PNWBOCES Curriculum Outline for Integrated AlgebraMay 18, June 21, July 5-6, 2006

Time frame includes instructional days, review, and tests

Real Number System Time Frame: 6 days

Content Indicators: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. Students will understand meanings of operations and procedures,

and how they relate to one another.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)

Process Indicators:A.PS.1 Use a variety of problem solving strategies to understand new mathematical content A.PS.4 Use multiple representations to represent and explain problem situations (e.g., verbally,

numerically, algebraically, graphically) Students will apply and adapt a variety of appropriate strategies to solve problems.A.PS.5 Choose an effective approach to solve a problem from a variety of strategies (numeric, graphic,

algebraic) A.PS.10 Evaluate the relative efficiency of different representations and solution methods of a problemA.CM.12 Understand and use appropriate language, representations, and terminology when describing

objects, relationships, mathematical solutions, and rationaleA.CN.8 Develop an appreciation for the historical development of mathematics A.CM.3 Present organized mathematical ideas with the use of appropriate standard notations, including

the use of symbols and other representations when sharing an idea in verbal and written form.

Vocabulary:Closure PropertyAssociative PropertyCommutative PropertyDistributive PropertyIdentity PropertyInverse propertyEquivalentNumber Theory

Real NumbersIrrational NumbersRational NumbersNatural Numbers (Counting)IntegerFieldGroupConnection

SubsetSetSet Builder NotationUniversal Set ElementFinite Sample SpaceUnion of setsVenn DiagramComplement of a subset

DenominatorNumeratorFractionRadicalMultiple RepresentationsSimplest Form DecimalAbsolute ValueProcedure

1

Resources:

Textbook Performance Indicator(s) Section # or Page #Amsco: Integrated Algebra I A.A.29, A.A.30, A.A.31 2-7

A.N.1 2-2

McDougal Littell: Algebra IISBN: 978-061859402-3

A.A.29, A.A.30, A.A.31 p.71-72

A.N.1 p.73-79 (question #’s 53-56), 89-93, 96-101, 103-108, 120, 123, 189(#’s40-43), 939 (#’s38-45)

Glencoe: Algebra – NY VersionISBN: 0-07-8733162

A.A.29 6-1A.A.30 14-3A.A.31 6-3A.N.1 1-4, 1-5, 1-6A.RP.11 p. 70, 775A.PS.4 p. 43-49

Algebraic Expressions, Equations and Inequalities 14 days

Content Indicators:A.A.1 Translate a quantitative verbal phrase into an algebraic expressionA.A.2 Write a verbal expression that matches a given mathematical expressionA.N.6 Evaluate expressions involving absolute value(s), and exponential expression(s) 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.22 Solve all types of linear equations in one variableA.A.24 Solve linear inequalities in one variable A.A.6 Analyze and solve verbal problems whose solution requires solving a linear equation in one

variable or linear inequality in one variableA.A.25 Solve equations involving fractional expressions Note: Expressions which result in linear

equations in one variable.A.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.23 Solve literal equations for a given variable

Process Indicators:A.CM.8 Reflect on strategies of others in relation to one’s own strategyA.CM.10 Use correct mathematical language in developing mathematical questions that elicit, extend, or

challenge other students’ conjecturesA.CM.11 Represent word problems using standard mathematical notationA.CN.1 Understand and make connections among multiple representations of the same mathematical

ideaA.R.4 Select appropriate representations to solve problem situationsA.R.5 Investigate relationships between different representations and their impact on a given problem

2

Vocabulary:EquationEvaluateFormulaExpressionVariableSymbolInequality

InterpretationsCommunicateOrganizeTranslateAnalyzeFormulateStrategyExplainSystematic ApproachCommunicateComprehensionConclusionConjectureDecodingStandard mathematical NotationTechnical WritingNumericallyVerbally

Algebraic ProblemArithmetic OperationsAlgebraic ExpressionAlgebraic EquationCoefficientLinear Equation in one variableSolution SetLinear Inequality in one variableLiteral equationVerbal Expression Algebraically Verbal SentenceSatisfies the equationMeansExtremes

DiagramProfitDiscountPercent of increase/decreaseProductProportionQuotientRatioSum

Resources:Textbook Performance Indicator(s) Section # or Page #Educational Design: New York Math A – Semesters 1 and 2

A.A.1 Chapter 4, Section 5, p. 178 18A.A.4 Chapter 4, Section 6, p. 183-187A.N.6 p. 52, Lakeland packet of handoutsA.A.22 Chapter 4, Section 2-4, 7-8, p. 162-

177, 189-199A.A.25 Section 9, p. 200-205, Lakeland

packet of handoutsA.A.6 Chapter 5, Section 1-7, p. 213-263

Chapter 6, Section 4, p. 290-293Lakeland packet of handouts

A.A.23 Chapter 5, Section 8, p. 264-267Lakeland packet of handouts

Glencoe/McGraw Hill (Merrill): Integrated Mathematics Course 1

A.A.1 p. 71-77A.A.2 p. 71-77A.N.6 p. 41-49A.A.3 p. 74-79A.A.4 p. 78-79, p. 113-115A.A.5 p. 88-89A.A.22 p. 88-89, p. 94-101A.A.24 p. 116-120A.A.6 p. 94-101, p. 123-124A.A.25 p. 82A.A.21 p. 82 46-51

