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Integrated Algebra Curric.doc 1

Integrated Algebra Curriculum

Course Description:

Course Essential Questions:

Integrated Algebra Regents Exam Information:Approximate Percentage of Questions Assessing Each StrandStrand: Percent: Time allotted: Focus Unit(s):Number Sense and Operations: 6-10% (? weeks) 1, 11, 14Algebra: 50-55% (? weeks) 2 9, 12Geometry: 14-19% (? weeks) 10Measurement: 3-8% (? weeks)Probability and Statistics: 14-19% (? weeks) 13, 14

Format:Question Type: Number of Questions:Multiple-choice 302-credit open ended 33-credit open ended 34-credit open ended 3


Reference Sheet:

The Regents Examination in Integrated Algebra will include a reference sheet containing theformulas specified below.


Integrated Algebra Mathematical Language

The language below is language that all students should be familiar with and should be usedthroughout instruction. Definitions for most words and expressions can be found in theHS Glossary.

Problem Solvingalgebraicallyconceptconjectureconstraintequivalent

formulategeneralizationgraphicallymultiple representationsnumerically

parameterpatternrelative efficiencystrategyverbally

Reasoning and Proofappropriateapproximationargumentclaimconclusionconjecture

counterexampleexplaininductive reasoninglogical argumentmathematical conjectureproof

refutesystematic approachvalidityVenn diagramverify

Communicationaccuracyanalyzeargumentcoherentcommunicatecomprehensionconclusionconjecturedecoding

elicitequationevaluateextendformulafunctiongraphinterpretationmathematical visual

rationalestandard (mathematical)

notationstrategytabletechnical writingterminologyvalid

Connectionscoherent wholeconceptconnection

formulatephysical modelprocedure

quantitative modelrepresentation

Representationangle of elevationarraychartcomparediagramequationfunction

graphinterpretmathematical phenomenaorganizephysical phenomenaprofitrecord

social phenomenasymboltabletechnologytranslate


Number Sense and Operationsabsolute valuealgebraic problemarithmetic operationarrangements (permutations)associative propertyclosure propertycommutative propertycounting techniquesdecimaldenominatordiscountdistributive propertyexponential expression

expressionfactorialfieldfractionFundamental Principle of

Countinggroupidentity propertyinverse propertylike/unlike radical termsnumber theorynumeratorpercent of increase/ decrease

productproperties of the Real

numbersproportionality/direct

variationquotientradicalradicandreal numbersscientific notationsimplest formvariable

Algebraacute angleadjacent side/anglealgebraic equationalgebraic expressionalgebraic fractionanalyzeaxis of symmetrybinomialcoefficientcommon basecomplement of a subsetcoordinatescosinedependentdifference of two perfect

squareselementequationexponentexponential growth and

decayexpressionfactoringfractional expressiongreatest common factor

(GCF)hypotenuseindependent variableinequalityinteger

integral coefficientintegral exponentintegral root(s)intersection of setsinterval notationlead coefficientlegs of a right triangleline parallel to the xor y-

axislinear equation in one

variablelinear inequality in one

variableliteral equationlowest terms fractionmonomialmultiplication property of

zeroopposite side/angleparabolaparallelpolynomialproductproperties of exponentsproportionPythagorean Theoremquadratic equationquantitativequotientratio

relationright angleright triangleroot(s) of an equationroster formsetset-builder notationsineslopesolution setsubsetsumsystem of linear

inequalitiessystems of linear equationstangenttranslate (from verbal to

symbolic)trigonometrytrinomialundefinedunion of setsuniversal setvariableverbal expressionverbal sentencevertexx-axisy-axis


Geometryabsolute value functionangleareaaxis of symmetry of a

parabolacirclecoefficientcylinderdecagonexponential functionfunctiongeneralizegeometric shapegraph of a relationhexagon

investigatenonagonoctagonordered pairparabolic functionparallelogrampentagonperimeterpolygonquadrilateralquarter-circlerational coefficientrectanglerectangular solidregular polygon

relationrhombusroots of a parabolic

functionsector of a circlesemi-circlespatial reasoningsquaresurface areatrapezoidtrianglevertexvisualizationvolume

