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CaliforniaMath Content StandardsGrades 6–8

correlated to the

McDougal LittellCalifornia Structure and Method:Course 1Course 2Algebra 1

McDougal Littell California Structure and Method

Course 1

Publisher: McDougal LittellProgram Title: McDougal Littell California Structure and Method: Course 1, Course 2, Algebra 1Components: Pupil Edition (PE), Teacher’s Edition (TE), California Standards Key Concepts Book (CSKCB),California Standards Review and Practice (CASRP), Algebra Skills Resources (ASR), Resource Book (RB),Practice Masters (PM), Study Guide for Reteaching and Practice (RP)Grade Level(s): 6-8

© California Department of Education Basic Grade-Level Program Standards Map SBE Approved November 2006Page 1

STANDARDS MAP for a Basic Grade-Level Program

Grade 6 - Mathematics

Publisher Citations

StandardNo.

Standard Language Primary Citations Supporting Citations

NUMBER SENSE

1.0 Students compare and order positive andnegative fractions, decimals, and mixednumbers. Students solve problems involvingfractions, ratios, proportions, andpercentages:

PE/TE: 66-72, 191-194, 210-225, 226-239,289-310, 312-313CSKCB: S2-S28

CASRP: 2-10

See all references for NS 1.1-NS 1.4 below.


1.1 Compare and order positive and negativefractions, decimals, and mixed numbers andplace them on a number line.

PE/TE:Decimals: 66-69, 70-72, 197 (Exs. 25-30);Fractions/Mixed Numbers: 182, 191-194,282;

Integers: 366-369CSKCB: S2-S7, T6-T7

CASRP: 2-3, 114, 117-118

RB: 34, 38-40, 75, 76-78

PM: 12, 27, 28 (Exs. 13-18)

1.2 Interpret and use ratios in different contexts(e.g., batting averages, miles per hour) to showthe relative sizes of two quantities, usingappropriate notations (a/b, a to b, a:b).

PE/TE: 226-230, 231, 237

CSKCB: S8-S13, T8-T15

CASRP: 4-5, 126, 130-131

RB: 89, 90-92

PM: 33

1.3 Use proportions to solve problems (e.g.,determine the value of N if 4/7 = N/21, find thelength of a side of a polygon similar to a knownpolygon). Use cross-multiplication as a methodfor solving such problems, understanding it asthe multiplication of both sides of an equation bya multiplicative inverse.

PE/TE: 231-233, 234-236, 237-239, 312-315

CSKCB: S14-S21, T8-T11

CASRP: 6-8, 127, 130-131

RB: 89, 90-92

PM: 33, 44



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1.4 Calculate given percentages of quantities andsolve problems involving discounts at sales,interest earned, and tips.

PE/TE: 282–285, 286-288, 289-291, 292-295, 296-299, 300-302, 303-307, 308-311,312-313, E15-E16, E17-E18TE: T56-T57, T58-59

CSKCB: S22-S28CASRP: 9-10, 128, 130-131

RB: 108, 109, 110, 111, 112, 113-116

PM: 40-42

2.0 Students calculate and solve problemsinvolving addition, subtraction,multiplication, and division:

PE/TE: 77-92, 210-225, 226-239, 370–385CSKCB: P56-P59, S29-S35

CASRP: 11-21



2.1 Solve problems involving addition, subtraction,multiplication, and division of positive fractionsand explain why a particular operation was usedfor a given situation.

PE/TE:Addition and subtraction: 210-213, 214-216;Multiplication and Division: 217-218, 219-221,222-225

CSKCB: P56-P59CASRP: 11-13, 118-120, 122, 124-125

RB: 83, 84, 85, 90-92

PM: 31, 32

2.2 Explain the meaning of multiplication anddivision of positive fractions and perform thecalculations (e.g., 5/8 ÷ 15/16 = 5/8 x 16/15 =2/3).

PE/TE: 217-218, 219-221, 222-225, E13-E14TE: T54-T55, 209b-209c

CASRP: 14-15, 122, 124-125

RB: 83, 84, 85, 90-92PM: 32

2.3 Solve addition, subtraction, multiplication, anddivision problems, including those arising inconcrete situations, that use positive andnegative integers and combinations of theseoperations.

PE/TE:Addition and Subtraction: 370-374, 375-377,386-388, 413-415, E19-E20, E21-22;Multiplication and Division: 378-379, 380-382,383-385, 386-388, 413-415

TE: T60-T61, T62-T63CSKCB: S29-S35CASRP: 16-18, 117, 119-121, 124-125

RB: 136, 137, 139, 140-142

PM: 49-51



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2.4 Determine the least common multiple and thegreatest common divisor of whole numbers; usethem to solve problems with fractions (e.g., tofind a common denominator to add two fractionsor to find the reduced form for a fraction).

PE/TE:GCD (GCF): 163-165, E7-E8;LCM: 166-169, E9-E10;Use of GCD and LCM: 182-185, 191-194,210-213, 214-216TE: T48-T49, T50-T51CSKCB: P37-P40, P47-P51, S36-S43

CASRP: 19-21, 115, 118-120, 122, 124-125

RB: 63, 64-66

PM: 24, 25, 26, 27, 31



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ALGEBRA AND FUNCTIONS

1.0 Students write verbal expressions andsentences as algebraic expressions andequations; they evaluate algebraicexpressions, solve simple linear equations,and graph and interpret their results:

PE/TE: 32-38, 43-51, 264-273, 386-399TE: T46-T47

CSKCB: S44-S50CASRP: 22-28

See all references for AF 1.1-AF 1.4 below.


1.1 Write and solve one-step linear equations in onevariable.

PE/TE: 36-38, 43-45, 46-48, 49-51, 248-250,251-254, 255-256, 257-259, 260-263, 264-266, 267-269, 270-273, 386-388, E3-E4

TE: T44-T45CSKCB: S44-S50

CASRP: 22-23, 133, 135-136

RB: 21, 22, 25, 26-28, 101, 102-104

PM: 7, 9, 10, 35-38, 51

1.2 Write and evaluate an algebraic expression for agiven situation, using up to three variables.

PE/TE: 2-4, 32-35, 62 (Exs. 45-52)

CASRP: 24-25, 132, 135-136

RB: 10, 14-16, 21, 26-29, 95

PM: 3, 7, 11

1.3 Apply algebraic order of operations and thecommutative, associative, and distributiveproperties to evaluate expressions; and justifyeach step in the process.

PE/TE:Properties: 5-8, 9-12, 13-15, 16-17, 263, 370-374, 375-377, 378-379, 380-382, 383-385

CASRP: 26-27, 123-125

RB: 7, 9, 10, 13, 14-16PM: 3, 4, 5, 37

1.4 Solve problems manually by using the correctorder of operations or by using a scientificcalculator.

PE/TE: 13-15, 16-17,76 (Calculator Investigation), 385 (CalculatorInvestigation)CASRP: 28, 123-125

RB: 7, 9, 10, 13, 14-16

PM: 5

2.0 Students analyze and use tables, graphs, andrules to solve problems involving rates andproportions:

PE/TE: 226-239, 312-313






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2.1 Convert one unit of measurement to another(e.g., from feet to miles, from centimeters toinches).

PE/TE: 35 (Exs. 25-32), 109-112, 226-230,324 (Ex. 5), 347-350, 351-353TE: T17CASRP: 29-31, 139-141

RB: 46, 52-54

PM: 17 (Exs. 13-18), 46, 51, 52, 53, 54

2.2 Demonstrate an understanding that rate is ameasure of one quantity per unit value ofanother quantity.

PE/TE: 226-230, 234-236, 312-313

CSKCB: S51-S54CASRP: 32-33, 129-131

RB: 89, 90-92

PM: 33

2.3 Solve problems involving rates, average speed,distance, and time.

PE/TE: 226-230, 234-236, 264-266

CSKCB: S51-S54CASRP: 34-35, 129-131

RB: 89, 90-92

PM: 34, 37

3.0 Students investigate geometric patterns anddescribe them algebraically:

PE/TE: 128-131, 320-334, 343-350, 358-359

CSKCB: S55-S61, T12-T19CASRP: 36-39



3.1 Use variables in expressions describinggeometric quantities (e.g., P = 2w + 2l, A =1/2bh, C = pd - the formulas for the perimeter ofa rectangle, the area of a triangle, and thecircumference of a circle, respectively).

PE/TE: 469;Perimeter: 124-127;

Area: 320-324, 325-329, 330-334, 335-338;Circumference: 128-131CSKCB: S55-S61, T12-T19

CASRP: 36-37, 134-136

RB: 49, 51, 52-54, 122, 124, 125, 126, 127,128-130

PM: 37, 45, 46, 48



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3.2 Express in symbolic form simple relationshipsarising from geometry.

PE/TE: 469;Circumference: 128-131;Area: 320-334, 325-329, 330-334;Euler’s Formula: 340;

Volume: 343-346, 347-350;Surface area: 354-357;

Pythagorean theorem: 358-359CSKCB: T16-T19

CASRP: 38-39, 134-136

RB: 49, 51, 52-54, 122, 124, 125, 126, 127,128-130PM: 45, 47



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MEASUREMENT AND GEOMETRY

1.0 Students deepen their understanding of themeasurement of plane and solid shapes anduse this understanding to solve problems:

PE/TE: 118-131, 320-334, 330-338, 343-350,354-357

CSKCB: P84, S55-S61CASRP: 40-45

See all references for MG 1.1-MG 1.3 below.


