McDougal Littell California · PDF fileCalifornia Math: Course 1 Course 2 Algebra 1. ... for...

CaliforniaMath Content StandardsGrades 6–8

correlated to the

McDougal LittellCalifornia Math:Course 1Course 2Algebra 1

McDougal Littell California Math

Course 1

Publisher: McDougal Littell, Inc.Program Title: McDougal Littell California Math Course 1, Course 2, and Algebra 1Components: Pupil Edition (PE), Teacher’s Edition (TE), California Standards Review and Practice (CASRP)Grade Level(s): 6–8

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

Grade 6 - Mathematics

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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: pp. 167-172 (See Example 2 andrelated exercises), 255-259, 274-280, 325-330, 331-335See all references for NS 1.1-NS 1.4 below.

PE/TE: pp. 58-60, 185-186, 290-292, 339-342

CASRP: pp. 2-10See 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: pp. 27-34, 35-39, 40-46, 62-65, 167-172 (See Example 2 and related exercises)

PE/TE: pp. 53, 54, 58-60, 61, 179, 180, 185-186, 187CASRP: pp. 2-3, 114, 117-118

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: pp. 255-259, 260-264, 489-494, 495-499

PE/TE: pp. 273, 288, 290-291, 293

CASRP: pp. 4-5, 126, 130-131

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: pp. 265-271, 274-280, 281-286, 294-297, 306-311, 495-499

PE/TE: pp. 273 287, 288, 291-292, 293, 500,501, 506, 507CASRP: pp. 6-8, 127, 130-131

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

PE/TE: pp. 301-304, 305-311, 312-317, 319-324, 325-330, 331-335, 344-347

PE/TE: pp. 318, 336, 337, 339-342, 343CASRP: pp. 9-10, 128, 130-131

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

PE/TE: pp. 81-85, 87-93, 94-100, 101-106,107-113, 134-140, 141-147, 148-152, 154-158

See all references for NS 2.1-NS 2.4 below.

PE/TE: pp. 117-120, 182-186

CASRP: pp. 11-21See all references for NS 2.1-NS 2.4 below.

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: pp. 69-73, 74-80, 81-85, 87-93, 94-100, 122-125

PE/TE: pp. 86, 114, 115, 117-119, 121

CASRP: pp. 11-13, 118-120, 122, 124-125



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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: pp. 87-93, 94-100, 122-125 PE/TE: 114, 115, 119, 121

CASRP: pp. 14-15, 122, 124-125

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

PE/TE: pp. 134-140, 141-147, 148-153, 154-158, 160-166, 167-172, 173-178, 188-191

PE/TE: pp. 159, 179, 180, 182-186, 187

CASRP: pp. 16-18, 117, 119-121, 124-125

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: pp. 10-14, 15-20, 21-25, 27-34, 35-39, 62-65, 74-80, 81-85

PE/TE: pp. 26, 53, 54, 57-59, 61, 86, 115,117-118, 121CASRP: pp. 19-21, 115, 118-120, 122, 124-125



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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: pp. 197-201, 202-206, 225-232, 233-239, 630-634, 636-640, 643-647,(See Example 2 and related exercises)

See all references for AF 1.1-AF 1.4 below.

PE/TE: pp. 243-246CASRP: pp. 22-28


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

PE/TE: 219-224, 225-232, 233-239, 248-251 PE/TE: pp. 122, 240, 241, 245-246, 247

CASRP: pp. 22-23, 133, 135-136

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

PE/TE: pp. 70-71 (See Example 2 andrelated exercises), 197-201, 202-206, 208-210 (See Example 4 and related exercises),212-217, 248-251, 630-634 (See Examples1-2 and related exercises)

PE/TE: pp. 218, 241, 243-245, 247

CASRP: pp. 24-25, 132, 135-136

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

PE/TE: pp. 160-166, 167-172 (See Examples3-5 and related exercises), 173-178, 188-193, 197-200, 248-251

PE/TE: pp. 179, 180, 185-186, 187, 218CASRP: pp. 26-27, 123-125

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

PE/TE: pp. 160-166, 169-172 (See Examples4-5 and related exercises), 173-178, 197-200

PE/TE: pp. 179, 180, 185, 187

CASRP: pp. 28, 123-125

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

PE/TE: pp. 260-264, 266-272, 274-279, 515-519, 520-526, 527-531, 642-647


PE/TE: pp. 290-292

CASRP: pp. 29-35See all references for AF 2.1-AF 2.3 below.