Measurementappropriate unitconversioncubic uniterror

linear measurelinear unitmagnitudemeasurement system

raterelative errorsquare unitunit

Statistics and Probabilityappropriatenessbiasedbivariatebox-and-whisker plotcalculated probabilitycategorizecausationcentral tendencycomplementconditional probabilitycorrelationcumulative frequency

distribution tablecumulative frequency

histogramdatadependent eventsdependent variableelement

empirical probabilityexperimental designextrapolationfavorable eventfinite sample spacefive statistical summaryfrequency distribution

tablehistogramindependent eventsindependent variableinterpolationline of best fitlinear transformationmaximummeanmeasure of central

tendencymedian

minimummodemutually exclusive eventsnot mutually exclusive

eventspercentile rankprobabilityqualitativequantitativequartiles (specifically:

first, second, thirdor lower, middle,upper)

rangesample spacescatter plotseriesunivariate


Integrated Algebra Unit Sequence and Timeline:(Note: Due to the need to include an additional unit in January for 8th grade students, the

timeframes given are not valid for 8th grade classes. Please modify the calendar asneeded.)

Unit 1 Number and OperationsLength: ~ 3 weeksTimeframe: Early September to late September

Unit 2 Variables and ExpressionsLength: ~ 1.5 weeksTimeframe: Late September

Unit 3 Solving Linear Equations and InqualitiesLength: ~ 5 weeksTimeframe: Early October to early November

Unit 4 Multiplying and Dividing PolynomialsLength: ~ 1.5 weeksTimeframe: Mid-November

Unit 5 Factoring and Solving QuadraticsLength: ~ 3 weeksTimeframe: Early December to late December

Unit A 8th Grade Geometry UnitLength: ~ 5 weeksTimeframe: Early January

Unit 6 Algebraic FractionsLength: ~ 2 weeksTimeframe: Early January to mid-January

Unit 7 Functions and RelationsLength: ~ 1 weekTimeframe: Mid-January to late January

Unit 8 Coordinate GeometryLength: ~ 3.5 weeksTimeframe: Late January to mid-February

Unit 9 Systems of EquationsLength: ~ 2.5 weeksTimeframe: Late February to early March


Unit 10 Working with ShapesLength: ~ 1.5 weeksTimeframe: Mid-March to late March

Unit 11 RadicalsLength: ~ 1.5 weeksTimeframe: Late March to early April

Unit 12 TrigonometryLength: ~ 2 weeksTimeframe: Mid-April to late April

Unit 13 StatisticsLength: ~ 3 weeksTimeframe: Early May to late May

Unit 14 ProbabilityLength: ~ 2 weeksTimeframe: Late May to early June

Unit 15 Review for Regents ExamLength: ~ ? weeksTimeframe: Mid-June


Unit 1 Numbers and OperationsLength: ~ 3 weeksTimeframe: Early September to late September

State Standards:A.N.1 Identify and apply the properties of real numbers (closure, commutative, associative,

distributive, identity, inverse) Note: Students do not need to identify groups and fields,but students should be engaged in the ideas.

A.M.2 Solve problems involving conversions within measurement systems, given therelationship between the units

Local Standards (Stricken text is covered in a different unit):TBD

Big Ideas and Essential Questions:All mathematics is governed by specific rules (properties).

Prior Knowledge:TBD

Unit Objectives: Students will be ableto identify by example commutative prop of addition and multiplication, associative

property of addition and multiplication, distributive propertyto identity properties of addition and multiplication, inverse properties of addition and

multiplication, multiplicative property of zero.to identify and give examples of rational and irrational numbersto apply operations to signed numbersto apply the rules of order of operationsto define absolute value and evaluate absolute value expressionsto evaluate exponential expressionsto convert between fractions, decimals and percentsto convert within a measurement system and solve problems using conversions

Resources:Amsco: Ch. 1, 2, and 5Unified: Ch1, 7

See AECSD curriculum database for additional resources and lesson ideas.