1.1 Understand the concept of a constant such as p;know the formulas for the circumference andarea of a circle.

PE/TE:!: p: 128;

Circumference: 128-131;Area: 330-334, 347-350, 354-357

CSKCB: S55-S61CASRP: 40-41,137, 140-141

RB: 49, 51, 52-54, 121, 122, 127, 128-130PM: 19, 46

1.2 Know common estimates of p (3.14; 22/7) anduse these values to estimate and calculate thecircumference and the area of circles; comparewith actual measurements.

PE/TE:Circumference: 128-131;

Calculator investigation of p: 137;Area: 330-334, 347-350, 354-357

CSKCB: S55-S61CASRP: 42-43, 137, 140-141

RB: 49, 51, 52-54, 121, 122, 127, 128-130

PM: 19, 46

1.3 Know and use the formulas for the volume oftriangular prisms and cylinders (area of base xheight); compare these formulas and explain thesimilarity between them and the formula for thevolume of a rectangular solid.

PE/TE: 343-346, 347-350

CASRP: 44-45, 138, 140-141

RB: 124, 126, 127, 128-130

PM: 47, 48



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2.0 Students identify and describe the propertiesof two-dimensional figures:

PE/TE: 113-131

CSKCB: P69-P74, S62-S64, T12-T15CASRP: 46-52



2.1 Identify angles as vertical, adjacent,complementary, or supplementary and providedescriptions of these terms.

PE/TE: 113-117

CSKCB: S62-S64CASRP: 46-47, 142, 144-145

RB: 46, 52-54

PM: 18

2.2 Use the properties of complementary andsupplementary angles and the sum of the anglesof a triangle to solve problems involving anunknown angle.

PE/TE: 118-122, 270CSKCB: S62-S64

CASRP: 48-49, 142, 144-145

RB: 46, 52-54PM: 19, 38

2.3 Draw quadrilaterals and triangles from giveninformation about them (e.g., a quadrilateralhaving equal sides but no right angles, a rightisosceles triangle).

PE/TE: 118-122, 123-127, 138-141

CSKCB: P68-P73CASRP: 50-52, 143-145

RB: 50, 51, 52-54

PM: 19, 20



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STATISTICS, DATA ANALYSIS, ANDPROBABILITY

1.0 Students compute and analyze statisticalmeasurements for data sets:

PE/TE: 413-418, 424-426TE: T64-T65, 403b-403c

CSKCB: S66CASRP: 53-60

See all references for SDAP 1.1-SDAP 1.4below.


1.1 Compute the range, mean, median, and mode ofdata sets.

PE/TE: 413-415, 416-418, 422-423, 424-426,E23-E24

TE: T64-T65CSKCB: S66

CASRP: 53-54, 146, 148-149

RB: 147, 152-154

PM: 54, 55

1.2 Understand how additional data added to datasets may affect these computations.

PE/TE: 413-415

TE: 403b-403cCASRP: 55-56, 147-149

PM: 54

1.3 Understand how the inclusion or exclusion ofoutliers affects these computations.

TE: 403b-403c

CASRP: 57-58, 408-411, 147-149

1.4 Know why a specific measure of centraltendency (mean, median) provides the mostuseful information in a given context.

PE/TE: 416-418, E23-E24

TE: T64-T65, 403b

CASRP: 59-60, 146, 148-149

PM: 54-55

2.0 Students use data samples of a populationand describe the characteristics andlimitations of the samples:

PE/TE: 438-439






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2.1 Compare different samples of a population withthe data from the entire population and identify asituation in which it makes sense to use asample.

PE/TE: 438-439

CSKCB: S65-S68CASRP: 61-62, 150, 153-154

2.2 Identify different ways of selecting a sample(e.g., convenience sampling, responses to asurvey, random sampling) and which methodmakes a sample more representative for apopulation.

PE/TE: 438-439

CSKCB: S65-S68

CASRP: 63-64, 150, 153-154

2.3 Analyze data displays and explain why the wayin which the question was asked might haveinfluenced the results obtained and why the wayin which the results were displayed might haveinfluenced the conclusions reached.

PE/TE: 404-407, 408-412, 424-426CSKCB: S69-S73

CASRP: 65-67, 151, 153-154

RB: 146, 147, 152-154PM: 53, 55

2.4 Identify data that represent sampling errors andexplain why the sample (and the display) mightbe biased.

PE/TE: 438-439

TE: 403a-403bCSKCB: S74-S76

CASRP: 68-69, 152-154

2.5 Identify claims based on statistical data and, insimple cases, evaluate the validity of the claims.

PE/TE: 404-407, 408-412, 424-426, 438-439

TE: 403a-403bCSKCB: S77-S80

CASRP: 70-71, 152-154

PM: 53, 55



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3.0 Students determine theoretical andexperimental probabilities and use these tomake predictions about events:

PE/TE: 427-437




3.1 Represent all possible outcomes forcompound events in an organized way (e.g.,tables, grids, tree diagrams) and express thetheoretical probability of each outcome.

CSKCB: S81-S84

CASRP: 72-73, 155, 158-159

RB: 99-100, 148

3.2 Use data to estimate the probability of futureevents (e.g., batting averages or number ofaccidents per mile driven).

PE/TE: 427-429

TE: 403fCASRP: 74-75, 156, 158-159

RB: 151, 152-154

PM: 55

3.3 Represent probabilities as ratios, proportions,decimals between 0 and 1, and percentagesbetween 0 and 100 and verify that theprobabilities computed are reasonable; knowthat if P is the probability of an event, 1- P is theprobability of an event not occurring.

PE/TE: 427-429, 431-434, 435-437

CSKCB: S85-S91CASRP: 76-77, 156, 158-159

RB: 150, 151, 152-154

PM: 55, 56

3.4 Understand that the probability of either of twodisjoint events occurring is the sum of the twoindividual probabilities and that the probability ofone event following another, in independenttrials, is the product of the two probabilities.

PE/TE: 435-437

CASRP: 78-79, 156, 158-159

RB: 151, 152-154

PM: 56

3.5 Understand the difference between independentand dependent events.

CSKCB: S92-S94CASRP: 80-81, 157-159

RB: 150



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MATHEMATICAL REASONING

1.0 Students make decisions about how toapproach problems:

Occurs throughout.Examples:

PE/TE:(Gr. 6, NS 2.0) PE/TE, pp. 18-23;

(Gr. 6, AF 3.1) PE/TE, pp. 335-338;(Gr. 6, NS 2.3) PE/TE, p. 374 (Ex. 6);

(Gr. 6, NS 2.0) PE, pp. E1-E2/TE, pp. T42-T43CASRP:

(Gr. 6, NS 2.3; Gr. 6, AF 1.2; Gr. 6, AF 3.1;Gr. 6, MG 1.2) CASRP, pp. 82-87

See all references for MR 1.1-MR 1.3 below.

Occurs throughout.


1.1 Analyze problems by identifying relationships,distinguishing relevant from irrelevantinformation, identifying missing information,sequencing and prioritizing information, andobserving patterns.

Occurs throughout.

Examples:

PE/TE:(Gr. 6, NS 2.0) PE/TE, pp. 18-23;

(Gr. 6, AF 1.1) PE/TE, pp. 49-51;(Gr. 6, NS 1.3) PE/TE, pp.234-235;

(Gr. 6, NS 1.3) PE/TE, pp. 264-273;(Gr. 6, NS 2.0) PE, pp. E1-E2/TE, pp. T42-T43

CASRP:(Gr. 6, NS 2.3) CASRP, pp. 82-83

Occurs throughout.

Examples:

RB:(Gr. 6, NS 2.0) RB, p. 13;

(Gr. 6, NS 2.0) RB, p. 11;(Gr. 6, NS 2.0) RB, p. 23;(Gr. 6, NS 2.0) RB, p. 24;

(Gr. 6, NS 2.1) RB, p. 84;(Gr. 6, NS 2.1) RB, p. 87



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1.2 Formulate and justify mathematical conjecturesbased on a general description of themathematical question or problem posed.

Occurs throughout.

Examples:PE/TE:

(Gr. 6, AF 1.3) PE/TE, p. 15 (Exs. 37-38);(Gr. 6, NS 2.3) PE/TE, p. 374

(Ex. 6);(Gr. 6, SDAP 2.3) PE/TE, p. 412 (Ex. 16);

(Gr. 6, NS 2.4) PE, pp. E7-E8/TE, pp. T48-T49CASRP:

(Gr. 6, AF 1.2) CASRP, pp. 84-85

Occurs throughout.

Examples:RB:

(Gr. 6, MG 1.0) RB, p. 72;(Gr. 6, AF 1.2) RB, p. 135

1.3 Determine when and how to break a probleminto simpler parts.

Occurs throughout.

Examples:PE/TE:

(Gr. 6, NS 2.1) PE/TE, p. 245 (Ex. 6);(Gr. 6, AF 3.1) PE/TE, pp. 335-338;

(Gr. 6, MG 1.0) PE/TE, p. 363 (Exs. 1, 6);(Gr. 6, NS 1.3) PE/TE, p. 363 (Ex. 9);

(Gr. 6, NS 2.1) PE/TE, p. 401 (Ex. 1)CASRP:

(Gr. 6, AF 3.1; Gr. 6 MG 1.2) CASRP, pp.86-87

Occurs throughout.

Examples:RB:

(Gr. 6, NS 2.0) RB, p. 42;(Gr. 6, AF 3.1) RB, p. 49;

(Gr. 6, MG 1.3) RB, p. 124



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2.0 Students use strategies, skills, and conceptsin finding solutions:

Occurs throughout.