3

A.A.23 p. 110-112Glencoe: Algebra 1 – NY State A.A.2 p. 8-9 11-18, 31-42

A.A.3 p. 16-17A.A.4 p. 124 13-20A.N.6 p.71 (34-56 all)A.A.25 p. 146 (26 – 39) allA.A.6 p. 139 ( 39-50) all

p. 146-147 (48 -54) allA.A.23 p. 16-19 (1-25) allA.A.5 p. 124-125 (21, 22,45 -51 all)A.A.21 p. 16-19 (1-25) allA.A.24 Chapter 6 Sections 6.1 – 6.3

p. 318 - 337A.CM.11 Section 3.2, p. 131-132; Section

3.4, p. 142-148; Section 3.5 p. 153-154

McDougal Littell – Algebra 1 A.CM.8 Section 3.5, p. 160-162A.CM.11A.R.5

Operations with Polynomials 9 days

Content Indicators:A.A.13 Add, subtract, and multiply monomials and polynomialsA.A.12 Multiply and divide monomial expressions with a common base, using the properties of

exponents Note: Use integral exponents onlyA.A.14 Divide a polynomial by a monomial or binomial, where the quotient has no remainderA.N.4 Understand and use scientific notation to compute products and quotients of numbers

Process Indicators:A.CM.4 Explain relationships among different representations of a problem

Vocabulary:CoefficientIntegral CoefficientIntegral ExponentLead CoefficientExponential Expression

MonomialBinomialTrinomialPolynomial

ExponentProperties of ExponentsCommon BaseScientific notation

Resources:Textbook Performance Indicator(s) Section # or Page #Amsco: Mathematics A (2002) A.A.12, A.A.13, A.A.14, A.N.4 p. 235-268Amsco: Integrated Mathematics Course 1 (3rd ed)

A.N.4 p. 292-296A.A.12 p. 297-299A.A.13 p. 266-286

4

A.A.14 p. 299-301Glencoe/McGraw Hill: Integrated Mathematics Course 1 (1995)

A.A.1 p. 71-77A.A.2 p. 71-77A.N.6 p. 41-49A.A.3 p. 74-79A.A.4 p. 78-79, p. 113-115A.A.5 p. 88-89A.A.22 p. 88-89, p. 94-101A.A.24 p. 116-120A.A.6 p. 94-101, p. 123-124A.A.25 p. 82A.A.21 p. 82 46-51A.A.23 p. 110-112

Educational Design: Mathematics A Semester 1 and 2

A.CM.4 Section 3.1 p. 108; 3.2 p. 113; 3.4 p. 126; 3.5 p. 132; 3.6 p. 139; 3.7 p. 140-146; Review 1-3 p. 151-152Section 10.3 p. 504-505, 510; 10.4 p. 513

A.A.13 Section 3.1, pp. 104-108Section 3.2, pp. 109-113Section 3.6, pp. 133-137Section 3.7, pp. 142-146Section 10.3, pp. 506 – 510Section 10.4 pp. 511-518Section 10.5, pp. 515-518

A.A.12 Section 3.1, p. 104-108Section 3.2, pp. 109-113Section 3.3, pp. 114-119Section 3.4, pp. 12—126Section 3.7, pp. 142-146

A.A.14 Section 3.8, pp. 147-150A.N.4 Section 3.5, pp. 127-132

Glencoe: Algebra - NY State ISBN -0-07-873316-2

A.A.13 Chapter 1, Section 8.4, p. 406-424,p.432-471

A.A.12 Chapter 1, Section 8.4, p. 406-424A.A.14 Chapter 1, Section 8.4, p. 666-671A.N.4 Chapter 1, Section 8.4, p. 425-430

Amsco: Integrated Mathematics Course 1 (2nd ed)

A.A.13 Chapter 8, Section 8.1 to 8.4, p. 232 -242Chapter 9, Section 9-1 to 9-5, p. 256-270

A.A.12 Chapter 8, Section 8-5, p. 243-244Section 8-6, p. 244-246Section 8-7 p. 246 - 248

A.A.14 Chapter 9, Section 9-6, 9-7, p. 270-274

A.N.4 Chapter 8, Section 8-8, p. 249-251Section 8-9, p. 251 -253

5

Factoring and Quadrati cs 9 days

Content Indicators:A.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.27 Understand and apply the multiplication property of zero to solve quadratic equations with

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

quadratic expressionA.A.8 Analyze and solve verbal problems that involve quadratic equations

