmetic or geometricsequence (e.g., given a geometric sequence,find the 20th term).CC.MP.1. Make sense of proble










Mathematics -IntermediateAlgebra - Unit #3

Students will understand how graphingequations and inequalities may result in asolution, range of solutions, or no solution

Students will understand how graphingequations and inequalities may result in asolution, range of solutions, or no solution

Why is it important to know how varioustechniques for solving systems of equationsor inequalities? How do you solve a systemof linear equations by graphing? How doyou solve a system of equations bysubstitution? How do you solve a system oflinear equations by elimination a variable? How do you solve a system of linear systemsby multiplying first? How do you usesystems of equations to solve real worldproblems? How do you use graphing tosolve a system of linear inequalities?

A1.1.2.2.1. Write and/or solve a system oflinear equations (including problemsituations) using graphing, substitution,and/or elimination.A1.1.2.2.2. Interpret solutions to problems inthe context of the problem situation.A1.1.3.2.1. Write and/or solve a system oflinear inequalities using graphing.A1.1.3.2.2. Interpret solutions to problems inthe context of the problem situation.CC.2.2.HS.D.10. Represent, solve, andinterpret equations/inequalities and systemsof equations/inequalities algebraically andgraphically.CC.2.2.HS.D.7. Create and graph equationsor inequalities to describe numbers orrelationships.CC.2.2.HS.D.9. Use reasoning to solveequations and justify the solution method.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.





The solution to an inequality is not just oneanswer but a range of answers.

The solution to an inequality is not just oneanswer but a range of answers.

How does solving linear inequalities helpsolve real life problems? How do you solveand graph inequalities using addition andsubtraction? How do you solve inequalitiesusing multiplication and division? How doyou solve multi-step inequalities? How doyou solve compound inequalities? How doyou solve absolute value equations? Howdo you solve absolute value inequalities? How do you graph linear inequalities in twovariables?

A1.1.3.1.1. Write or solve compoundinequalities and/or graph their solution setson a number line (may include absolutevalue inequalities).A1.1.3.1.2. Identify or graph the solution setto a linear inequality on a number line.A1.1.3.1.3. Interpret solutions to problems inthe context of the problem situation.CC.2.2.HS.D.10. Represent, solve, andinterpret equations/inequalities and systemsof equations/inequalities algebraically andgraphically.CC.2.2.HS.D.7. Create and graph equationsor inequalities to describe numbers orrelationships.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Writing, graphing and solving quadraticfunctions using a variety of methods andperform operations with square roots andcomplex numbers

Writing, graphing and solving quadraticfunctions using a variety of methods andperform operations with square roots andcomplex numbers

How do you graph a parabola? Whatstrategies are appropriate when solving agiven quadratic equation? What shape andbasic properties of the graph of a quadraticfunction? How is the concept of minimumor maximum used in real world problems? When graphing a quadratic function, whatare the advantages in having it written invertex form or intercept form? How canfactoring be used to solve a quadraticequation when the leading coefficient is 1? How is the Zero-Product property used tosolve equations? How do you use factoringto solve a quadratic equation when t

A2.1.1.1.1. Simplify/write square roots interms of i (e.g., ?(-24) = 2i?6).A2.1.1.1.2. Simplify/evaluate expressionsinvolving powers of i (e.g., i^6 + i^3 = �1 �i).A2.1.1.2.1. Add and subtract complexnumbers (e.g., (7 � 3i) � (2 + i) = 5 � 4i).A2.1.1.2.2. Multiply and divide complexnumbers (e.g., (7 � 3i)(2 + i) = 17 + i).A2.1.2.2.1. Factor algebraic expressions,including difference of squares andtrinomials.A2.1.3.1.1. Write and/or solve quadraticequations (including factoring and using theQuadratic Formula).A2.2.2.1.3. Determine, use, and/or interpretminimum and maximum values over aspecified interval of a graph of a p







he leading coefficient is not 1? How do youuse square roots to solve a quadraticequation? How do you simplify anexpression with square roots? How do youperform operations on complex numbers? Why do we need imaginary numbers? Howis the process of completing the square usedto solve quadratics equations? How do youfind the number that is added to both sidesof the equation to complete the square? How do you use the quadratic formula andthe discriminant? How do you solvequadratic inequalities in one variable? Whatsteps do you use to graph a quadraticinequality in two variables?

olynomial, exponential, or logarithmicfunction.A2.2.2.1.4. Translate a polynomial,exponential, or logarithmic function fromone representation of a function to another(graph, table, and equation).CC.2.1.HS.F.6. Extend the knowledge ofarithmetic operations and apply to complexnumbers.CC.2.1.HS.F.7. Apply concepts of complexnumbers in polynomial identities andquadratic equations to solve problems.CC.2.2.HS.D.4. Understand the relationshipbetween zeros and factors of polynomials tomake generalizations about functions andtheir graphs.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Graph and solve polynomial functions forzeros to solve real world problems Graphpolynomial functions, perform operationswith polynomial equations and find zeros.