Examples:PE/TE:

(Gr. 6, NS 2.0) PE/TE, pp. 78-79;(Gr. 6, NS 2.0) PE/TE, pp. 93-95;

(Gr. 6, AF 3.1) PE/TE, p. 267;(Gr. 6, AF 3.1) PE/TE, pp. 320-324;

(Gr. 6, SDAP 3.4) PE/TE, pp. 435-437CASRP:(Gr. 6, NS 1.4; Gr. 6, NS 2.2; Gr. 6, AF 2.0;Gr. 6, AF 3.2; Gr. 6, MG 1.1; Gr. 6,SDAP 3.1) CASRP, pp. 88-101


Occurs throughout.


2.1 Use estimation to verify the reasonableness ofcalculated results.

Occurs throughout.

Examples:PE/TE:

(Gr. 6, NS 2.0) PE/TE, pp.78-79;(Gr. 6, NS 2.2) PE/TE, p. 222;

(Gr. 6, NS 2.0) PE/TE, p. 245CASRP:

(Gr. 6, NS 1.4) CASRP, pp. 88-89

Occurs throughout.

Examples:RB:

(Gr. 6, NS 2.0) RB, p. 94;(Gr. 6, AF 3.1) RB, p. 106;

(Gr. 6, NS 1.4) RB, p. 111

2.2 Apply strategies and results from simplerproblems to more complex problems.

Occurs throughout.

Examples:PE/TE:

(Gr. 6, AF 1.1) PE/TE, pp. 46-48;(Gr. 6, NS 2.0) PE/TE, p. 175;

(Gr. 6, SDAP 3.4) PE/TE, pp. 435-437CASRP:

(Gr. 6, SDAP 3.1) CASRP, pp. 90-91

Occurs throughout.

Examples:RB:

(Gr. 6, MG 2.0) RB, p. 8;(Gr. 6, NS 2.1) RB, p. 69;

(Gr. 6, MG 1.3) RB, p. 124;



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2.3 Estimate unknown quantities graphically andsolve for them by using logical reasoning andarithmetic and algebraic techniques.

Occurs throughout.

Examples:PE/TE:

(Gr. 6, SDAP 2.3) PE/TE, pp. 404-407;(Gr. 6, SDAP 1.1) PE/TE, pp. 424-426

CASRP:(Gr. 6, AF 2.0) CASRP, pp. 92-93

Occurs throughout.

Examples:RB:

(Gr. 6, SDAP 2.3) RB, p. 146;(Gr. 6, SDAP 2.3) RB, p. 147 (Exs. 1, 2)

2.4 Use a variety of methods, such as words,numbers, symbols, charts, graphs, tables,diagrams, and models, to explain mathematicalreasoning.


PE/TE:(Gr. 6, AF 3.1) PE/TE, p. 267;

(Gr. 6, MG 2.2) PE/TE, pp. 270-271;(Gr. 6, NS 2.0) PE/TE, p. 317;

(Gr. 6, AF 3.1) PE/TE, pp. 320-324;(Gr. 6, MG 1.2) PE/TE, pp. 330-334;

(Gr. 6, NS 1.1) PE, pp. E11-E12/TE, pp. T52-T53;(Gr. 6, NS 2.2) PE pp. E13-E14/TE pp. T54-T55



RB:(Gr. 6, NS 2.0) RB, p. 33;

(Gr. 6, MG 2.0) RB, p. 123;(Gr. 6, SDAP 3.1) RB, p. 146

2.5 Express the solution clearly and logically byusing the appropriate mathematical notation andterms and clear language; support solutions withevidence in both verbal and symbolic work.

Occurs throughout.

Examples:PE/TE:(Gr. 6, NS 2.4) PE/TE, pp. 163-165;

(Gr. 6, SDAP 2.3) PE/TE, pp. 408-412CASRP:

(Gr. 6, AF 3.2; Gr. 6 MG 1.1) CASRP, pp.96-97

Occurs throughout.

Examples:RB:(Gr. 6, SDAP 3.1) RB, pp. 99-100;

(Gr. 6, SDAP 2.3) RB, p. 153 (Exs. 10-12)



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2.6 Indicate the relative advantages of exact andapproximate solutions to problems and giveanswers to a specified degree of accuracy.

Occurs throughout.

Examples:PE/TE:

(Gr. 6, NS 2.0) PE/TE, p. 93-95;(Gr. 6, NS 2.0) PE/TE, pp. 470-472

CASRP:(Gr. 6, MG 1.1) CASRP, pp. 98-99

Occurs throughout.

Examples:RB:

(Gr. 6, NS 1.4, NS 2.0) RB, p. 37 (Ex. 7);(Gr. 6, NS 2.0) RB, p. 106;

(Gr. 6, SDAP 2.3) RB, p. 146

2.7 Make precise calculations and check the validityof the results from the context of the problem.


PE/TE:(Gr. 6, NS 2.0) PE/TE, p. 57



RB:(Gr. 6, NS 2.0) RB, p. 18;

(Gr. 6, NS 1.4) RB, p. 112

3.0 Students move beyond a particular problemby generalizing to other situations:

Occurs throughout.

Examples:PE/TE:(Gr. 6, NS 2.0) PE/TE, p. 29;

(Gr. 6, MG 2.3) PE/TE, p. 127 (Exs. 28-32);(Gr. 6, NS 2.4) PE/TE, pp. 182-185;

(Gr. 6, NS 2.1) PE/TE, pp. 214-216;(Gr. 6, NS 1.4) PE, pp. E17-E18/ TE,pp. T58-T59

CASRP:(Gr. 6, NS 1.4; Gr. 6, AF 2.1; Gr. 6, SDAP3.2) CASRP, pp. 102-107


Occurs throughout.




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3.1 Evaluate the reasonableness of the solution inthe context of the original situation.

Occurs throughout.

Examples:PE/TE:

(Gr. 6, NS 2.0) PE/TE, p. 29;(Gr. 6, NS 1.4) PE, pp. E17-E18/ TE, pp.T58-T59


Occurs throughout.

Examples:RB:

(Gr. 6, NS 2.0) RB, p. 18;(Gr. 6, NS 2.0) RB, p. 111

3.2 Note the method of deriving the solution anddemonstrate a conceptual understanding of thederivation by solving similar problems.

Occurs throughout.

Examples:PE/TE:(Gr. 6, NS 2.4) PE/TE, pp. 182-185;

(Gr. 6, NS 2.1) PE/TE, pp. 214-216;(Gr. 6, NS 1.3) PE/TE, pp. 231-236;

(Gr. 6, MG 1.2) PE/TE, pp. 354-357;(Gr. 6, SDAP 3.4) PE/TE, pp. 435-437


Occurs throughout.

Examples:RB:(Gr. 6, SDAP 2.3) RB, p. 74

3.3 Develop generalizations of the results obtainedand the strategies used and apply them in newproblem situations.

Occurs throughout.

Examples:PE/TE:(Gr. 6, MG 2.2) PE/TE, p. 122 (Exs. 29-31);

(Gr. 6, MG 2.3) PE/TE, p. 127 (Exs. 28-32);(Gr. 6, NS 2.4) PE/TE, p. 193 (Ex. 31);

(Gr. 6, AF 3.1) PE/TE, pp. 335-337CASRP:

(Gr. 6, SDAP 3.2) CASRP, pp. 106-107

Occurs throughout.

Examples:RB:(Gr. 6, MR 2.0) RB, p. 48


Course 2

Publisher: McDougal Littell, Inc.Program Title: McDougal Littell California Structure and Method: Course 1, Course 2, Algebra 1Components: Pupil Edition (PE), Teacher’s Edition (TE), California Standards Key Concepts Book (CSKCB),California Standards Review and Practice (CASRP), Algebra Skills Resources (ASR), Resource Book (RB),Practice Masters (PM), Study Guide for Reteaching and Practice (RP)Grade Level(s): 6-8



Grade 7 - Mathematics

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NUMBER SENSE

1.0 Students know the properties of, and computewith, rational numbers expressed in a varietyof forms:

PE/TE: T48-T49, T54-T55, 40-47, 51-58,79-94, 98-99, 118-135, 241-259

CSKCB: P11-P24, S2-S35, T1-T13CASRP: 2-18

See all references for NS1.1-NS1.7 below.


1.1 Read, write, and compare rational numbers inscientific notation (positive and negative powersof 10), compare rational numbers in general.

PE/TE: 44-47, 73-74, 98-99, 115-117,131-134

CASRP: 2-3, 140-142

RB: 22 (Exs. 9-14), 27 (Exs. 10-11),32 (Exs. 1-2, 5-6), 39 (Exs. 1-6)

PM: 11 (Exs. 11-12, 17-24)

1.2 Add, subtract, multiply, and divide rationalnumbers (integers, fractions, and terminatingdecimals) and take positive rational numbers towhole-number powers.

PE/TE:Whole number powers: 40-43, 56-58;Add, subtract, multiply, divide integers:79-94;

Add, subtract, multiply, divide fractions:106-109, 118-130;Add, subtract, multiply, divide decimals:51-58

CSKCB: P11-P24, S2-S21, T1-T13CASRP: 4-6, 143-144, 146-147

RB: 22 (Exs. 1-8), 27 (Exs. 1-5),32 (Exs. 9-18), 37, 39, 49, 51, 53 PM:Powers: 7

Integer number operations: 12-14; Rational number operations: 18-20

1.3 Convert fractions to decimals and percents anduse these representations in estimations,computations, and applications.