Process Indicators:A.PS.1 Use a variety of problem solving strategies to understand new mathematical content A.PS.4 Use multiple representations to represent and explain problem situations (e.g., verbally,

numerically, algebraically, graphically)A.PS.5 Choose an effective approach to solve a problem from a variety of strategies (numeric, graphic,

algebraic)A.PS.10 Evaluate the relative efficiency of different representations and solution methods of a problemA.CM.12 Understand and use appropriate language, representations, and terminology when describing

objects, relationships, mathematical solutions, and rationaleA.CN.8 Develop an appreciation for the historical development of mathematics

Vocabulary:FactoringGreatest Common FactorDifference of two perfect squares

Integral RootsRoots of an equationQuadratic EquationSolution set(s)Zeroes of a function

Resources:Textbook Performance

Indicator(s)Section # or Page #

Glencoe/McGraw Hill: Algebra 1 – New York Math A Edition

A.A.19 Chapter 10 – Section 4 (pages 581-586)

A.A.20 Chapter 10 – Section 3 (pages 574-580)

A.A.27 Chapter 10 – Section 6 (pages 594-600)A.A.8 Chapter 10 – Section 6 (pages 594-600)

Glencoe/McGraw Hill: Algebra 1 – New York Math A Edition – Study Guide Masters

A.A.19 10-4 (page 72)A.A.20 10-3 (page 71)A.A.27 10-6 (page 74)A.A.8 10-6 (page 74)

Glencoe/McGraw Hill: Algebra 1 – New York Math A Edition – Practice

A.A.19 10-4 (page 72)A.A.20 10-3 (page 71)A.A.27 10-6 (page 74)

6

MastersAmsco: Preparing for the Regents Examination – Mathematics A (2002)ISBN 1-56765-535-1

A.A.19 Chapter 4 (pages 114-115)A.A.20 Chapter 4 (pages 119-120)A.A.27 Chapter 4 (pages 123-137)A.A.28 Chapter 4 (pages 124-130)A.A.8 Chapter 4 (pages 140-145)

Educational Design: NYS Math A Regents CoachISBN 0-87694-843-3

A.A.19 Lesson 9 (pages 31- 35)A.A.20 Lesson 9 (pages 31- 35)A.A.27 Lesson 18 (pages 69-73)A.A.8 Lesson 18 (pages 69-73)

WestSea Publishing Co. Inc.: Regents High School Mathematics AISBN 0-937820-85-7

A.A.19 Unit 3 – Operations (page 42)A.A.20 Unit 3 – Operations (page 43)A.A.27 Unit 7 – Patterns/Functions (page 247-255)A.A.8 Unit 7 – Patterns/Functions (page 256-259)

Algebra PowerPoint: Teaching Made Easy as Pi – Written and Published by James Wenk

A.A.19 Lesson 10-3a (slides 1-7)

A.A.20 Lesson 10-5 (slides 1-8)A.A.27 Lesson 10-4 (slides 1-5)

Website – (Regents Prep) A.A.19 http://regentsprep.org/Regents/math/factor/Lfactps.htm`

http://regentsprep.org/Regents/math/factor/PracFact1.htmA.A.27 http://regentsprep.org/Regents/math/faceq/LFacEq.htm

http://regentsprep.org/Regents/math/faceq/PfacEq.htm

McDougal Littell: Algebra 1

A.A.19 Section 10.7, p. 619-624A.A.20 Section 10.8, p. 625-632A.A.27 Section 10.4, p. 597-602A.A.28 Sections 10.5, 10.6, 10.7, 10.8 p. 604-631A.A.8 Sections 10.5, 10.6, 10.7, 10.8 p. 604-631A.PS.10 Sections 9.1 p. 505, 603, 610, 618A.PS.5 p. 573

Amsco: Integrated Algebra Course 1 (2nd ed)

A.A.19 Chapter 13, Section 5, p. 418-420A.A.20 Chapter 13, Section 7, p. 423-428A.A.27 Chapter 20, Section 2, p. 681-685A.A.28 Chapter 20, Section 7, p. 702-704A.A.8 Chapter 20, Section 3, p. 685-688

Amsco: Integrated Algebra Course 1 (3rd ed)

A.A.19 Section 18-5, p. 632-634A.A.20 Section 18-8, p. 641-644A.A.27 Section 21-2, p. 705-710A.A.28 Section 21-2, p. 705-710A.A.8 Section 21-6, p. 723-726

Educational Design: Mathematics A Semesters 1 and 2

A.PS.1 p. 504-505

Internet Resources:http://illuminations.nctm.org/LessonDetail.aspx?ID=L381http://illuminations.nctm.org/LessonDetail.aspx?ID=L376

7

Rational Expressions and Equations 10 days

Content Indicators: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.18 Multiply and divide algebraic fractions and express the product or quotient in simplest formA.A.17 Add or subtract fractional expressions with monomial or like binomial denominatorsA.A.26 Solve algebraic proportions in one variable which result in linear or quadratic equationsA.N.5 Solve algebraic problems arising from situations that involve fractions, decimals, percents