Graph and solve polynomial functions forzeros to solve real world problems Graphpolynomial functions, perform operationswith polynomial equations and find zeros.

How do you graph and solve polynomialfunctions? How do you simplify algebraicexpressions with exponents? How can youevaluate and graph a polynomial function? How do we classify a polynomial function? How do you add, subtract, and multiplypolynomials? What are the special productpatterns? What are the different factoringtechniques for polynomials? How can yousolve a higher degree polynomial equation? If you know one zero of a polynomialfunction how can you determine anotherone? How can you find all the zeros of apolynomial function when

A2.1.2.2.1. Factor algebraic expressions,including difference of squares andtrinomials.A2.1.3.1.1. Write and/or solve quadraticequations (including factoring and using theQuadratic Formula).A2.1.3.1.4. Write, solve, and/or apply linearor exponential growth or decay (includingproblem situations).CC.2.2.HS.D.3. Extend the knowledge ofarithmetic operations and apply topolynomials.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use of




the leading coefficient is 1? How can youdetermine the possible number of positive,negative, and imaginary zeros of apolynomial function? When does a graphhave a local maximum or local minimum?



Use rational exponents, operation on radicalfunctions, simplify radical expressions,graph and solve radical equations to solvereal world problems.

Use rational exponents, operation on radicalfunctions, simplify radical expressions,graph and solve radical equations to solvereal world problems.

How do you solve and graph radical andinverse functions? What is the relationshipbetween nth roots and rational exponents? How are the properties of rational exponentsrelated to the properties of integerexponents? What operations can beperformed on a pair of functions to obtain athird function? How do you find the inverserelation of a given function? What do thegraphs of square root and cube rootfunctions look like? Why is necessary tocheck every apparent solution of a radicalequation in the orginal equation?

A2.1.2.1.1. Use exponential expressions torepresent rational numbers.A2.1.2.1.2. Simplify/evaluate expressionsinvolving positive and negative exponentsand/or roots (may contain all types of realnumbers�exponents should not exceedpower of 10).A2.1.3.1.2. Solve equations involvingrational and/or radical expressions (e.g.,10/(x + 3) + 12/(x � 2) = 1 or ?((x^2) + 21x)= 14).CC.2.1.HS.F.2. Apply properties of rationaland irrational numbers to solve real world ormathematical problems.CC.2.2.HS.D.8. Apply inverse operations tosolve equations or formulas for a givenvariable.CC.2.2.HS.D.10. Represent, solve, andinterpret equations/inequalities and systemsof equations/inequalities algebraically andgraphically.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Graph and solve exponential and logarithmicequations, and write and apply exponentialand power functions to solve real worldproblems.

Graph and solve exponential and logarithmicequations, and write and apply exponentialand power functions to solve real worldproblems.

What is the relationship between exponentialand logarithmic functions? What does thegraph of an exponential growth functionlook like? What does the







graph of an exponential decay function looklike? When is the natural base e useful? What is the relationship between exponentialand logarithmic functions? How can youuse a calculator to evaluate alogarithm when the base is no 10 or e? Dologarithmic equations sometimes haveextraneous solutions? How do youdetermine whether a set of data fits anexponential pattern or a power pattern?

A2.1.2.1.4. Simplify or evaluate expressionsinvolving logarithms and exponents (e.g.,log2(8) = 3 or log4(2) = ?).A2.1.3.1.3. Write and/or solve a simpleexponential or logarithmic equation(including common and natural logarithms).A2.1.3.1.4. Write, solve, and/or apply linearor exponential growth or decay (includingproblem situations).CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


The denominator or a rational function iscritical in the graph and solution of thefunction.

The denominator or a rational function iscritical in the graph and solution of thefunction.