PE/TE:Computations: 131-134, 241-244;

Applications: 245-248, 252-259;Estimation: 531-533

CASRP: 7-8, 137, 141-142, 145-147

RB: 51 (Exs. 5-8), 53 (Exs. 22-27),86 (Exs. 6-8), 89, 91

PM: 20, 32-34



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1.4 Differentiate between rational and irrationalnumbers.

PE/TE: 108 (top of page),131-134, 359 (top of page)

CSKCB: S22-S23CASRP: 9-10, 139, 141-142

PM: 20 (Exs. 7-10)

1.5 Know that every rational number is either aterminating or repeating decimal and be able toconvert terminating decimals into reducedfractions.

PE/TE: T48-T49, T54-T55, 131-135CSKCB: S24-S27

CASRP: 11-12, 137, 141-142

RB: 51 (Exs. 5-6), 53 (Exs. 22-27)PM: 20

1.6 Calculate the percentage of increases anddecreases of a quantity.

PE/TE: 249-251

CASRP: 13-15, 145-147

RB: 89, 91 (Ex. 15)

PM: 33, 34

1.7 Solve problems that involve discounts, markups,commissions, and profit and compute simple andcompound interest.

PE/TE: 252-263

CSKCB: S28-S35CASRP: 16-18, 145-147

RB: 88, 89 (Exs. 2-4, 7-8), 91 (Exs. 16, 19-20)

PM: 33-34



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2.0 Students use exponents, powers, and rootsand use exponents in working with fractions:

PE/TE: 40-43, 56-58, 95-97,356-363,388-389




2.1 Understand negative whole-number exponents.Multiply and divide expressions involvingexponents with a common base.

PE/TE:Multiply and divide: 40-43,482-483;

Negative whole number exponents: 95-96;Scientific notation: 98-99CASRP: 19-20

RB: 37 (Exs. 13-16)PM: 14 (Exs. 22-35)

2.2 Add and subtract fractions by using factoring tofind common denominators.

PE/TE: 115-121

CSKCB: S36-S38CASRP: 21-22, 143, 146-147

RB: 47 (Exs. 6-7)

PM: 18

2.3 Multiply, divide, and simplify rational numbers byusing exponent rules.

PE/TE: 40-43, 56-58, 95-97,109 (Exs. 34-43), 114 (Exs. 1-10)

CSKCB: S39-S41CASRP: 23-24, 148, 151-152

RB: 27 (Exs. 3-5), 37 (Exs. 13-16)

PM: 7 (Exs. 11-35), 14 (Exs. 28-35)

2.4 Use the inverse relationship between raising to apower and extracting the root of a perfect squareinteger; for an integer that is not square,determine without a calculator the two integersbetween which its square root lies and explainwhy.

PE/TE: 356-360, 388-389

CASRP: 25-26, 138, 141-142

RB: 124 (Exs. 1-5), 129 (Exs. 1-5)

PM: 45 (Exs. 1-12)

2.5 Understand the meaning of the absolute value ofa number; interpret the absolute value as thedistance of the number from zero on a numberline; and determine the absolute value of realnumbers.

PE/TE: 72-74, 77 (Ex. 13-18), 78-80, 86(Ex. 66), 101 (Exs. 5-8)CSKCB: S42-S43

CASRP: 27-28, 138, 141-142

RB: 32 (Exs. 3-4, 7-8), 39 (Exs. 3-4, 17-18)

PM: 11 (Exs. 9-10)



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ALGEBRA AND FUNCTIONS

1.0 Students express quantitative relationshipsby using algebraic terminology, expressions,equations, inequalities, and graphs:

PE/TE: 2-4, 5-11, 12-15, 20-26, 40, 44, 51-58, 111, 146, 159, 167-173, 272, 284-299,440-469, 476, 492CSKCB: S44-S53, T14-T17

CASRP: 29-40

See all references for AF1.1-AF1.5 below.


1.1 Use variables and appropriate operations to writean expression, an equation, an inequality, or asystem of equations or inequalities thatrepresents a verbal description (e.g., three lessthan a number, half as large as area A).

PE/TE:Algebraic expressions: 20-23;Equations and inequalities: 24-26, 167-173,284-287, 294-297

CSKCB: T14-T17CASRP: 29-31, 153, 156-157

RB: 13, 15 (Exs. 18-21)

PM: 5

1.2 Use the correct order of operations to evaluatealgebraic expressions such as 3(2x + 5)2.

PE/TE: 5-8, 56-58 (simplifying andevaluating expressions), 94 (Exs. 1-10),95-96, 102 (Exs. 25-33), 109 (Exs. 34-43)

CASRP: 32-33, 149, 151-152

RB: 10 (Exs. 4-10), 15 (Exs. 9-10),25, 27 (Exs. 18-20)

PM: 3 (Exs. 22-31), 7 (Exs. 29-37),9 (Exs. 20-23)

1.3 Simplify numerical expressions by applyingproperties of rational numbers (e.g., identity,inverse, distributive, associative, commutative)and justify the process used.

PE/TE: 40-43, 51-58, 63 (Exs. 1-10), 66(Exs. 12-22), 88-91, 95-96, 144-145,152-155.CSKCB: S44-S53

CASRP: 34-35, 149-152

RB: 10 (Exs. 1-14), 25 (Exs. 1-9),27 Test (Ex.18-20)PM: 9, 12-15

1.4 Use algebraic terminology (e.g., variable,equation, term, coefficient, inequality, expression,constant) correctly.

PE/TE: 2-3, 9, 12, 20-26, 40, 44, 56, 111,146, 159, 272, 476, 492CASRP: 36-37, 149, 151-153, 156-157,159, 162-163

RB: 13, 15-17, 21, 22



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1.5 Represent quantitative relationships graphicallyand interpret the meaning of a specific part of agraph in the situation represented by the graph.

PE/TE:Coordinate plane: 272-275,280-283;

System of equations: 284-287;Solving Problems: 288-293, 298-299;

Graphing inequalities: 294-297;Statistical graphs: T66-T67, 258, 440;

Number line: 72-73, 75-76, 79-81CASRP: 38-40, 158, 162-163

RB: 98-104, 146, 147, 151-154

PM: 35-38, 43, 44, 53, 55, 56, 60

2.0 Students interpret and evaluate expressionsinvolving integer powers and simple roots:

PE/TE: 40-43, 95-96, 98-99, 482-483CSKCB: T8-T11

CASRP: 41-44



2.1 Interpret positive whole-number powers asrepeated multiplication and negative whole-number powers as repeated division ormultiplication by the multiplicative inverse.Simplify and evaluate expressions that includeexponents.

PE/TE:Positive powers: 40-43;Simplifying expressions: 56-58;

Negative powers: 95-96, 98-99, 101(Exs. 38-41);Fractional powers: 388-389

CSKCB: T8-T11CASRP: 41-42

RB: 22 (Exs. 1–8), 27 (Exs. 1–7),37 (Exs.13–16)PM: 9 (Exs. 20–22)

2.2 Multiply and divide monomials; extend theprocess of taking powers and extracting roots tomonomials when the latter results in a monomialwith an integer exponent.

PE/TE: 482-483, 484-491CASRP: 43-44, 150-152

RB: 159 (Exs. 5–6), 165 (Exs. 7–9)PM: 58 (Exs. 1–14)



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3.0 Students graph and interpret linear and somenonlinear functions:

PE/TE: 271e-271f, 272-275, 280-282,288-293, 298-299




3.1 Graph functions of the form y = nx2 and y = nx3

and use in solving problems.PE/TE: 282 (Ex. 40)CASRP: 45-46, 161-163

3.2 Plot the values from the volumes of three-dimensional shapes for various values of theedge lengths (e.g., cubes with varying edgelengths or a triangle prism with a fixed height andan equilateral triangle base of varying lengths).

PE/TE: 326-334

CASRP: 47-48, 161-163

3.3 Graph linear functions, noting that the verticalchange (change in y- value) per unit of horizontalchange (change in x- value) is always the sameand know that the ratio ("rise over run") is calledthe slope of a graph.

PE/TE: 271e-271f, 272-282, 288-293

CSKCB: S54-S60CASRP: 49-51, 160, 162-163

RB: 98 (Exs. 13-14), 99, 101 (Exs. 1–3),102 (Exs. 7-8), 103 (Exs. 6–8)PM: 36-37, 38 (Exs. 1-2)

3.4 Plot the values of quantities whose ratios arealways the same (e.g., cost to the number of anitem, feet to inches, circumference to diameter ofa circle). Fit a line to the plot and understand thatthe slope of the line equals the quantities.

PE/TE: 188, 234-237, 238-239, 288-293,298-299CSKCB: S61-S63

CASRP: 52-54, 159, 162-163

RB: 102 (Ex. 10), 103 (Ex. 8)

PM: 38 (Exs. 1-2)



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4.0 Students solve simple linear equations andinequalities over the rational numbers:

PE/TE: 230-237, 245, 252-254, 260-263,288-293, 303, 344-347, 353

CSKCB: S64-S76, T14-T21CASRP: 55-59



4.1 Solve two-step linear equations and inequalitiesin one variable over the rational numbers,interpret the solution or solutions in the contextfrom which they arose, and verify thereasonableness of the results.