Unit 2 Variables and ExpressionsLength: ~ 1.5 weeksTimeframe: Late September

State Standards:A.N.6 Evaluate expressions involving factorial(s), absolute value(s), and exponential

expression(s)A.A.1 Translate a quantitative verbal phrase into an algebraic expressionA.A.2 Write a verbal expression that matches a given mathematical expressionA.A.13 Add, subtract, and multiply monomials and polynomials


Big Ideas and Essential Questions:Mathematics can be used to model real situations.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto recognize and utilize algebraic terminologyto add and subtract polynomialsto translate verbal phrases into algebraic expressionsto translate algebraic expressions in verbal phrases

Resources:Amsco: Ch. 4Unified: 7-3; Ch. 3



Unit 3 Solving Linear Equations and InequalitiesLength: ~ 5 weeksTimeframe: Early October to early November

State Standards:A.N.1 Identify and apply the properties of real numbers (closure, commutative, associative,

distributive, identity, inverse) Note: Students do not need to identify groups and fields,but students should be engaged in the ideas.

A.N.5 Solve algebraic problems arising from situations that involve fractions, decimals, percents(decrease/increase and discount), and proportionality/direct variation

A.A.3 Distinguish the difference between an algebraic expression and an algebraic equationA.A.4 Translate verbal sentences into mathematical equations or inequalitiesA.A.5 Write algebraic equations or inequalities that represent a situationA.A.6 Analyze and solve verbal problems whose solution requires solving a linear equation in

one variable or linear inequality in one variableA.A.21 Determine whether a given value is a solution to a given linear equation in one variable

or linear inequality in one variableA.A.22 Solve all types of linear equations in one variableA.A.23 Solve literal equations for a given variableA.A.24 Solve linear inequalities in one variableA.A.25 Solve equations involving fractional expressions Note: Expressions which result in

linear equations in one variable.A.A.26 Solve algebraic proportions in one variable which result in linear or quadratic equationsA.M.1 Calculate rates using appropriate units (e.g., rate of a space ship versus the rate of a snail)


Big Ideas and Essential Questions:Many real life situations can be modeled and analyzed using linear equations.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto identify the difference between an expression and an equationto simplify and solve linear equations (including all multi-step )to describe the steps of solving equations through use of propertiesto clear fractions in a linear equation before solvingto solve literal equationsto solve and check linear inequalitiesto graph linear inequalities using a number lineto translate verbal sentences into equations and inequalitiesto write algebraic equations/inequalities that represent a situationto analyze and solve problems with linear equations/inequalitiesto form and solve proportions


to solve verbal problems including fractions, percents (increase/decrease ) ratio, andproportions

to compare rates

Resources:Split Unit: one test for solving equations and inequalitiesone test for applications

Amsco: Ch 6; Ch 9; Ch 12; Ch 19-7 19-10Unified: Ch3; Ch4; 9-1 9-3



Unit 4 Multiplying and Dividing PolynomialsLength: ~ 1.5 weeksTimeframe: Mid-November

State Standards:A.N.4 Understand and use scientific notation to compute products and quotients of numbersA.A.12 Multiply and divide monomial expressions with a common base, using the properties of

exponents Note: Use integral exponents only.A.A.13 Add, subtract, and multiply monomials and polynomialsA.A.14 Divide a polynomial by a monomial or binomial, where the quotient has no remainder


Big Ideas and Essential Questions:All of the rules that apply to numbers also apply to variables.Scientific notation makes it easier to work with very large and very small numbers

(really).

Prior Knowledge:TBD

Unit Objectives: Students will be ableto multiply monomials by monomialsto multiply monomials by polynomialsto multiply binomials by binomialsto divide monomials by monomialsto divide polynomials by monomialsto convert between numbers in scientific notationto multiply numbers expressed in scientific notationto divide numbers expressed in scientific notation

Resources:Amsco: Ch. 8Unified: Ch. 7



Unit 5 Factoring and Solving QuadraticsLength: ~ 3 weeksTimeframe: Early December to late December