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

PE/TE: pp. 214-217 (See Examples 3-4 andrelated exercises), 515-519, 520-526, 527-531

PE/TE: pp. 218 (Exercise 4), 532, 561, 563-564, 567

CASRP: pp. 29-31, 139-141

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

PE/TE: pp. 260-264, 266-272, 274-280, 642-647

PE/TE: pp. 273, 288, 291-292, 293, 648, 650,651CASRP: pp. 32-33, 129-131

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

PE/TE: pp. 211-218, 221-224 (See Example5 and related exercises), 236-239 (SeeExample 4 and related exercises), 260-264,266-272, 274-279, 643-647 (See Example 2and related exercises)

PE/TE: pp. 273, 288, 291, 293, 648, 649, 654CASRP: pp. 34-35, 129-131



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3.0 Students investigate geometric patterns anddescribe them algebraically:

PE/TE: pp. 539-546, 547-554, 580-587, 588-593, 595-600, 631-635 (See Example 4 andrelated exercises)


PE/TE: pp. 563-566, 610-612

CASRP: pp. 36-39See all references for AF 3.1-AF 3.2 below.

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

PE/TE: pp. 212-217, 220-224 (See Example4 and related exercises), 533-538, 539-546,549-553, 555-559, 568-571, 581-587, 589-593, 596-600, 601-605, 614-617

PE/TE: pp. 218, 241, 245, 247, 560, 561, 565-566, 567, 594, 607, 608, 611-612, 613CASRP: pp. 36-37, 134-136

3.2 Express in symbolic form simple relationshipsarising from geometry.

PE/TE: pp. 211-217, 533-538, 539-546, 549-553, 555-559,

568-571, 581-587, 588-593,595-600, 601-606, 614-617

PE/TE: pp. 218, 241, 245, 247, 560, 561, 565-566, 567, 594, 607, 608, 611-612, 613

CASRP: pp. 38-39, 134-136



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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: pp. 473-479, 482-487, 533-538, 539-546, 547-554, 580-587, 588-593, 595-600See all references for MG 1.1-MG 1.3 below.

PE/TE: pp. 563-566, 610-612CASRP: pp. 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: pp. 547-554, 555-559, 568-571 PE/TE: pp. 560, 561, 566, 567

CASRP: pp. 40-41,137, 140-141

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

PE/TE: pp. 547-554, 555-559, 568-571, 588-593, 601-605, 614-617

PE/TE: pp. 560, 561, 566, 567, 594, 607, 608,611-612, 613

CASRP: pp. 42-43, 137, 140-141

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: pp. 595-600, 601-605, 608-609, 614-617

PE/TE: pp. 607, 608, 612, 613

CASRP: pp. 44-45, 138, 140-141

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

PE/TE: pp. 463-467, 468-472, 473-479, 480,482-488, 489-494See all references for MG 2.1-MG 2.3 below.

PE/TE: pp. 503-506

CASRP: pp. 46-52

See all references for MG 2.1-MG 2.3 below.

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

PE/TE: pp. 463-467, 468-472, 508-511 PE/TE: pp. 481, 501, 503-504, 507

CASRP: pp. 46-47, 142, 144-145

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: pp. 463-467, 468-472, 473-479,

508-511

PE/TE: pp. 481, 501, 503-505, 507

CASRP: pp. 48-49, 142, 144-145

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: pp. 474-480, 482-488 PE/TE: pp. 481, 500, 501, 505, 507CASRP: pp. 50-52, 143-145



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STATISTICS, DATA ANALYSIS, ANDPROBABILITY

1.0 Students compute and analyze statisticalmeasurements for data sets:

PE/TE: pp. 364-370, 371-377

See all references for SDAP 1.1-SDAP 1.4below.

PE/TE: pp. 403-406

CASRP: pp. 53-60


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

PE/TE: pp. 156 (See Example 3 and relatedexercises), 364-369, 371-377, 378, 408-411

PE/TE: pp. 378, 401, 404-405, 407

CASRP: pp. 53-54, 146, 148-149

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

PE/TE: pp. 365-369 (See Example 2 andrelated exercises)

PE/TE: pp. 378, 402, 404, 407, 411CASRP: pp. 55-56, 147-149

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

PE/TE: pp. 372-377, 408-411 PE/TE: pp. 378, 402, 404-405, 407

CASRP: pp. 57-58, 147-149

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

PE/TE: pp. 365-370 (See Examples 3-4 andrelated exercises), 410

PE/TE: pp. 401, 404, 407

CASRP: pp. 59-60, 146, 148-149

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

PE/TE: pp. 353-358, 359-363, 392-398


PE/TE: pp. 403-406

CASRP: pp. 61-71


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: pp. 353-358, 403-407 PE/TE: pp. 401, 403-404, 407, 410