PE/TE:Equations: 155-158; Inequalities: 162(Exs. 49-52), 163-166, 169-173

CSKCB: S64-S73, T14-T17CASRP: 55-57, 154, 156-157

RB: 63, 64 (Exs. 7-22), 65 (Exs. 6-17),66 (Exs. 6-19), 67 (Exs. 33-41)PM: 22-24

4.2 Solve multistep problems involving rate, averagespeed, distance, and time or a direct variation.

PE/TE: 168 (Ex. 20), 169-175, 230-237,245-263, 288-293, 303, 344-347, 353CSKCB: S74-S76, T18-T21

CASRP: 58-59, 155-157

RB: 91 (Ex. 7)PM: 31 (Exs.10–15)



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MEASUREMENT AND GEOMETRY

1.0 Students choose appropriate units ofmeasure and use ratios to convert within andbetween measurement systems to solveproblems:

PE/TE: 169-173, 234-240, 307-311,327-329, 344-347CSKCB: P82-P90, S77-S78, T18-T21

CASRP: 60-65

See all references for MG1.1-MG1.3 below.


1.1 Compare weights, capacities, geometricmeasures, times, and temperatures within andbetween measurement systems (e.g., miles perhour and feet per second, cubic inches to cubiccentimeters).

PE/TE: 233 (Exs. 7-8), 234, 292 (Ex. 8),293 (Exs. 9, 11), 307-311, 327-329, 344-347CSKCB: P82-P90, T18-T21

CASRP: 60-61, 164, 168-169

1.2 Construct and read drawings and models madeto scale.

PE/TE: 238-240CASRP: 62-63, 165, 168-169

RB: 91 (Ex.8)PM: 31 (Exs. 16–18)

1.3 Use measures expressed as rates (e.g., speed,density) and measures expressed as products(e.g., person-days) to solve problems; check theunits of the solutions; and use dimensionalanalysis to check the reasonableness of theanswer.

PE/TE: 169-173, 234-237, 252-254, 260-263, 344-347

CSKCB: S77-S78, T18-T21CASRP: 64-65, 166, 168-169

RB: 91 (Ex.7), 113 (Ex. 9), 115 (Ex. 17)

PM: 31 (Exs.10, 14-15), 42 (Exs. 9-11)



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2.0 Students compute the perimeter, area, andvolume of common geometric objects and usethe results to find measures of less commonobjects. They know how perimeter, area, andvolume are affected by changes of scale:

PE/TE: T60-T61, 188-190, 213-216,306-343

CSKCB: P92-P102CASRP: 66-75



2.1 Use formulas routinely for finding the perimeterand area of basic two-dimensional figures and thesurface area and volume of basic three-dimensional figures, including rectangles,parallelograms, trapezoids, squares, triangles,circles, prisms, and cylinders.

PE/TE:Perimeter of circle: 188, 189;Perimeter: 213-215;

Area: T60-T61, 306-325;Volume: 326-334, 340-343;

Surface area: 335-339;Circumference: T60-T61, 188-190

CSKCB: P92-P102CASRP: 66-68, 167-169, 176, 179-180

RB: 70 (Exs. 3-4), 73 (Exs. 1, 3),75 (Exs. 7-8), 77 (Exs. 3, 14), 108, 113, 115PM: 25 (Ex. 10), 28 (Exs. 1-4), 39,40 (Exs. 1-3), 41, 42

2.2 Estimate and compute the area of more complexor irregular two- and three-dimensional figures bybreaking the figures down into more basicgeometric objects.

PE/TE:307-309 (two-dimensional),313 (area of trapezoid),315-316 (Exs. 13-16, 20-21),319 (Exs. 21-24), 321-324, 335-343(area and volume)CASRP: 69-70, 167-169, 176, 179-180

RB: 108 (Exs. 10-12), 111, 112PM: 39 (Ex. 8), 40 (Exs. 4-11)

2.3 Compute the length of the perimeter, the surfacearea of the faces, and the volume of a three-dimensional object built from rectangular solids.Understand that when the lengths of alldimensions are multiplied by a scale factor, thesurface area is multiplied by the square of thescale factor and the volume is multiplied by thecube of the scale factor.

PE/TE: 213-216, 238-240, 312, 326-330,335-339

CASRP: 71-73, 176, 179-180

RB: 111, 113 (Exs. 5-7), 115 (Exs. 14-16)PM: 41-42



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2.4 Relate the changes in measurement with achange of scale to the units used (e.g., squareinches, cubic feet) and to conversions betweenunits (1 square foot = 144 square inches or [1 ft2]= [144 in2], 1 cubic inch is approximately 16.38cubic centimeters or [1 in3] = [16.38 cm3]).

PE/TE: 233 (Exs. 7-8), 238-239, 292-293,307-311, 327-329, 344

CSKCB: T18-T21CASRP: 74-75, 164, 168-169

3.0 Students know the Pythagorean theorem anddeepen their understanding of plane and solidgeometric shapes by constructing figures thatmeet given conditions and by identifyingattributes of figures:

PE/TE: T62-T63, 187, 191-193, 196, 204-208, 209-221, 274-275, 308-309, 313, 315,326, 329, 331-332, 334-336, 338-340, 343,364-377, 382CSKCB: S79-S99

CASRP: 76-90



3.1 Identify and construct basic elements ofgeometric figures (e.g., altitudes, mid-points,diagonals, angle bisectors, and perpendicularbisectors; central angles, radii, diameters, andchords of circles) by using a compass andstraightedge.

PE/TE: T62-T63, 187, 189 (Exs. 5-6), 192-193, 196, 201, 199 (Exs. 26-28), 202-203(Exs. 17 -18, 23, 26-27), 207-208 (Exs. 11-12, 22-24), 210, 212 (Exs. 17-22, 25), 215(Exs.13-18)

CASRP: 76-78, 170, 174-175

PM: 26 (Exs. 4-5)

3.2 Understand and use coordinate graphs to plotsimple figures, determine lengths and areasrelated to them, and determine their image undertranslations and reflections.

PE/TE: 217, 274-275, 308-309, 313, 315

CASRP: 79-80, 173-175

RB: 96

3.3 Know and understand the Pythagorean theoremand its converse and use it to find the length ofthe missing side of a right triangle and the lengthsof other line segments and, in some situations,empirically verify the Pythagorean theorem bydirect measurement.

PE/TE: 364-367, 373-377, 382

CSKCB: S79-S86

CASRP: 81-82, 171, 174-175

RB: 123, 124 (Exs. 9-10),129 (Exs. 7-10, 14-15)PM: 46 (Exs. 15-22)



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3.4 Demonstrate an understanding of conditions thatindicate two geometrical figures are congruentand what congruence means about therelationships between the sides and angles of thetwo figures.

PE/TE: 182, 184, 191-192, 195, 197, 200-201, 203 (Ex. 27), 209-210, 211(Exs. 7, 10, 16), 212 (Exs. 18-19), 217-221

CSKCB: S87-S92CASRP: 83-85, 172, 174-175

RB: 72, 74 (Exs. 10-14), 75 (Exs. 6, 9-10),77 (Exs.15-17)

PM: 26 (Exs. 4-5), 28 (Exs. 8-12)

3.5 Construct two-dimensional patterns for three-dimensional models, such as cylinders, prisms,and cones.

PE/TE: 329 (Exs. 19-20),335, 338 (Exs. 11-12)CASRP: 86-87, 177, 179-180

RB: 83, 109 (Exs. 1-3)

3.6 Identify elements of three-dimensional geometricobjects (e.g., diagonals of rectangular solids) anddescribe how two or more objects are related inspace (e.g., skew lines, the possible ways threeplanes might intersect).

PE/TE: 326, 331-332, 334 (Exs. 21-22),335-336, 339 (Ex. 20), 340 (spheres),343 (Exs. 21-22)

CSKCB: S93-S99CASRP: 88-90, 178-180



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STATISTICS, DATA ANALYSIS, ANDPROBABILITY

1.0 Students collect, organize, and represent datasets that have one or more variables andidentify relationships among variables withina data set by hand and through the use of anelectronic spreadsheet software program:

PE/TE: T66-T67, 298-299, 440-464

CSKCB: S100-S103

CASRP: 91-97

See all references for SDAP1.1- SDAP 1.3below.

See all references for SDAP1.1- SDAP 1.3below.

1.1 Know various forms of display for data sets,including a stem-and-leaf plot or box-and-whiskerplot; use the forms to display a single set of dataor to compare two sets of data.

PE/TE:Bar and line graphs: 440-448;Numerical data: 449-452;Frequency distribution: 453-456;

Stem-and-leaf: T66-T67, 457-458;Box-and-whisker: 459-460;

Histogram: 461-464CASRP: 91-93, 181, 184-185

RB: 147, 149, 151, 152 (Exs. 1-3), 153 154

PM: 53, 54, 55, 56, 60 (Exs. 10-12)

1.2 Represent two numerical variables on ascatterplot and informally describe how the datapoints are distributed and any apparentrelationship that exists between the two variables(e.g., between time spent on homework andgrade level).

PE/TE: 288-293, 298-299

CSPW: 76, 106-108

1.3 Understand the meaning of, and be able tocompute, the minimum, the lower quartile, themedian, the upper quartile, and the maximum of adata set.

PE/TE: T66-T67, 449-452, 453-456,459-460CSKCB: S100-S103

CASRP: 96-97, 183-185

RB: 151 (Exs. 4-7), 152 (Ex. 8), 153 (Ex. 6),154 (Ex. 6)PM: 54, 55



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MATHEMATICAL REASONING

1.0 Students make decisions about how toapproach problems:

Occurs throughout.

Examples:

PE/TE:(Gr. 7, AF 1.1) PE/TE, 27-31;(Gr. 7, NS 1.2) PE/TE, 59-63;(Gr. 7, NS 1.2) PE/TE, 69;(Gr. 7, NS 1.2) PE/TE, 129-130

CASRP:

(Gr. 7, NS 1.2; Gr. 7, MG 1.1; Gr. 7, MG 2.1)CASRP, 98-104

See all references for MR1.1-MR1.3 below.