State Standards:A.A.8 Analyze and solve verbal problems that involve quadratic equationsA.A.19 Identify and factor the difference of two perfect squaresA.A.20 Factor algebraic expressions completely, including trinomials with a lead coefficient of

one (after factoring a GCF)A.A.26 Solve algebraic proportions in one variable which result in linear or quadratic equationsA.A.27 Understand and apply the multiplication property of zero to solve quadratic equations

with integral coefficients and integral rootsA.A.28 Understand the difference and connection between roots of a quadratic equation and

factors of a quadratic expression


Big Ideas and Essential Questions:Many real life situations can be modeled and analyzed using quadratic equations.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto factor out the greatest common factorto factor trinomials with coefficient a = 1to factor a difference of 2 perfect squaresto factor completely; GCF first, then as 2 binomials ( a =1 )to compare linear and quadratic equationsto solve quadratic equations using multiplication property of zeroto recognize the relationship between roots and factors of quadratic equationsto analyze and solve verbal problems including proportions that result in quadratics

Resources:Split unit assessment: one test on factoringone test on solving quadratics

Amsco: Ch 18; 21-1 21-3; 21-6Unified: Ch 7



Unit A 8th Grade Geometry UnitLength: ~ 5 weeksTimeframe: Early January

State Standards:8.A.12 Apply algebra to determine the measure of angles formed by or contained in parallel lines

cut by a transversal and by intersecting lines8.G.1 Identify pairs of vertical angles as congruent8.G.2 Identify pairs of supplementary and complementary angles8.G.3 Calculate the missing angle in a supplementary or complementary pair8.G.4 Determine angle pair relationship when given two parallel lines cut by a transversal8.G.5 Calculate the missing angle measurements when given two parallel lines cut by a

transversal8.G.6 Calculate the missing angle measurements when given two intersecting lines and an angle8.G.7 Describe and identify transformations in the plane using proper function notation

(rotations, reflections, translations, dilations)8.G.8 Draw the image of a figure under rotations of 90 and 180 degrees8.G.9 Draw the image of a figure under a reflection over a given line8.G.10 Draw the image of a figure under a translation8.G.11 Draw the image of a figure under a dilation8.G.12 Identify the properties preserved and not preserved under a reflection, rotation,

translation, and dilation


Big Ideas and Essential Questions:TBD

Prior Knowledge:TBD

Unit Objectives: Students will be ableto apply algebra to determine the measure of angles formed by or contained in parallel

lines cut by a transversal and by intersecting linesto identify pairs of vertical angles as congruentto identify pairs of supplementary and complementary anglesto calculate the missing angle in a supplementary or complementary pairto determine angle pair relationship when given two parallel lines cut by a transversalto calculate the missing angle measurements when given two parallel lines cut by a

transversalto calculate the missing angle measurements when given two intersecting lines and an

angleto describe and identify transformations in the plane using proper function notation (

rotations, reflections, translations, dilations. )to draw the image of a figure under rotations of 90 and 180 degrees


to draw the image of a figure under a reflection over a given lineto draw the image of a figure under a translationto draw the image of a figure under a dilationto identify the properties preserved and not preserved under a reflection, rotation,

translation, and dilation

Resources:Utilize the 8th grade curriculum.

This chapter must be completed after Unit 5 to ensure that it is done before theassessment.



Unit 6 Algebraic FractionsLength: ~ 2 weeksTimeframe: Early January to mid-January

State Standards:A.A.15 Find values of a variable for which an algebraic fraction is undefinedA.A.16 Simplify fractions with polynomials in the numerator and denominator by factoring both

and renaming them to lowest termsA.A.17 Add or subtract fractional expressions with monomial or like binomial denominatorsA.A.18 Multiply and divide algebraic fractions and express the product or quotient in simplest

form


Big Ideas and Essential Questions:Properties of fractions apply to algebraic fractions the same way they apply to fractions.All the rules that apply to numeric fractions also apply to algebraic fractions.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto identify for what values an algebraic fraction is undefinedto simplify algebraic fractions by factoring: GCF and binomial factorsto multiply algebraic fractions (and simplify)to divide algebraic fractions (and simplify)to add and subtract algebraic fractions with like and unlike monomial denominators (and

simplify)to add and subtract algebraic fractions with like binomial denominators (and simplify)

Resources:Amsco: Ch. 19Unified: supplement



Unit 7 Functions and RelationsLength: ~ 1 weekTimeframe: Mid-January to late January