(decrease/increase and discount), and proportionality/direct variation

Process Indicators: A.CM.1 Communicate verbally and in writing a correct, complete, coherent, and clear design (outline)

and explanation for the steps used in solving a problemA.CM.5 Communicate logical arguments clearly, showing why a result makes sense and why the

reasoning is valid

Vocabulary:Fractional ExpressionProportionality/direct variation

Lowest terms fractionUndefinedAppropriate UnitConversionerror

Resources:Textbook Performance Indicator(s) Section # or Page #Merrill: Integrated Math Course III (Bumby, Klutch)

A.A.15 p.21A.A.16 p.26-28A.A.18 p.26-28A.A.17 p. 30-32A.A.26 p.25A.N.5 p.40-43

Amsco: Integrated Math (3rd A.A.15 p.646

8

edition) (Dressler) Course IGlencoe: Algebra I, ISBN: 0-07-865113-1 c2005

A.A.15 Textbook p. 648-651Handouts: Study guide p. 711, 712Skill practice p. 714Reading to learn p. 715

A.A.16 Textbook p. 648-651Handouts: Study guide p. 711, 712Skill practice p. 714Reading to learn p. 715

A.A.18 Textbook p. 655-671Handouts: Study guide p. 717, 718, 723,724, 729, 730 Skill practice p. 719, 720, 725, 726, 731, 732Reading to learn p. 721, 727, 733

A.A.17 Textbook p. 672-683Handouts: Study guide p. 735, 736, 741, 742Skill practice p. 737, 738, 743, 744Reading to learn p. 739, 745

A.A.26 Textbook p. 684-689Handouts:Study guide p. 747, 748Skill practice p. 749, 750Reading to learn p. 757

A.N.5 Textbook p. 690-695Handouts:Study guide p. 753, 754Skill practice p. 755, 756Reading to learn p. 757

A.CM.1/A.CM.2 p. 653 56, 57; p. 664 45; p. 671 43; p. 67650; p. 683 59; p. 688 43

Amsco: Integrated Mathematics Course I

A.A.16 p.647-650A.A.18 p.650-655A.A.17 p. 655-657

A.A.26 p.420-423A.N.5 p. 666-667

Merrill: Integrated Mathematics Course I

A.A.26 p. 179-186

A.N.5 p. 181, 185-186

Amsco: Mathematics A A.A.39 p. 589A.A.33 p. 601A.A.37 p. 608

Educational Design: Math A Semester 3

A.A.38 p. 381

9

Internet Resources:http://regentsprep.orghttp://www.edhelper.comhttp://www.maths.mq.edu.au/numeracy/web_mums/module2/worksheet23/module2.pdfhttp://www.lphs.net/academics/math/10arley/algebraic%20fractions.dochttp://www.lboro.ac.uk/research/helm/c_helm_backup_24nov03/helm_website/documents/wbol_blk06.pdf

Radical Expressions 6 days

Content Indicators: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

Process Indicators: A.RP.10 Extend specific results to more general cases

Vocabulary:Radical Radicand Like/Unlike radical terms

Resources:Textbook Performance Indicator(s) Section # or Page #McDougal Littell: Algebra 1 A.N.2 Chapter 9 Section 2, p. 511-516

A.N.3 Chapter 12 Section 2, p. 716-721Amsco: Integrated Mathematics Course 1 (2nd ed)

A.N.2 Chapter 19, Section 4, p. 647-651A.N.3 Chapter 19, Section 10, 11, 12, p.

660-666Amsco: Integrated Mathematics Course 1 (3rd ed)

A.N.2 Chapter 20 Section 4, p. 691-693A.N.3 Chapter 20 Section 5, p. 693-696

Chapter 20 Section 6, p. 696-698Chapter 20 Section 7, p. 698-700

Internet Resources:http://illuminations.nctm.org/LessonDetail.aspx?ID=L622

10

Coordinate Plane and Graphical Analysis 20 days

Content Indicators:A.G.4 Identify and graph linear, {quadratic (parabolic), absolute value, and exponential functions}A.A.39 Determine whether a given point is on a line, given the equation of the lineA.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.M.1 Calculate rates using appropriate units (e.g., rate of a space ship versus the rate of a snail)A.A.34 Write the equation of a line, given its slope and the coordinates of a point on the line A.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 x- or 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 form A.G.4 Identify and graph linear, quadratic (parabolic), absolute value, and exponential functionsA.G.10 Determine the vertex and axis of symmetry of a parabola, given its graph (See A.A.41) Note:

The vertex will have an ordered pair of integers and the axis of symmetry will have an integral value.A.A.41 Determine the vertex and axis of symmetry of a parabola, given its equation (See A.G.10)A.G.8 Find the roots of a parabolic function graphically Note: Only quadratic equations with integral

solutionsA.G.4 Identify and graph linear, quadratic (parabolic), absolute value, and exponential functionsA.G.3 Determine when a relation is a function, by examining ordered pairs and inspecting graphs of

relationsA.G.5 Investigate and generalize how changing the coefficients of a function affects its graph