CASRP: pp. 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: pp. 353-358, 360-363 (See Examples3-4 and related exercises)

PE/TE: pp. 378, 401, 403-404, 407CASRP: pp. 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: pp. 359-363, 381-384 (See Example3 and related exercises), 387-391 (SeeExample 1 and related exercises), 392-398,408-411

PE/TE: pp. 378, 400, 401, 403-404, 406

CASRP: pp. 65-67, 151, 153-154



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

PE/TE: pp. 359-363, 366-369 (See Example4 and related exercises)

PE/TE: pp. 378, 401, 403-404, 407

CASRP: pp. 68-69, 152-154

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

PE/TE: pp. 359-363, 365-370 (See Examples3-4 and related exercises), 381-384 (SeeExample 3 and related exercises), 387-391,393-400 (See Examples 2 and 3 and relatedexercises), 408-411

PE/TE: pp. 378, 400, 401, 403-406, 407

CASRP: pp. 70-71, 152-154

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

PE/TE: pp. 415-420, 421-426, 434-440, 441-446See all references for SDAP 3.1-SDAP 3.5below.

PE/TE: pp. 450-456

CASRP: pp. 72-81


3.1 Represent all possible outcomes for compoundevents in an organized way (e.g., tables, grids,tree diagrams) and express the theoreticalprobability of each outcome.

PE/TE: pp. 421, 434-440, 441-446 PE/TE: pp. 447, 448, 452, 453, 456-457

CASRP: pp. 72-73, 155, 158-159

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

PE/TE: pp. 420-426, 433, 450-453, 454-457 PE/TE: pp. 433, 439, 448-449, 451, 453

CASRP: pp. 74-75, 156, 158-159

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: pp. 415-420, 421-426, 427-432, 434-440, 441-446, 454-457

PE/TE: pp. 433, 447, 448, 450-452, 453CASRP: pp. 76-77, 156, 158-159

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: pp. 427-432, 441-446 PE/TE: pp. 433, 447, 448, 451-452, 453

CASRP: pp. 78-79, 156, 158-159

3.5 Understand the difference between independentand dependent events.

PE/TE: pp. 441-446 PE/TE: pp. 447, 448, 452, 453

CASRP: pp. 80-81, 157-159



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MATHEMATICAL REASONING

1.0 Students make decisions about how toapproach problems:

Occurs throughout. Examples:(Gr. 6, NS 1.1) PE/TE, pp. 47-52;

(Gr. 6, NS 1.1) PE/TE, pp. 56-61;(Gr. 6, NS 2.3) PE/TE, p. 148;

(Gr. 6, AF 1.2) PE/TE, p. 248;(Gr. 6, NS 1.3) TE, p. 287;

(Gr. 6, NS 1.4) PE/TE, p. 330;(Gr. 6, NS 1.3) TE, p. 510;

(Gr. 6, MG 1.1) TE, p. 547See all references for MR 1.1-MR 1.3 below.

Occurs throughout. Examples:(Gr. 6, NS 2.3) PE/TE, p. 152 (Ex. 61);

(Gr. 6, MG 2.2) PE/TE, p. 466 (Ex. 38);(Gr. 6, AF 3.2) PE/TE, p. 584 (Ex. 18)

(Gr. 6, NS 2.3; Gr. 6, AF 1.2; Gr. 6, AF 3.1;Gr. 6, MG 1.2) CASRP, pp. 82-87See all references for MR 1.1-MR 1.3 below.

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

Occurs throughout. Examples:(Gr. 6, NS 2.1) TE, p. 86;

(Gr. 6, AF 1.1) PE/TE, p. 122 ;(Gr. 6, NS 2.3), PE/TE, p. 142;


(Gr. 6, NS 1.1) TE, p. 179;(Gr. 6, AF 3.1), TE, p. 218;(Gr. 6, NS 1.3) PE/TE, p. 267;


(Gr. 6, NS 1.3) TE, p. 287;(Gr. 6, NS 1.4) TE, p. 318;

(Gr. 6, SDAP 3.5), TE, p. 447;(Gr. 6, SDAP 3.5) TE, p. 457;