State Standards:A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given

the elements in roster formA.A.30 Find the complement of a subset of a given set, within a given universeA.A.31 Find the intersection of sets (no more than three sets) and/or union of sets (no more than

three sets)A.G.3 Determine when a relation is a function, by examining ordered pairs and inspecting graphs

of relations


Big Ideas and Essential Questions:A function denotes a special relationship between independent and dependent variables.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto define and identify the difference between relations and functionsto identify when a relation is a functionto read and use set builder notationto read and use interval notationto identify the intersection of 2 or more setsto identify the complement of a set

Resources:Amsco: supplementUnified: supplement



Unit 8 Coordinate GeometryLength: ~ 3.5 weeksTimeframe: Late January to mid-February

State Standards:A.A.9 Analyze and solve verbal problems that involve exponential growth and decayA.A.32 Explain slope as a rate of change between dependent and independent variablesA.A.33 Determine the slope of a line, given the coordinates of two points on the lineA.A.34 Write the equation of a line, given its slope and the coordinates of a point on the lineA.A.35 Write the equation of a line, given the coordinates of two points on the lineA.A.36 Write the equation of a line parallel to the xor y-axisA.A.37 Determine the slope of a line, given its equation in any formA.A.38 Determine if two lines are parallel, given their equations in any formA.A.39 Determine whether a given point is on a line, given the equation of the lineA.A.41 Determine the vertex and axis of symmetry of a parabola, given its equation (See

A.G.10)A.G.4 Identify and graph linear, quadratic (parabolic), absolute value, and exponential functionsA.G.5 Investigate and generalize how changing the coefficients of a function affects its graphA.G.6 Graph linear inequalitiesA.G.8 Find the roots of a parabolic function graphically Note: Only quadratic equations with

integral solutions.


Big Ideas and Essential Questions:Graphs can help you analyze the relationship between two variables.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto identify the difference between a relation and a function graphically.to recognize the solution set of a linear equation of two variables is represented by a lineto determine if a given point is a solution ( on the line ) given the equationto find slope given two points on a lineto identify the slope and y intercept given an equation in any formto graph linear equations using slope/intercept methodto compare graphs of functions and their coefficientsto identify if two lines are parallel given their equationsto identify and graph linear equations parallel to the x and y axesto write the equations of lines parallel to x and y axesto write the equation of a line given its slope and one pointto write the equation of a line given 2 pointsto graph linear inequalitiesto define vertex and axis of symmetry


to find vertex and axis of symmetry given the equation of a quadraticto graph parabolasto identify the roots, vertex and axis of symmetry given a parabolato compare parabolic graphs and coefficientsto graph absolute value functionsto graph exponential functionsto apply graphs of linear, quadratic, exponential growth and decay to real world

applications i.e. interpret slope as a rate of change

Resources:Split Unit: one test on graphing linear equationsone on graphing quadratic equations

Amsco: 16-1 16-8; 16-13; 21-8; supplement exponential graphsUnified: Ch 13; supplement parabolas, absolute value, exponential graphs

Websites:http://serc.carleton.edu/quantskills/methods/quantlit/expGandD.htmlHere is a great resource for Exponential Growth and decay:http://www.regentsprep.org/Regents/math/ALGEBRA/AE7/indexAE7.htm



Unit 9 Systems of EquationsLength: ~ 2.5 weeksTimeframe: Late February to early March

State Standards:A.A.7 Analyze and solve verbal problems whose solution requires solving systems of linear

equations in two variablesA.A.10 Solve systems of two linear equations in two variables algebraically (See A.G.7)A.A.11 Solve a system of one linear and one quadratic equation in two variables, where only

factoring is required Note: The quadratic equation should represent a parabola and thesolution(s) should be integers

A.A.40 Determine whether a given point is in the solution set of a system of linear inequalitiesA.G.7 Graph and solve systems of linear equations and inequalities with rational coefficients in

two variables (See A.A.10)A.G.9 Solve systems of linear and quadratic equations graphically Note: Only use systems of

linear and quadratic equations that lead to solutions whose coordinates are integers.