Process Indicators: A.PS.6 Use a variety of strategies to extend solution methods to other problemsA.PS.7 Work in collaboration with others to propose, critique, evaluate, and value alternative approaches

to problem solvingA.PS.9 Interpret solutions within the given constraints of a problemA.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equations, and objects created

using technology as representations of mathematical concepts A.R.8 Use mathematics to show and understand mathematical phenomena (e.g.,compare the graphs of

the functions represented by the equations and )

Vocabulary:ChartGraph

FunctionAbsolute Value Function

TechnologyConstraint

Axis of symmetryCoordinates

11

Table Parabolic FunctionQuadratic Function

GraphicallyParameterPatternRefuteMathematical VisualRelationx-intercepty-intercept

Line parallel to axesParabolaParallelSlopeVertexx-axisy-axisOrdered PairRoots of a Parabolic FunctionRoots of a Quadratic FunctionZeros of a functionSolution Set

Resources:Textbook Performance Indicator(s) Section # or Page #Glencoe: Algebra 1 A.A.32 p. 258 ex. 6 (Rate of change)

A.M.1 p. 261 39, 40, 53-55 (Rate of change)A.A.33 p. 260 15-34 (slope given 2 points)A.A.34/A.A.35 p. 284 11-33 (Writing Equations of Lines)

p. 289 15-26 (Writing Equations of Lines)p. 290 53,54 (Writing Equations of Lines)

A.A.36 p. 290 27, 28 (Equations parallel to axes)A.G.3 p. 229 4-9, 17-24 (Determine if a function)

p. 230 29-31 (Determine if a function)A.G.4 p. 559 27-32A.G.5 p. 531-532 (graphing calculator investigation)A.G.8 p. 536 11-16, 21-32 (Find roots graphically)A.G.10/A.A.41 p. 528 18-29 (Determine vertex and A.O.S.

given graph/equation)A.R.1 p. 260-262 35, 36, 50-57, 61A.R.8 p. 278-279, p. 531-532

Glencoe: Geometry A.A.36 p. 143 28, 31 (Equations parallel to axes)p. 148 36, 38, 41 (Equations parallel to axes)

Amsco: Mathematics A A.G.3 p. 779 1-11 (Determine if a function)p. 780 15-2211 (Determine if a function)

A.G.10/A.A.41 p. 785-787 17-29, 33, 35-38 (Determine vertex and A.O.S. given graph/equation)

Addison Wesley: Intermediate Algebra

A.A.32/A.M.1 p. 101-102 53-67 (Rate of change)A.G.4 p. 567 1-28 (Graphing Exponential Functions)

Merrill Integrated Mathematics Course 2

A.G.8 p. 380 5-30 (Find roots graphically)A.G.10/A.A.41 p. 376 8-27 (Determine vertex and A.O.S.

given graph/equation)Handout A.G.5

Systems of Equations and Inequalities 15 days

Content Indicators:A.G.6 Graph linear inequalities

12

A.G.7 Graph and solve systems of linear equations and inequalities with rational coefficients in two variables (See A.A.10)

A.A.40 Determine whether a given point is in the solution set of a system of linear inequalitiesA.A.10 Solve systems of two linear equations in two variables algebraically (See A.G.7)A.A.7 Analyze and solve verbal problems whose solution requires solving systems of linear equations

in two variablesA.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.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 the solution(s) should be integers.

Process Indicators: A.PS.7 Work in collaboration with others to propose, critique, evaluate, and value alternative approaches

to problem solvingA.CN.2 Understand the corresponding procedures for similar problems or mathematical concepts

Vocabulary:Counter ExampleSolution Set

System of Linear EquationsSystems of Linear Inequalities

Quadratic-Linear System of Equations

References:Textbook Performance Indicator(s) Section # or Page #Glencoe: Algebra 1 A.G.6 p. 355-357 (graphing inequalities)

A.G.7 p. 372 15-40 (graphing systems)p. 375 1-10 (Graphing Calculator)p. 397 12-28 (Graphing systems)

A.A.10 p. 379 11-28 (Substitution)p. 385 12-29 (Elimination)

A.G.9 p. 553 1-6 (Graphing Calculator)A.A.7 p. 373 44-54 (Word Problems Systems)

p. 380 30, 31, 33, 34, 35, 36, 37p. 385 30-36 (Word Problems Systems)

A.PS.7 p. 391 27-38Amsco: Mathematics A A.G.6 p. 640 (graphing inequalities)

A.A.10 p. 656 1-20 (substitution)p. 654 3-47 (Elimination)p. 657 21-36 (either method)

A.G.9 p. 793 3-27 (Quadratic-Linear systems graphically)

A.A.11 p. 798 7-27, 37, 38 (Quadratic-Linear systems algebraically)

A.A.7 p. 660-661 1-29 (Word Problems systems)McDougal Littell: Algebra 1 A.A.40 p. 432-435

A.PS.7 p. 421-422 10-45

13

Exponential Equations and Graphs 5 days

Content Indicators:A.A.9 Analyze and solve verbal problems that involve exponential growth and decay

Process Indicators: A.RP.3 Recognize when an approximation is more appropriate than an exact answer