How do we graph a rational function whosegraph is discontinuous in the coordinateplane? What is the difference betweendirect, inverse and joint variation? How doyou graph simple rational functions? Howdo you find vertical and horizontalasymptotes of a rational function? How doyou multiply or divide rational functions? How do you add or subtract rationalexpressions with different denominators? How do you simplify a complex fraction? What are the steps for solving rationalequations? How do you compare functionsrepresented in different ways?

A2.1.3.1.2. Solve equations involvingrational and/or radical expressions (e.g.,10/(x + 3) + 12/(x � 2) = 1 or ?((x^2) + 21x)= 14).CC.2.2.HS.D.6. Extend the knowledge ofrational functions to rewrite in equivalentforms.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.

Mathematics -Pre-Calculus/Trigonometry - Unit#1.A

01.A - GRAPHS IN THE PLANE -Equations and their g

How do y








raphs can help identify the relationship thatexists between two variables.

Apply different techniques to graphing onthe coordinate plane Graph Equations GraphTransformations

ou find the distance and midpoint of a linesegment? How are symmetry and interceptsuseful in graphing an equation? How do youwrite and graph equations of a circle? Howdo you write and graph linear equations? How do you determine if two lines areparallel or perpendicular? How do youidentify and graph commonly usedfunctions? How do transformations affectshape and position of a graph?

Mathematics -Pre-Calculus/Trigonometry - Unit#1.B

01.B - FUNCTIONS - Functions can be usedto model and solve real life problems.

Mathematics -Pre-Calculus/Trigonometry - Unit#12

12 - LIMITS & INTRO TO CALCULUS -Intuitively understanding limits and thelimiting process is vital before students canapply derivatives and integrals to real lifesituations.


02 - POLYNOMIAL & RATIONALFUNCTIONS - Polynomial and rationalfunctions can be used to model and solvereal life problems.


03 - EXPONENTIAL & LOGARITHMICFUNCTIONS - Exponential and logarithmicfunctions can be used to model and solvereal life problems.


04.A - INTRO TO TRIGONOMETRY -Trigonometric functions can be used to solvereal life problems involving angles.


04.B - GRAPHS OF TRIG FUNCTIONS -Many scientific phenomena can berepresented by the periodic nature oftrigonometric graphs.


05 - ANALYTIC TRIGONOMETRY -Fundamental trig identities can be used toevaluate trig functions, simplify trigexpressions, and rewrite trig expressions.


06 - ADDITIONAL TOPICS INTRIGONOMETRY - Trigonometry can beused to solve real life problems involvingtriangles and vectors.


































09.A - SEQUENCES & SERIES -Sequences and series can be used to modeland solve real life problems.


09.B - PROBABILITY & STATISTICS -Probability and statistics can be used toanalyze chance and data in real lifesituations.

Mathematics -Probability &Statistics - Unit#1

Probability and Statistics is an introductionto how data is used to make decisions in thereal world.

Students will gain an overview of whatprocedures are necessary to obtain statisticsthat are as accurate as possible.

What are the basic concepts and goals ofStatistics? What is Statistics? How can databe classified? What are the elements ofexperimental design?

CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


A Chi-Squared distribution can be used totest a hypothesis that compares three ormore populations

A Chi-Squared distribution can be used totest a hypothesis that compares three ormore populations. Sometimes it is necessaryto test a hypothesis that compares three ormore populations.

How is the process for comparing three ormore populations different than comparingtwo populations? How is a chi-squareddistribution used to see if afrequency distribution fits a claimeddistribution? How would you use acontingency table to find expectedfrequencies? How would you use achi-squared distribution to see if twovariables are independent? How do youperform a two-sample F-test to comparevariances? How would you use ANOVA totest claims involving three or more means?

CC.2.4.HS.B.1. Summarize, represent, andinterpret data on a single count ormeasurement variable.CC.2.4.HS.B.2. Summarize, represent, andinterpret data on two categorical andquantitative variables.CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


















There are hypothesis tests that do not requireany specific conditions concerning the shapeof a population however stronger evidence isneeded to reach a conclusion.

A Nonparametric Test does not require anyspecific conditions concerning the shape ofthe distribution or the value of anypopulation parameters.