Big Ideas and Essential Questions:Systems allow analysis of more complicated situations.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto solve linear systems graphicallyto solve linear systems algebraically by substitution methodto solve linear systems algebraically by addition (elimination) method(include least common multiple)to analyze and solve verbal problems as systems of equationsto solve linear/quadratic systems by graphingto solve linear/quadratic systems algebraically ( only factoring required, quadratic is a

parabola, solutions are integers )to determine the solution set of system of inequalities by graphingto determine if a point is in the solution set of a system of inequalities

Resources:Amsco: Ch 17; 21-10; 21-11Unified: Ch 14



Unit 10 Working with ShapesLength: ~ 1.5 weeksTimeframe: Mid-March to late March

State Standards:A.G.1 Find the area and/or perimeter of figures composed of polygons and circles or sectors of a

circle Note: Figures may include triangles, rectangles, squares, parallelograms,rhombuses, trapezoids, circles, semi-circles, quarter-circles, and regular polygons(perimeter only).

A.G.2 Use formulas to calculate volume and surface area of rectangular solids and cylindersA.M.3 Calculate the relative error in measuring square and cubic units, when there is an error in

the linear measure


Big Ideas and Essential Questions:Perimeter/circumference is one dimensional; area is two dimensional; volume is three

dimensional.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto identify when to use perimeter, area, and volumeto find perimeter/circumference of polygons, circles, and circle sectorsto find area of polygons, circles and circle sectorsto find surface area of rectangular solids and cylindersto find the volume of rectangular solids and cylindersto apply appropriate formula given a real life situationto calculate and analyze relative error in measuring square and cubic units when error

occurs in linear measure

Resources:Amsco: 4-6 4-9Unified: Ch 10; Ch 6



Unit 11 RadicalsLength: ~ 1.5 weeksTimeframe: Late March to early April

State Standards:A.N.2 Simplify radical terms (no variable in the radicand)A.N.3 Perform the four arithmetic operations using like and unlike radical terms and express the

result in simplest form


Big Ideas and Essential Questions:Radicals are exponents. Therefore, all the rules for exponents apply to radicals.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto simplify radicals (no variable in the radicand)to multiply and divide radicals ( like and unlike radicals )to add and subtract radicals ( like and unlike radicals )

Resources:Amsco: Ch 20Unified: Ch 8



Unit 12 TrigonometryLength: ~ 2 weeksTimeframe: Mid-April to late April

State Standards:A.A.42 Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths

of the sidesA.A.43 Determine the measure of an angle of a right triangle, given the length of any two sides

of the triangleA.A.44 Find the measure of a side of a right triangle, given an acute angle and the length of

another sideA.A.45 Determine the measure of a third side of a right triangle using the Pythagorean theorem,

given the lengths of any two sides


Big Ideas and Essential Questions:Given certain information about a right triangle, you can find the measures of sides and

angles.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto apply the Pythagorean Theorem to real world applicationsto identify and form trigonometric ratios ( sine, cosine, tangent)to find an acute angle given lengths of sidesto find length of a side given an acute angle and one sideto trigonometric ratios to real world problems i.e. angle of depression and angle of

elevationto determine when to use the Pythagorean theorem versus trigonometry

Resources:Amsco: 21 -5; 21-5; Ch 22Unified: Supplement



Unit 13 StatisticsLength: ~ 3 weeksTimeframe: Early May to late May

State Standards:A.S.1 Categorize data as qualitative or quantitativeA.S.2 Determine whether the data to be analyzed is univariate or bivariateA.S.3 Determine when collected data or display of data may be biasedA.S.4 Compare and contrast the appropriateness of different measures of central tendency for a

given data setA.S.5 Construct a histogram, cumulative frequency histogram, and a box-and-whisker plot, given

a set of dataA.S.6 Understand how the five statistical summary (minimum, maximum, and the three

quartiles) is used to construct a box-and-whisker plotA.S.7 Create a scatter plot of bivariate dataA.S.8 Construct manually a reasonable line of best fit for a scatter plot and determine the

equation of that lineA.S.9 Analyze and interpret a frequency distribution table or histogram, a cumulative frequency

distribution table or histogram, or a box-and-whisker plotA.S.10 Evaluate published reports and graphs that are based on data by considering:

experimental design, appropriateness of the data analysis, and the soundness of theconclusions