Vocabulary:ConjectureConstraintAnalyze

Quantitative ModelExponential Growth and Decay

Exponential Function

References:Textbook Performance Indicator(s) Section # or Page #Glencoe: Algebra 1 A.A.9 Chapter 10, Section 5, 6McDougal Littell: Algebra 1 (2007) A.A.9 Chapter 8, Section 5, 6Holt, Rinehart, and Winston A.A.9 Chapter 6, p. 354-360Prentice Hall Mathematics A.A.9 Chapter 8, p. 430-438

Right Triangle 7 days

Content Indicators:A.A.45 Determine the measure of a third side of a right triangle using the Pythagorean theorem, given

the lengths of any two sidesA.A.42 Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the

sidesA.A.44 Find the measure of a side of a right triangle, given an acute angle and the length of another sideA.A.43 Determine the measure of an angle of a right triangle, given the length of any two sides of the

triangle

Process Indicators: A.R.6 Use mathematics to show and understand physical phenomena (e.g., find the height of a building

if a ladder of a given length forms a given angle of elevation with the ground)A.CM.6 Support or reject arguments or questions raised by others about the correctness of mathematical

work

Vocabulary:ProofRefute

Angle of elevationAngle of depression

AngleAcute AngleAdjacent side/anglesTriangle

Right AngleRight triangleHypotenuseLegs of a right triangleTrigonometryOpposite side/anglePythagorean theoremCosineSine Tangent

14

Resources:Textbook Performance Indicator(s) Section # or Page #Key Curriculum Press: Interactive Mathematics Program, Year 1ISBN 1-55953-250-5

A.A.42 p.464-471

Key Curriculum Press: Interactive Mathematics Program, Year 2ISBN 1-55953-263-7

A.A.45 p.226-233,p.283-286

A.A.42 p.219-221

Merrill: Integrated Mathematics Course I

A.A.45 p. 230-232

Merrill: Integrated Mathematics Course II

A.A.42 p.501-502, 511-512

A.A.44 p.507-510,p.514-515

A.A.43 p. 507-510, p.514-515Amsco: Course I A.A.45 p.717-722Glencoe: Algebra ISBN 0-07-873316-2

A.R.6 p. 609 41-47; p. 629 61, 62; p. 630 63-65

Area and Volume 9 days

Content Indicators:A.M.2 Solve problems involving conversions within measurement systems, given the relationship

between the unitsA.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, rhombi, 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 cylinders A.M.3 Calculate the relative error in measuring square and cubic units, when there is an error in the

linear measure

Process Indicators: A.RP.4 Develop, verify, and explain an argument, using appropriate mathematical ideas and language A.RP.5 Construct logical arguments that verify claims or counterexamples that refute them

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A.RP.6 Present correct mathematical arguments in a variety of formsA.RP.7 Evaluate written arguments for validityA.CN.6 Recognize and apply mathematics to situations in the outside world

Vocabulary:AreaSpatial ReasoningVisualizationSurface AreaVolumeCubic UnitLinear measureLinear UnitMagnitudeMeasurement systemRelative errorSquare unitUnitMathematical Visual

Geometric ShapeCircleQuarter CircleSemi CircleSectorPolygonRegular polygonPentagonHexagonOctagonNonagonDecagon

QuadrilateralParallelogramRectangleRhombusSquareTrapezoid

Rectangular SolidsCylinderVolume

Resources:Textbook Performance Indicator(s) Section # or Page #Glencoe: Algebra 1 A.G.1

A.PS.2A.PS.3A.R.1A.CM.3A.CM.13A.CN.2

p. 5 9-12; p. 6 WHAT! (Activity); p. 9 49; p. 122 3; p. 124 23, 25; p. 125 37; p. 134 69, 70; p. 147 54; p. 153 47; p. 168 10-12; p. 169 34, 35; p. 373 42, 43; p. 413 13, 14; p. 420 5; p. 422 38, 39; p. 447-448 37, 38, 51, 62; p. 479 67; p. 493 56; p. 512 23, 24, 42; p. 542 14; p. 550 32,33; p. 595 38, 39; p. 609 48, 51; p. 673 3, 46; p. 813-816; p. 856 19

A.G.2A.PS.3A.CM.3A.R.1

p. 9 44; p. 122 Activity; p. 125 41-44; p. 409 19, 20; p. 414-415 46-48, 60; p. 456 43, 44; p. 670 39; p. 817; p. 860 4

Amsco: Mathematics A A.M.2A.PS.2

Chapter 12 Section 3

A.G.1 Chapter 4, Sections 6-8 A.G.2 Chapter 4, Section 9 (Volume only)A.M.3A.RP.3

Chapter 12, Section 8

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Merrill: Integrated Mathematics Course 1

A.M.2A.PS.2

p. 182-183 1-15Chapter 8, Section 1, 9

A.G.1A.PS.2A.PS.3A.R.1A.CM.3A.CM.13A.CN.2

Chapter 8 Section 2-6

A.G.2A.PS.3A.CM.3A.R.1

Chapter 8, Section 7, 8 (Volume only)