How can non-parametric tests be used to testclaims involving one or more populations? How can a sign test be used to test claimsabout medians? How can you use theWilcoxon Signed Rank test to find thedifference between medians of dependentsamples? How can you use the WilcoxonSigned Rank test to find the differencebetween medians of independent samples? How is the Kruskal-Wallis test used to testfor differences among three or morepopulations medians? How does theSpearman Rank CorrelationCoefficient determine significantcorrelation? How is the runs test used todetermine whether a data set is random?

CC.2.4.HS.B.1. Summarize, represent, andinterpret data on a single count ormeasurement variable.CC.2.4.HS.B.2. Summarize, represent, andinterpret data on two categorical andquantitative variables.CC.2.4.HS.B.3. Analyze linear models tomake interpretations based on the data.CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.

Mathematics -Probability &Statistics - Unit#2.1

The first step to understanding data is toorganize it.

It is easier to understand data if it isorganized in a way that can display trends.

What Processes used to organize and displaydata sets? How do you construct frequencydistributions? How do you convertfrequency distributions into graphs? Howdo you graph and interpret quantitative data?How do you graph and interpret qualitativedata sets? How do you graph and interpretpaired data? When is it appropriate to useeach type of statistical graph?

CC.2.1.HS.F.4. Use units as a way tounderstand problems and to guide thesolution of multi-step problems.CC.2.1.HS.F.5. Choose a level of accuracyappropriate to limitations on measurementwhen reporting quantities.CC.2.4.HS.B.1. Summarize, represent, andinterpret data on a single count ormeasurement variable.CC.2.4.HS.B.2. Summarize, represent, andinterpret data on two categorical andquantitative variables.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use of










Mathematics -Probability &Statistics - Unit#2.2

Descriptive Statistics can be used to describedata.

Central Tendency and measures of spreadmake real data easier to understand. Statistics can be used to describe trends,averages, and variations in data.

How can statistics describe trends, averages,and variations in data? How do youinterpret measures of central tendency? How do you measure the variability of a dataset? How do you interpret standarddeviation? How is the standard deviation forgrouped data different than non-groupeddata? How do you determine measures ofposition? How do you find and interpretz-scores?

CC.2.1.HS.F.3. Apply quantitative reasoningto choose and interpret units and scales informulas, graphs, and data displays.CC.2.1.HS.F.5. Choose a level of accuracyappropriate to limitations on measurementwhen reporting quantities.CC.2.4.HS.B.1. Summarize, represent, andinterpret data on a single count ormeasurement variable.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Probability is the possibility of somethinghappening verses the total number ofchances.

The Methods we use to generalize resultsfrom a sample to a population are based onprobability.

How can we determine the probability thatan event will occur? What are thecomponents of a probability experiment? How do you find conditional probabilities? How do you determine the probability that atleast one of two events will occur? How doyou determine the number of ways an eventcan occur?

CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.CC.2.4.HS.B.6. Use the concepts ofindependence and conditional probability tointerpret data.CC.2.4.HS.B.7. Apply the rules ofprobability to compute probabilities ofcompound events in a uniform probabilitymodel.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use of











Discrete probability distributions arecommon in business, science, engineeringand many other fields.

There are multiple occurrences of discreteprobability distributions in business, science,engineering, and many other fields.

How can discrete probability distributions beapplied in real-life situations? What is adiscrete probability distribution? How doyou use a binomial distribution to computeprobabilities? How do you use thegeometric distribution to computeprobabilities? How do you use the Poissondistribution to compute probabilities? Howcan you distinguish between binomial,geometric and Poisson distributions?

CC.2.2.HS.D.1. Interpret the structure ofexpressions to represent a quantity in termsof its context.CC.2.2.HS.D.2. Write expressions inequivalent forms to solve problems.CC.2.4.HS.B.6. Use the concepts ofindependence and conditional probability tointerpret data.CC.2.4.HS.B.7. Apply the rules ofprobability to compute probabilities ofcompound events in a uniform probabilitymodel.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


The normal probability distribution and thearea underneath the curve relates to theprobability of an event and is applicable tomany real-world situations.

The students will learn how to recognizenormal distributions and how to use theirproperties in real-life applications.

How are normal (bell-shaped) distributionsused to solve real-life problems? What arethe properties of a normal distribution? How would you calculate the probabilitiesfor normally distributed variables? How doyou calculate and interpret standardz-scores? How do you apply the CentralLimit Theorem? How can the normaldistribution be used to approximate binomialprobabilities?