Occurs throughout.


1.1 Analyze problems by identifying relationships,distinguishing relevant from irrelevant information,identifying missing information, sequencing andprioritizing information, and observing patterns.

Occurs throughout.

Examples:

PE/TE:(Gr. 7, AF 1.1) PE/TE, 27-31;(Gr.7, NS 1.2) PE/TE, 37 (Exs. 1-7);(Gr. 7, NS 1.2) PE/TE, 59-63;(Gr. 7, NS 1.2) PE/TE, 69;(Gr. 7, NS 1.2) PE/TE, 103;(Gr. 7, NS 1.2) PE/TE, 129-130;(Gr. 7, AF 1.1) PE/TE, 179;(Gr. 7, NS 1.7) PE/TE, 353 (Exs. 4-5);

CASRP:(Gr. 7, NS 1.2) CASRP, 98-100

Occurs throughout.

Examples:

RB: (Gr. 7, NS 1.2) RB, 12;(Gr. 7, NS 1.2) RB, 23-24;(Gr. 7, NS 1.2) RB, 35; (Gr. 7, MG 2.1) RB, 73



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1.2 Formulate and justify mathematical conjecturesbased on a general description of themathematical question or problem posed.

Occurs throughout.

Examples:PE/TE:(Gr. 7, NS 1.2) TE, T46-T47;(Gr. 7, NS 1.2) PE, E3-E4;(Gr. 7, NS 1.2) PE/TE, 43 (Ex. 48);(Gr. 7, NS 2.5) PE/TE, 82 (Ex. 53);(Gr. 7, NS 1.2) PE/TE, 117 (Ex. 45);(Gr. 7, MG 3.1) PE/TE, 216 (Ex. 21);(Gr. 7, MG 2.1) 310 (Exs. 17-22);(Gr. 7, MG 2.3) 329 (Exs. 21-22)

CASRP:

(Gr. 7, MG 1.1) CASRP, pp. 101-102

Occurs throughout.

Examples:RB: (Gr. 7, NS 2.1) RB, 157

1.3 Determine when and how to break a problem intosimpler parts.

Occurs throughout.

Examples:PE/TE:

(Gr. 7, NS 1.2) PE/TE, 27-31;(Gr. 7, NS 1.2) PE/TE, 59-63;(Gr. 7, NS 1.2) PE/TE, 141;(Gr. 7, MG 2.1) PE/TE, 214-216;(Gr. 7, NS 1.3) PE/TE, 269 (Ex. 8);(Gr. 7, MG 3.3) PE/TE, 290-293;(Gr. 7, MG 2.1) PE/TE, 353 (Ex. 8)

CASRP:

(Gr. 7, MG 2.1) CASRP, 103-104

Occurs throughout.

Examples:RB: (Gr. 7, NS 1.2) RB, 46;(Gr. 7, AF 4.2) RB, 57;(Gr. 7, AF 1.1) RB, 99-100



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2.0 Students use strategies, skills, and conceptsin finding solutions:

Occurs throughout.

Examples:PE/TE:T50-T51, 55, 59-61, 155-158, 163-166, 170-173, 217-218, 227, 284-285, 288-290, 336

CASRP:

(Gr. 7, NS 1.0; Gr. 7, NS 1.1; Gr. 7, NS 1.2;Gr. 7, AF 1.0; Gr. 7, MG 2.1; Gr. 7, SDAP1.1; Gr. 7, SDAP 1.1) CASRP, 105-121


Occurs throughout.


2.1 Use estimation to verify the reasonableness ofcalculated results.

Occurs throughout.

Examples:

PE/TE:(Gr. 7, NS 1.2) PE/TE, 59-63;(Gr. 7, NS 1.2) PE/TE, 62 (Exs. 5-6);(Gr. 7, AF 1.1) PE/TE. 169-173;(Gr. 7, MG 2.1) PE/TE, 227 (Exs. 1, 9, 10, 11);(Gr. 7, NS 2.4) PE/TE, 358-360;(Gr. 7, NS 1.2) PE/TE, 531-533

CASRP:(Gr. 7, NS 1.1; Gr. 7, NS 1.2) CASRP,105-106

Occurs throughout.

Examples:

RB: (Gr. 7, NS 1.2) RB, 30;(Gr. 7, NS 1.2) RB, 33;(Gr. 7, NS 1.2) RB, 48; (Gr. 7, NS 1.2) RB, 68



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2.2 Apply strategies and results from simplerproblems to more complex problems.

Occurs throughout.

Examples:PE/TE:(Gr. 7, AF 4.1) PE/TE, 155-158;(Gr. 7, AF 4.1) PE/TE, 163-166;(Gr. 7, NS 1.7) PE/TE, 303 (Exs.4-6);(Gr. 7, MG 2.3) PE/TE, 336-339;(Gr. 7, NS 1.2) PE/TE, 437 (Exs. 1, 7);(Gr. 7, NS 1.7) PE/TE, 473 (Ex. 1)

CASRP:(Gr. 7, MG 2.1) CASRP, 107-108

Occurs throughout.

Examples:RB: (Gr. 7, NS 1.2) RB, 46; (Gr. 7, AF 4.2)RB, 57; (Gr. 7, AF 1.1) RB, 99-100

2.3 Estimate unknown quantities graphically andsolve for them by using logical reasoning andarithmetic and algebraic techniques.

Occurs throughout.

Examples:PE/TE:

(Gr. 7, AF 3.3) PE/TE, 284-287;(Gr. 7, AF 3.3) PE/TE, 288-293;

CASRP:(Gr. 7, SDAP 1.1; Gr. 7, SDAP 1.2) CASRP,109-110

Occurs throughout.

Examples:RB: (Gr. 7, AF 1.1) RB, 99; (Gr. 7, MG 2.2)RB, 112

2.4 Make and test conjectures by using bothinductive and deductive reasoning.

Occurs throughout.

Examples:PE/TE:(Gr. 7, NS 2.5) PE/TE. 82 (Ex. 53);(Gr. 7, AF 2.0) PE/TE. 96 (Exs. 47-48);(Gr. 7, NS 1.1) PE/TE, 117 (Ex. 45;(Gr. 7, MG 3.1) PE/TE, 199 (Exs. 29-30)

CASRP:(Gr. 7, AF 1.0) CASRP, 111-112

Occurs throughout.

Examples:RB: (Gr. 7, AF 4.2) RB, 59; (Gr. 7, MG 2.1)RB, 109



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2.5 Use a variety of methods, such as words,numbers, symbols, charts, graphs, tables,diagrams, and models, to explain mathematicalreasoning.

Occurs throughout.

Examples:PE/TE:(Gr. 7, AF 4.1) PE/TE, 277 (Example 3);(Gr. 7, AF 4.1) PE/TE, 280-285;(Gr. 7, NS 2.4) PE/TE, 361-363;(Gr. 7, MG 2.1) PE/TE, 437 (Exs. 6, 8)

CASRP:(Gr. 7, NS 1.0) CASRP, 113-115

Occurs throughout.

Examples:RB: (Gr. 7, NS 1.2) RB, 11-12;(Gr. 7, NS 1.2) RB, 35; (Gr. 7, AF 4.1) RB, 58

2.6 Express the solution clearly and logically by usingthe appropriate mathematical notation and termsand clear language; support solutions withevidence in both verbal and symbolic work.


PE/TE:(Gr. 7, NS 1.1) PE/TE, 98-99;(Gr. 7, NS 1.5) PE/TE, 131-135;(Gr. 7, MG 3.1) PE/TE, 182-194

CASRP:(Gr. 7, NS 1.0) CASRP, 116-117


RB: (Gr. 7, MG 3.4) RB, 75 (Exs. 9-10);(Gr. 7, MG 2.1) RB, 112

2.7 Indicate the relative advantages of exact andapproximate solutions to problems and giveanswers to a specified degree of accuracy.


PE/TE:(Gr. 7, NS 1.2) PE/TE, 48-50;(Gr. 7, MS 1.2) PE/TE, 303 (Exs. 1, 8, 9);(Gr. 7, MG 2.1) PE/TE, 317-319;(Gr. 7, MG 2.3) PE/TE, 331-334;(Gr. 7, NS 2.4) PE/TE, 356-357

CASRP:(Gr. 7, NS 1.0) CASRP, 118-119


RB: (Gr. 7, MG 2.1) RB, 108;(Gr. 7, MG 2.1) RB, 113-115;(Gr. 7, NS 2.4) RB, 124



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2.8 Make precise calculations and check the validityof the results from the context of the problem.

Occurs throughout.

Examples:PE/TE:(Gr. 7, NS 1.2) PE/TE, 27-31;(Gr. 7, NS 1.2) PE/TE, 59-63;(Gr. 7, AF 1.1) PE/TE. 169-173;

CASRP:(Gr. 7, NS 1.0) CASRP, 120-121

Occurs throughout.

Examples:RB: (Gr. 7, NS 1.2) RB, 56;(Gr. 7, NS 1.2) RB, 94 (Exs. 1-5);(Gr. 7, NS 1.7) RB, 106 (Exs. 2, 4)

3.0 Students determine a solution is completeand move beyond a particular problem bygeneralizing to other situations:


PE/TE:(Gr. 7, NS 1.2) PE/TE. 51-55;(Gr. 7, NS 1.2) PE/TE, 79-93;(Gr. 7, NS 1.5) PE/TE, 131-135;(Gr. 7, AF 4.1) PE/TE, 159-166

CASRP:(Gr. 7, AF 1.0; Gr. 7, AF 1.1; Gr. 7, MG 2.1)CASRP, 122-127


Occurs throughout.