Key Curriculum Press: Discovering Geometry

A.G.1 p. 333-335 1-15p. 413 1-9p. 414 15, 19p. 418-419 1-12, 19p. 423-424 1, 2, 4-6p. 427 1-8p. 428 12p. 435 1-15p. 439 1-12

A.G.2 p. 450 1-11p. 455-458 1-47p. 517-519 1-18p. 522-526 1-21p. 532-533 1-14p. 547-548 1-9p. 554-557 1-28

Prentice Hall Geometry A.M.2 p. 574 1-26p. 747 1-30

A.G.1 p. 536-539 1-44p. 542-545 1-42p. 548-550 1-43p. 570-573 27-39, 54-75p. 577-580 1-43

A.G.2 p. 611-614 1, 2, 5, 8-15, 17, 18, 21, 22, 24-31, 36-40p. 627-630 1-3, 9-18, 20-45

A.M.3 p. 749 1-11

Probability 12 days

Content Indicators:A.N.6 Evaluate expressions involving factorial(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.19 Determine the number of elements in a sample space and the number of favorable events

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A.S.22 Determine, based on calculated probability of a set of events, if:o some or all are equally likely to occur o one is more likely to occur than another o whether or not an event is certain to happen or not to happen

A.S.20 Calculate the probability of an event and its complement A.S.21 Determine empirical probabilities based on specific sample dataA.S.18 Know the definition of conditional probability and use it to solve for probabilities in finite

sample spaces A.S.23 Calculate the probability of:

o a series of independent eventso a series of dependent eventso two mutually exclusive eventso two events that are not mutually exclusive

Process Indicators: A.RP.1 Recognize that mathematical ideas can be supported by a variety of strategiesA.RP.2 Use mathematical strategies to reach a conclusion and provide supportive arguments for a

conjectureA.RP.11 Use a Venn diagram to support a logical argumentA.CM.9 Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or

conjectures of othersA.CM.2 Use mathematical representations to communicate with appropriate accuracy, including

numerical tables, formulas, functions, equations, charts, graphs, Venn diagrams, and other diagramsA.CN.3 Model situations mathematically, using representations to draw conclusions and formulate new

situations

Vocabulary:ValidityBiasFundamental principle of CountingFactorialArrangements (permutations)sample space

ProbabilityCalculated ProbabilityConditional ProbabilityEmpirical ProbabilityTheoretical ProbabilityExperimental Design

ComplementDependent EventIndependent EventDependent VariableIndependent VariableFavorable EventMutually Exclusive EventsEvents Not Mutually Exclusive

Resources:Textbook Performance Indicator(s) Section # or Page #Amsco: Mathematics AISBN 1-56765-546-7

A.N.6 p. 507A.N.7 p. 493-495A.N.8 p. 511-512A.S.20 p. 472-473A.S.23 p. 496-497

p. 502-503p. 517-518

A.RP.2 p. 456A.CM.2 p. 458, 461

Pearson Prentice Hall: Skills and Concepts Review Course 1, Course 2,

A.N.6 Review 295A.N.7 Review 294, 205, 94, 95

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and Course 3 (Workbook)ISBN 0-13-115685-3

A.S.19 Review 297, 261, 202, 90A.S.21 Review 198A.S.22 Review 203A.S.23 Review 96, 296, 206, 208, 298

Amsco: Course 1 Integrated MathematicsISBN 0-87720-230-3

A.N.6 p. 506A.N.7 p. 493A.N.8 p. 510-511A.S.23 p. 496

Amsco: Preparing for the Regents Examination Mathematics A (Workbook)ISBN 1-56765-535-1

A.S.18 p. 380-391

Internet Resources:www.mathgoodies.comhttp//:jc-schools.net/PPTs-math.htmlwww-stat.stanford.edu/~susan/surprise/www.regentsprep.org

Statistics 20 days

Content Indicators: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.16 Recognize how linear transformations of one-variable data affect the data’s mean, median, mode,

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

third quartilesA.S.6 Understand how the five statistical summary (minimum, maximum, and the three quartiles) is

used to construct a box-and-whisker plotA.S.5 Construct a histogram, cumulative frequency histogram, and a box-and-whisker plot, given a set

of dataA.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.12 Identify the relationship between the independent and dependent variables from a scatter plot

(positive, negative, or none)A.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.17 Use a reasonable line of best fit to make a prediction involving interpolation or extrapolationA.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.10 Evaluate published reports and graphs that are based on data by considering: experimental

design, appropriateness of the data analysis, and the soundness of the conclusions