CC.2.2.HS.D.1. Interpret the structure ofexpressions to represent a quantity in termsof its context.CC.2.4.HS.B.1. Summarize, represent, andinterpret data on a single count ormeasurement variable.CC.2.4.HS.B.6. Use the concepts ofindependence and conditional probability tointerpret data.CC.2.4.HS.B.7. Apply the rules ofprobability to compute probabilities ofcompound events in a uniform probabilitymodel.CC.MP.1. Make sense of proble











When dealing with data there is a range inwhich expected values will occur. Thisrange is the confidence interval.

The students will use formulas andtechnology to create confidence intervals.

How are confidence intervals used toestimate population parameters? How doyou calculate a point estimate and margin oferror? How can you construct and interpretconfidence intervals for the populationmean? How do you determine the requiredminimum sample size when estimating thepopulation mean? How is the t-distributionapplied to real-life applications? How do yoconstruct a confidence interval for apopulation proportion? How do youinterpret information on a chi-squaredistribution table?

CC.2.1.HS.F.4. Use units as a way tounderstand problems and to guide thesolution of multi-step problems.CC.2.1.HS.F.5. Choose a level of accuracyappropriate to limitations on measurementwhen reporting quantities.CC.2.2.HS.D.1. Interpret the structure ofexpressions to represent a quantity in termsof its context.CC.2.2.HS.D.2. Write expressions inequivalent forms to solve problems.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Hypothesis Testing is an importantprocedure used to check the validity of aclaim in an experiment

Hypothesis Testing gives a scientificprocedure for assessing the validity of aclaim about a population.

What are the components of a hypothesistest? How do you apply a p-value to test amean value? How do you preform a z-testto test the mean of one

CC.2.4.HS.B.1. Summarize, represent, andinterpret data on a single count ormeasurement variable.CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.CC.MP.1. Make sense of proble









sample? How do you use a t-test to test apopulation mean? How do you use the z-testto test a population proportion? How wouldyou apply the chi-square to test a variance orstandard deviation?



Hypothesis Testing for two variables is usedto check the validity of a claim regardingtwo independent or dependent events

Hypothesis Test can be used to compare twopopulations.

How can Hypothesis testing be used todetermine if differences in samples representactual differences in populations? How doyou perform a two-sample z-test betweenmeans using large independent samples? How do you perform a two-sample z-testbetween means using small independentsamples? How do you decide whether twosamples are independent or dependent? How do you perform a t-test to test the meanof the differences for a population of paireddata? How do you perform a z-test for thedifferences between two populationsproportions?

CC.2.4.HS.B.1. Summarize, represent, andinterpret data on a single count ormeasurement variable.CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.


Strong Correlation between two variablesdoes not automatically mean that onevariable has a direct affect on another.

Correlation can be used to determine thesignificance of the relationship betweenpaired data.

How is correlation used in analyzing paireddata? How do you calculate a correlationcoefficient? How do you determine if acorrelation is significant? How do youcalculate the equation of a regression line?How can you prediction interval? How doyou find and use multiple regression topredict y-values?

CC.2.1.HS.F.3. Apply quantitative reasoningto choose and interpret units and scales informulas, graphs, and data displays.CC.2.1.HS.F.4. Use units as a way tounderstand problems and to guide thesolution of multi-step problems.CC.2.1.HS.F.5. Choose a level of accuracyappropriate to limitations on measurementwhen reporting quantities.CC.2.2.HS.D.10. Represent, solve, andinterpret equations/inequalities and systemsof eq









uations/inequalities algebraically andgraphically.CC.2.4.HS.B.2. Summarize, represent, andinterpret data on two categorical andquantitative variables.CC.2.4.HS.B.3. Analyze linear models tomake interpretations based on the data.CC.2.4.HS.B.5. Make inferences and justifyconclusions based on sample surveys,experiments, and observational studies.CC.MP.1. Make sense of problems andpersevere in solving them.CC.MP.2. Construct viable arguments andcritique the reasoning of others.CC.MP.3. Use appropriate toolsstrategically.CC.MP.4. Look for and make use ofstructure.CC.MP.5. Reason abstractly andquantitatively.CC.MP.6. Model with mathematics.CC.MP.7. Attend to precision.CC.MP.8. Look for and express regularity inrepeated reasoning.

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Scope and Sequence Report...Geometry - Unit #2 This chapter focuses on the role of reasoning in geometry. Students compare and contrast inductive and deductive reasoning and learn