3.1 Evaluate the reasonableness of the solution inthe context of the original situation.


PE/TE:(Gr. 7, NS 1.2) PE/TE, 59-63;(Gr. 7, NS 1.2) PE/TE, 62 (Exs. 5-6);(Gr. 7, AF 1.1) PE/TE. 169-173;(Gr. 7, NS 1.2) PE/TE, 393 (Exs. 1, 4, 5, 6)

CASRP:(Gr. 7, MG 2.1) CASRP, 122-123


RB: (Gr. 7, NS 1.2) RB, 13 (Exs. 8-9);(Gr. 7, NS 1.2) RB, 14 (Ex. 29);(Gr. 7, NS 1.2) RB, 15 (Ex. 22);(Gr. 7, NS 1.2) RB, 35; (Gr. 7, NS 1.2) RB, 132



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3.2 Note the method of deriving the solution anddemonstrate a conceptual understanding of thederivation by solving similar problems.

Occurs throughout.

Examples:PE/TE:(Gr. 7, NS 1.2) PE/TE, 48-50;(Gr. 7, NS 1.2) PE/TE. 118-130;(Gr. 7, NS 1.5) PE/TE, 131-135

CASRP:(Gr. 7, AF 1.0) CASRP, 124-125

Occurs throughout.

Examples:RB: (Gr. 7, NS 1.2) RB, 118;(Gr. 7, NS 1.2) RB, 121;(Gr. 7, NS 1.2) RB, 132;(Gr. 7, NS 1.2) RB, 133

3.3 Develop generalizations of the results obtainedand the strategies used and apply them to newproblem situations.


PE/TE:(Gr. 7, NS 1.2) PE/TE. 51-55;(Gr. 7, NS 1.2) PE/TE, 79-93;(Gr. 7, AF 4.1) PE/TE, 159-166;(Gr. 7, NS 2.4) PE/TE, 358-360

CASRP:(Gr. 7, AF 1.1) CASRP, 126-127


RB: (Gr. 7, NS 2.1) RB, 157;


Algebra 1

Publisher: McDougall Littell, Inc.Program Title: McDougal Littell California Structure and Method: Course 1, Course 2, Algebra 1Components: Pupil Edition (PE), Teacher’s Edition (TE), California Standards Key Concepts Book (CSKCB),California Standards Review and Practice (CASRP), Algebra Skills Resources (ASR), Resource Book (RB),Practice Masters (PM), Study Guide for Reteaching and Practice (RP)Grade Level(s): 6–8



Grade Eight – Mathematics (Algebra I)

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ALGEBRA I

1.0 Students identify and use the arithmeticproperties of subsets of integers and rational,irrational, and real numbers, including closureproperties for the four basic arithmeticoperations where applicable:

PE/TE: 45-53, 65-73, 79-82, 88, 507-511,685, 696

CSKCB: P16-P25, P42-P56, S92-S95,T8-T12, T17-T25

CASRP: 2-4, 91, 94-95

RP: 19-22, 27-30, 33-34, 183-184Tests: 9-11, 13-18

1.1 Students use properties of numbers todemonstrate whether assertions are true orfalse.

PE/TE: 130-133, 254 (Challenge),457-458 (Example 2), 460 (Exs. 15-22),475 (Challenge), 488 (Exs. 19-24),508, 511, 524 (Extra), 715-720

CSKCB: S92-S95CASRP: 5-6, 91, 94-95

RP: 51-52, 168 (Exs. 13-24), 184 (Exs. 7-18)

Tests: 4 (Exs. 14, 17, 20), 6 (Exs.17-18),8 (Exs. 17-18, 20),10 (Exs. 13-14, 21, Challenge),12 (Exs. 17, 19), 13 (Exs. 1, 6-7),24 (Exs. 5-13), 26 (Exs. 14-18),28 (Exs. 14-18), 99 (Exs.13-15)

2.0 Students understand and use such operationsas taking the opposite, finding the reciprocal,taking a root, and raising to a fractional power.They understand and use the rules ofexponents.

PE/TE: 645, 649, 652-653 (Exs. 50-71), 660-661 (Exs. 31-78)Exponents: 141-144, 152-157, 190-193

Rules of Exponents: 252-257Fractional Exponents: 334-335 (Exs. 68-71),551-553

Opposites: 36-38, 50-51,Reciprocal: 79-82

Roots: 517-534CSKCB: S2-S9, T8-T12, T17-T25

CASRP: 7-9, 92, 94-95ASR: 9, 20, 21, 36, 38, 39, 46, 47 (Exs. 1-3,10-24), 50, 63 (Exs. 13-22), 66, 67, 83, 124

RP: 17, 21, 33-36, 53-54, 57-60, 75-76, 101-102, 129-130, 187-192Tests: 13-14, 29-30 (Exs. 1-3, 10-16), 33(Exs. 1-3), 35 (Exs. 1-3, 6-7), 39 (Exs. 5-9),49 (Exs. 9-10), 64 (Challenge),66 (Exs. 14-16), 68 (Exs. 14-16),99 (Exs. 13-16), 100-101, 104 (Exs. 4-6),106 (Exs. 4-6)



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3.0 Students solve equations and inequalitiesinvolving absolute values.

PE/TE: 36-38, 482-489, 659 (Exs. 48-71)ASR: 9, 115, 116

CASRP: 10-12, 93-95

RP: 175-178Tests: 92-93 (Exs. 7-12), 94-95 (Exs. 3-10,13-14), 96-97 (Exs. 3-10, 13-14)

4.0 Students simplify expressions before solvinglinear equations and inequalities in one variable,such as 3(2x-5) + 4(x-2) = 12.

PE/TE: 98 (Exs. 34-45), 107-110, 116-118,462-467, 643-644, 658CSKCB: S10-S17

CASRP: 13-14, 96, 98-99ASR: 29, 33, 112

RP: 37-42, 45-46, 168 (Exs. 1-12), 169-170

Tests: 20, 21 (Exs. 4-8), 25, 27, 90-91

5.0 Students solve multistep problems, includingword problems, involving linear equations andlinear inequalities in one variable and providejustification for each step.

PE/TE: 98 (Exs. 34-45),104 (Exs. 29-52), 107-110, 112-115, 116-119, 121-129, 462-467, 469-474, 478-481,643-644, 658, 667-668, 677

CSKCB: S18-S25, S84-S87, T1-T3CASRP: 15-17, 97-99

ASR: 27-31, 32-35, 113-114

RP: 41-50, 169-174Tests: 19-22, 25-28, 90-91

6.0 Students graph a linear equation and computethe x- and y- intercepts (e.g., graph 2x + 6y = 4).They are also able to sketch the region definedby linear inequality (e.g., they sketch the regiondefined by 2x + 6y < 4).

PE/TE: 353-359, 366-369, 407 (Exs. 9-10,19-26), 502 (Exs. 11-12), 653 (Exs. 13-21),659 (Exs. 72-88)Inequalities: 490-494

CSKCB: S26-S36, S48-S55CASRP: 18-21, 104, 106-107

ASR: 89 (Exs. 26-28), 91 (Exs. 7-28), 117(Exs. 7-21)

RP: 136 (Exs. 17-24), 139-140, 179-180

Tests: 75 (Ex. 5), 77 (Ex. 5)

7.0 Students verify that a point lies on a line, givenan equation of the line. Students are able toderive linear equations by using the point-slopeformula.

PE/TE: 349-352, 371-373, 405 (Exs. 1-2),407-408, (Exs. 1-2, 27-31),413-414, 653-654 (Exs. 1-6, 59-64),CSKCB: S37–S47

CASRP: 22-23, 105-107ASR: 88, 92

RP: 133, 141

Tests: 69 (Ex. 2), 71 (Exs. 19-20),75 (Exs. 1, 4, 10), 77 (Exs. 1, 4, 8)



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8.0 Students understand the concepts of parallellines and perpendicular lines and how thoseslopes are related. Students are able to find theequation of a line perpendicular to a given linethat passes through a given point.

PE/TE: 366-370, 373 (Exs. 35-36),406 (Ex. 8), 407 (Exs. 19-22), 413-414CSKCB: S49 (Example 2), S52 (Ex. 17),T7 (Ex. 16)CASRP: 24-26, 108, 111-112

RP: 139-140Tests: 77 (Ex. 11)

9.0 Students solve a system of two linear equationsin two variables algebraically and are able tointerpret the answer graphically. Students areable to solve a system of two linear inequalitiesin two variables and to sketch the solution sets.

PE/TE: 413-452, 656-657, 695CSKCB: S48-S55

CASRP: 27-30, 109-112ASR: 101-110

RP: 153-166Tests: 81-89

10.0 Students add, subtract, multiply, and dividemonomials and polynomials. Students solvemultistep problems, including word problems, byusing these techniques.

PE/TE: 167-180, 645-646, 647 (Exs. 15-28,35-52), 651 (Exs. 105-118), 668-669,689-690Addition and subtraction: 146-151Multiplication: 152-154, 158-164, 200-203

Division: 189-193,194-199, 274-277CSKCB: S56-S65, T13-T16, T22-T25

CASRP: 31-35, 113-114, 116-117ASR: 37-38, 40-48, 50-52, 71

RP: 55-58, 61-64, 67-72, 111

Tests: 29-36, 39-40

11.0 Students apply basic factoring techniques tosecond-and simple third-degree polynomials.These techniques include finding a commonfactor for all terms in a polynomial, recognizingthe difference of two squares, and recognizingperfect squares of binomials.