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Process Indicators: A.PS.2 Recognize and understand equivalent representations of a problem situation or a mathematical

conceptA.PS.3 Observe and explain patterns to formulate generalizations and conjecturesA.PS.8 Determine information required to solve a problem, choose methods for obtaining the

information, and define parameters for acceptable solutionsA.RP.8 Support an argument by using a systematic approach to test more than one caseA.RP.9 Devise ways to verify results or use counterexamples to refute incorrect statements A.RP.10 Extend specific results to more general casesA.RP.12 Apply inductive reasoning in making and supporting mathematical conjecturesA.CM.7 Read and listen for logical understanding of mathematical thinking shared by other studentsA.CM.13 Draw conclusions about mathematical ideas through decoding, comprehension, and

interpretation of mathematical visuals, symbols, and technical writingA.CN.4 Understand how concepts, procedures, and mathematical results in one area of mathematics can

be used to solve problems in other areas of mathematicsA.CN.5 Understand how quantitative models connect to various physical models and representationsA.CN.7 Recognize and apply mathematical ideas to problem situations that develop outside of

mathematicsA.R.2 Recognize, compare, and use an array of representational formsA.R.3 Use representation as a tool for exploring and understanding mathematical ideasA.R.7 Use mathematics to show and understand social phenomena (e.g., determine profit from student

and adult ticket sales)

Vocabulary:appropriatenessbiasedbivariateunivariatecategorizecausationextrapolationfive statistical summaryfrequency distribution interpolationseries

box-and-whisker plotcumulative frequency distribution tablehistogramcumulative frequency histogramline of best fitscatter plot

tablecentral tendencycorrelationdataexperimental designmaximummeanmeasure of central tendencymedianminimummodepercentile rank

GeneralizationApproximationArgumentClaimConclusionConjectureExtend

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qualitativequantitativequartiles (specifically: first, second, thirdor lower, middle, upper)rangelinear transformation

References from statistics packet (Exploring Data using the TI-83 Plus):Investigating Data Sets A.S. 1, 2, 4, 5, 6, 9, 11Center Shape and Spread A.S. 2, 5, 9Box-and-Whisker (p. 39, 40, 41, 42) A.S. 5, 6, 9Histogram Using month Data A.S. 5, 6, 9Cheerios A.S. 4, 5, 6, 9, 11Tie-the-Knot Lab A.S. 7, 8, 12, 17Getting The Blues A.S. 7, 8, 12, 17Barbie Bungee Drop A.S. 7, 8, 12, 17Finding The Best Fit Line of Exponential Data A.S. 7, 8, 12, 17Lab …Data Analysis A.S. 7, 8, 12, 17High School Senior Vs. College Freshman GPA’s A.S. 7, 8, 12, 17Asteroid Activity A.S. 7, 8, 12, 17Chirping Frequency & Temp. for striped Ground cricket A.S. 7, 8, 12, 17Avg. Atmospheric Concentrations of CO2 A.S. 7, 8, 12, 17Quinine Lab A.S. 7, 8, 12, 17Bridges A.S. 7, 8, 12, 17Spring Lab A.S. 7, 8, 12, 17Do Tall People run Faster Than Short people A.S. 7, 8, 12, 17Is Old Faithful Faithful? A.S. 7, 8, 12, 17Modeling Exponential Data using Growth and Decay Lab A.S. 12, 13, 14Growth & Decay: Growth A.S. 12, 13, 14Growth & Decay: Decay A.S. 12, 13, 14Survivor Lab A.S. 12, 13, 14Power Regression A.S. 12, 13, 14

Other References:Textbook Performance Indicator(s) Section # or Page #Freeman: The Practice of Statistics by Yates et. al. (1999)

A.S.3 Chapter 5 p. 245-248A.S.10 Chapter 5A.S.15 Chapter 5 p. 256-261

Other websites for multiple topics:http://www.mathbits.comhttp://members.cox.net/powerpoint1/index.htmhttp://jc-schools.net/ppt.html

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www.jmap.orgwww.regentsprep.org

Putnam Northern Westchester BOCES Integrated Algebra Curriculum Outline

July 6, 2006

This document was prepared through the combined efforts of the following teachers:

Tina Alyson, Linda LoCasto, Marie May ArdsleyChristine Rutledge BriarcliffMark Kopchick, Nordt Rich,Elizabeth Goudie CarmelSusan Dudman Croton HarmonSusan Golden Irina Kanatayev, Maria Pearson Greenburgh7Kathleen Quaid Hendrick HudsonKaren Palmer IrvingtonAges Laub, Angela Dillon, Andrea Rothstein, Adrian Jacques LakelandJoe DiCioccio MahopacOsvaldo Mancebo Mt. VernonMaryLou Giannetto, Jay Jazayeri North SalemJoan Indusi,Lois Mayer, Susan Kreutzberg OssiningRegina Rettino Pearl RiverLaura Connors, Jonathan Totillo PelhamVirginia Nalbandian, Mary Prevost PleasantvilleJoe Mahoney, Mary Kay Cohen Putnam ValleyDebra De Vito YonkersMary Froats, Steve Laber Yorktown

Special thanks to Andra Meyerson for arranging for our use of the science wing and facilities at Ossining High School during our meeting days in July..Kudos go to Joe Mahoney, who diligently typed in the many needed changes to the document.

I personally thank each of you for bringing in your assignments, getting them organized into a manageable format and critiquing as we went through this process. This document is for your districts to use, to modify and to change as needed. The handouts distributed supplement what is included in this document.

Congratulations to all on a job well done.

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Eleanore Livesey PNWBOCES

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