A.S.11 Find the percentile rank of an item in a data set and identify the point values for first,second, and third quartiles

A.S.12 Identify the relationship between the independent and dependent variables from a scatterplot (positive, negative, or none)

A.S.13 Understand the difference between correlation and causationA.S.14 Identify variables that might have a correlation but not a causal relationshipA.S.15 Identify and describe sources of bias and its effect, drawing conclusions from dataA.S.16 Recognize how linear transformations of one-variable data affect the data’s mean,

median, mode, and rangeA.S.17 Use a reasonable line of best fit to make a prediction involving interpolation or

extrapolation


Big Ideas and Essential Questions:Statistics can be used to analyze data to help you make decisions.Statistics can be used to mislead people (including you).

Prior Knowledge:TBD

Unit Objectives: Students will be ableto categorize data as qualitative or quantitative


to determine univariate or bivariateto determine if collected or displayed data is biasto identify source of bias and effect ( using data )to determine measures of central tendency and when each is most appropriate for a given

set of datato recognize how linear transformations of 1 variable data affect the data’s mean, median,

mode and rangeto construct frequency and cumulative frequency histogramsto find percentile rank and find points values for quartilesto find minimum, maximum and quartiles of a set of datato construct a box and whisker plotto analyze and interpret histograms and box and whisker plotsto create bivariate scatter plotto determine line of best fit and its equationto utilize line of best fit to make predictions (involving interpolation or extrapolation)to identify relationship of independent and dependent variables from scatter plot (pos,

neg, none)to identify the difference between correlation and causationto identify variables that might have correlation without causalto evaluate published reports and graphs based on data: experimental design,

appropriateness of data analysis, soundness of conclusions

Resources:Amsco: 15 -1 -> 15-6; 16-9Unified: Ch 12; supplement most



Unit 14 ProbabilityLength: ~ 2 weeksTimeframe: Late May to early June

State Standards:A.N.6 Evaluate expressions involving factorial(s), absolute value(s), and exponential

expression(s)A.N.7 Determine the number of possible events, using counting techniques or the Fundamental

Principle of CountingA.N.8 Determine the number of possible arrangements (permutations) of a list of itemsA.S.18 Know the definition of conditional probability and use it to solve for probabilities in

finite sample spacesA.S.19 Determine the number of elements in a sample space and the number of favorable eventsA.S.20 Calculate the probability of an event and its complementA.S.21 Determine empirical probabilities based on specific sample dataA.S.22 Determine, based on calculated probability of a set of events, if:

• some or all are equally likely to occur• one is more likely to occur than another• whether or not an event is certain to happen or not to happen

A.S.23 Calculate the probability of:• a series of independent events• a series of dependent events• two mutually exclusive events• two events that are not mutually exclusive


Big Ideas and Essential Questions:Any event in life has a probability associated with it that ranges from certain to

impossible.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto recognize the difference between theoretical vs. empiricalto determine empirical probabilities based on data to analyze the sample space of an experiment to determine the likelihood a given event

will occur (include complement)to know the definition of conditional probabilityto utilize conditional probability to solve for probabilities in finite sample spacesto know the difference between and find the probability of single and compound eventsto calculate the probability of a series of independent eventsto calculate the probability of a series of dependent eventsto calculate the probability of two mutually exclusive events


to calculate the probability two events that are not mutually exclusiveto use the counting principle to determine the number of possible outcomesto evaluate factorialsto determine the number of possible arrangements (permutations) of a list of items

Resources:Amsco: Ch 13; 14-1 -> 14-5Unified: Ch 11



Unit 15 Review for Regents ExamLength: ~ ? weeksTimeframe: Mid-June

State Standards:All


Big Ideas and Essential Questions:Passing the Integrated Algebra Regents Exam is a graduation requirement.

Prior Knowledge:TBD

Unit Objectives: Students will be ableto ace the Integrated Algebra Regents exam

Resources:


integrated algebra curric - auburn school districtdistrict.auburn.cnyric.org/departments/math/math...

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