PE/TE: 213-238, 239, 241 (Exs. 7-22), 242(Exs. 17-34), 243 (Exs.17-25), 647-648 (Exs.29-46, 53-60, 69-118)

Monomial factors: 194-197Difference of two squares: 204-207

Perfect square of binomials: 208-212CSKCB: S66-S77

CASRP: 36-39, 113-114, 115-117ASR: 51, 53, 54 (Exs. 17-24), 55-59

RP: 77-78, 81-82, 84 (Exs. 25-42), 85-96

Tests: 39-40 (Exs. 10-15),41-42, 43 (Exs. 2-10), 45 (Exs. 8-19),47 (Exs. 8-19)



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12.0 Students simplify fractions with polynomials inthe numerator and denominator by factoringboth and reducing them to the lowest terms.

PE/TE: 247-250, 251-258, 282 (Exs. 1-4),649 (Exs. 1-16)CSKCB: S66-S73

CASRP: 40-41, 123, 126-127ASR: 65, 73 (Exs. 7-12)

RP: 99-100Tests: 49 (Exs. 1-8), 53 (Exs. 1-2),55 (Exs. 1-2), 59 (Ex. 30)

13.0 Students add, subtract, multiply, and dividerational expressions and functions. Studentssolve both computationally and conceptuallychallenging problems by using these techniques.

PE/TE: 281 (Exs. 4-6, 9-14),

282 (Exs. 6-13, 18-27), 283 (Exs. 31-36),649-651 (Exs. 17-28, 30-53, 72-118)Multiplying: 251-254

Dividing: 255-258Adding and Subtracting: 259-268

Mixed expressions: 270-273Long division: 274-277

Complex fractions: 278-279CSKCB: S66-S73, T8-T12CASRP: 42-44, 124, 126-127

ASR: 66, 67, 69-71, 73-74 (Exs. 7-24, 31-38)

RP: 101-104, 107-112

Tests: 49-50 (Exs. 9-18, Challenge),51-52 (Exs. 6-22), 53-54 (Exs. 3-6, 9-18),55-56 (Exs. 3-6, 9-18), 59 (Exs. 31-35)

14.0 Students solve a quadratic equation by factoringor completing the square.

PE/TE: 230-233, 234-238, 564-566, 576-578,595 (Exs. 3-4), 596 (Exs. 3-4, 9-10),648 (Exs. 119-140), 663 (Exs. 19-30, 49-62)CSKCB: S74-S77

CASRP: 45-47, 115-117ASR: 60-62, 64 (Exs. 43-50),136 (Exs. 10-33),139, 144-145 (Exs. 5-8, 25-38)

RP: 95-98, 205-206

Tests: 44 (Exs. 14-20), 45-46 (Exs. 20-22),47-48 (Exs. 20-22), 108 (Exs. 8-11),113 (Exs. 9-16), 115 (Exs. 9-16)



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15.0 Students apply algebraic techniques to solverate problems, work problems, and percentmixture problems.

PE/TE: 167-171 (Rate), 175 (Example 1),176-177 (Exs. 7, 11, 13),321-325 (Mixture/work), 326-330 (Work),434-436 (Exs. 13-15, 21-25, 32),438-442 (Rate), 668-669 (Exs. 1-5),672-673, 676-677

CSKCB: S78-S87CASRP: 48-50, 125-127

ASR: 43, 81-82, 106

RP: 67-68, 125-128, 163-164Tests: 31 (Exs. 7-8),32 (Challenge),34 (Exs. 14-15), 62-63, 84

16.0 Students understand the concepts of a relationand a function, determine whether a givenrelation defines a function, and give pertinentinformation about given relations and functions.

PE/TE: 374-377, 379-381, 383-387, 389-390,654-655CSKCB: S88-S91

CASRP: 51-52, 128, 130-131ASR: 93-95, 100 (Exs. 33-42)

RP: 143-148

Tests: 72-73

17.0 Students determine the domain of independentvariables and the range of dependent variablesdefined by a graph, a set of ordered pairs, or asymbolic expression.

PE/TE: 374-376, 379-381, 383-387, 389-390,406 (Exs. 11-13), 408 (Exs. 32-34),654-655 (Exs. 71-88)

CSKCB: S88CASRP: 53-55, 129-131

ASR: 93-94

RP: 143-146

Tests: 72-73

18.0 Students determine whether a relation definedby a graph, a set of ordered pairs, or a symbolicexpression is a function and justify theconclusion.

PE/TE: 389-390

CSKCB: S88-S89, S91CASRP: 56-57, 128, 130-131

19.0 Students know the quadratic formula and arefamiliar with its proof by completing the square.

PE/TE: 567-570

CASRP: 58-59, 118, 121-122

RP: 207-208

Tests: 109 (Exs. 12-16)

20.0 Students use the quadratic formula to find theroots of a second-degree polynomial and tosolve quadratic equations.

PE/TE: 567-570, 576—581, 595 (Exs. 5-6),596 (Exs. 5-6), 663 (Exs. 31-39, 49-62)

CASRP: 60-61, 118, 121-122

RP: 207-208, 213-214

Tests: 109 (Exs. 13-16)

21.0 Students graph quadratic functions and knowthat their roots are the x-intercepts.

PE/TE: 383-387, 408 (Ex. 39), 572-575, 581-582, 655 (Exs. 89-94), 700CASRP: 62-65, 119, 121-122

RP: 147-148, 209-210

Tests: 73 (Ex. 9)



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22.0 Students use the quadratic formula or factoringtechniques or both to determine whether thegraph of a quadratic function will intersect the x-axis in zero, one, or two points.

PE/TE: 572-575, 581-582, 595 (Exs. 7-8),596 (Exs. 7-8), 663 (Exs. 40-48), 700CASRP: 66-67, 119, 121-122

ASR: 139, 144 (Exs. 16-24)

RP: 209-210Tests: 110, 112 (Exs. 4, 7-8), 114 (Exs. 4, 7-8)

23.0 Students apply quadratic equations to physicalproblems, such as the motion of an object underthe force of gravity.

PE/TE: 234-238, 244 (Ex. 5), 579-581, 583,679 (12-7 Ex. 6)CASRP: 68-69, 120-122

ASR: 140 (Ex. 8)

Tests: 44 (Ex. 19), 111 (Exs. 12-17)

24.0 Students use and know simple aspects of alogical argument:

PE/TE: 130-133, 524, 715-720

CSKCB: S92–S95, T10–T12

CASRP: 70-75, 100, 102-103ASR: 32

RP: 51-52

Tests: 24 (Exs. 5-13), 26 (Exs. 14-18)

24.1 Students explain the difference betweeninductive and deductive reasoning and identifyand provide examples of each.

PE/TE: 130-134, 524, 715-717CASRP: 70-71, 100, 102-103

24.2 Students identify the hypothesis and conclusionin logical deduction.

PE/TE: 718-719CSKCB: S93

CASRP: 72-73, 100, 102-103, 120

24.3 Students use counterexamples to show that anassertion is false and recognize that a singlecounterexample is sufficient to refute anassertion.

PE/TE: 716-717, 720

CSKCB: S94-S95

CASRP: 74-75, 100, 102-103



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25.0 Students use properties of the number system tojudge the validity of results, to justify each stepof a procedure, and to prove or disprovestatements:

PE/TE: 48 (Exs. 35-36) 73 (Exs. 59-60),130-134, 193 (Exs. 61-62), 524, 716-717,720

CSKCB: S92-S95, T5-T7, T10-T12, T19-T25CASRP: 76-81, 101-103ASR: 32, 35 (Ex. 30)

RP: 51-52Tests: 24 (Exs. 5-13), 26 (Exs. 14-18),28 (Exs. 14-18)

25.1 Students use properties of numbers to constructsimple, valid arguments (direct and indirect) for,or formulate counterexamples to, claimedassertions.

PE/TE: 73 (Exs. 59-60),130-134, 193 (Exs. 61-62), 207 (Exs. 65-66),233 (Ex. 55), 524, 715-720CSKCB: S92-S95, T21, T23-T25

CASRP: 76-77, 101-103ASR: 32, 35 (Ex. 30)

RP: 51-52

Tests: 14 (Challenge-bottom of page),24, 26 (Exs. 14-18), 28 (Exs. 14-18)

25.2 Students judge the validity of an argumentaccording to whether the properties of the realnumber system and the order of operations havebeen applied correctly at each step.

PE/TE: 249 (Exs. 39-40), 715-719CSKCB: P61, S17 (Exs. 24, 25),S72 (Ex. 15), T16, T23-T25

CASRP: 78-79, 101-103

25.3 Given a specific algebraic statement involvinglinear, quadratic, or absolute value expressionsor equations or inequalities, students determinewhether the statement is true sometimes,always, or never.

PE/TE: 39 (Ex. 45), 93 (Ex. 6), 296 (Ex. 46),393 (Exs. 17-20), 467 (Exs. 59-66), 716-719CASRP: 80-81, 101-103

Tests: 4 (Exs. 14, 17, 20), 6 (Exs. 17, 18, 20),8 (Exs. 17, 18, 20), 11 (Exs. 1, 8),13 (Exs. 1, 7), 19 (Exs. 1, 8),29-30 (Exs. 1, 10, 14, 17, 21),33 (Exs. 1, 3), 35 (Exs. 1, 3),37 (Exs. 10-11), 39 (Exs. 5, 10),57 (Ex. 7), 108 (Ex. 1), 110 (Ex. 1),112 (Ex. 4), 114 (Ex. 4), 118 (Ex. 21)

CA 2415/2007

2007CC2

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