(Gr. 6, MG 2.1) TE, p. 481;(Gr. 6, NS 1.3) TE, p. 500;

(Gr. 6, MG 2.1) TE, p. 511;(Gr. 6, MG 1.1) PE/TE, p. 547;(Gr. 5, AF 1.5) PE/TE, p. 648


(Gr. 6, NS 2.3) PE/TE, p. 152 (Ex. 61);(Gr. 6, NS 1.4) PE/TE, p. 329 (Ex. 29);

(Gr. 6, SDAP 1.1) PE/TE,p. 367(Exs. 11-12);(Gr. 6, SDAP 1.1) PE/TE,p. 369 (Ex. 39);

(Gr. 6, MG 2.2) PE/TE, p. 466 (Ex. 38);(Gr. 6, AF 3.1) PE/TE, p. 537 (Ex. 18);

(Gr. 6, AF 3.2) PE/TE, p. 538 (Ex. 30);(Gr. 6, AF 3.2) PE/TE, p. 592 (Ex. 16);

(Gr. 6, MG 1.3) PE/TE, p. 605 (Ex. 29);(Gr. 5, AF 1.3) PE/TE, p. 632 (Ex. 21)

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



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

Occurs throughout. Examples:

(Gr. 6, NS 2.4) TE, p. 65;(Gr. 6, NS 2.2) TE, p. 114;

(Gr. 6, NS 2.3) PE/TE, p. 148;(Gr. 6, NS 2.3) TE, p. 190;(Gr. 6, AF 1.1) TE, p. 240;

(Gr. 6, AF 1.3) TE, p. 251;(Gr. 6, AF 2.0) TE, p. 287;

(Gr. 6, AF 2.2) TE, p. 296;(Gr. 6, SDAP 1.2) PE/TE, p. 378;

(Gr. 6, NS 1.2) PE/TE, p. 489;(Gr. 6, MG 2.1) PE/TE, p. 509;

(Gr. 6, AF 3.1) TE, p. 594;(Gr. 6, AF 3.2) PE/TE, p. 606;

(Gr. 5, MG 2.3) TE, p. 617



(Gr. 6, NS 2.3) PE/TE, p. 147 (Ex. 48);(Gr. 6, NS 1.3) PE/TE, p. 279 (Ex. 56);(Gr. 6, NS 1.4) PE/TE, p. 304 (Ex. 65);

(Gr. 6, SDAP 1.3) PE/TE, p. 375 (Ex. 13);(Gr. 6, SDAP 3.4) PE/TE, p. 431 (Ex. 21);

(Gr. 6, SDAP 3.4) PE/TE, p. 432 (Ex. 42);(Gr. 6, AF 3.2) PE/TE, p. 592 (Ex. 16)

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

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


(Gr. 6, NS 2.1) TE, p. 86;(Gr. 6, NS 2.3) TE, p. 159;

(Gr. 6, AF 2.3) PE/TE, p. 214;(Gr. 6, AF 1.2) PE/TE, p. 248;

(Gr. 6, NS 1.2) TE, p. 297;(Gr. 6, NS 1.4) PE/TE, p. 330;

(Gr. 6, NS 1.4) TE, p. 347;(Gr. 6, SDAP 3.4) PE/TE, p. 442;

(Gr. 6, MG 2.2) TE, p. 481;(Gr. 6, NS 1.3) TE, p. 510;(Gr. 6, MG 2.2) TE, p. 511;


(Gr. 6, MG 1.2) PE/TE, p. 588;(Gr. 5, AF 1.4) PE/TE, p. 659


(Gr. 6, NS 1.1) PE/TE, p. 33 (Ex. 46);(Gr. 6, AF 1.1) PE/TE, p. 231 (Ex. 66);


(Gr. 6, SDAP 3.5) PE/TE, p. 466 (Ex. 38);(Gr. 6, AF 3.2) PE/TE, p. 584 (Ex. 18);

(Gr. 6, AF 3.2) PE/TE, p. 593 (Ex. 26);(Gr. 7 AF 3.3) PE/TE, p. 639 (Ex. 34)

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



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


(Gr. 6, NS 1.1) PE/TE, pp. 47-52;(Gr. 6, NS 1.1) PE/TE, pp. 56-61;

(Gr. 6, NS 2.2) PE/TE, p. 94;(Gr. 6, NS 2.3) PE/TE, p. 153;(Gr. 6, SDAP 2.5) TE, p. 400;

(Gr. 6, SDAP 1.2) PE/TE, p. 409;(Gr. 6, MG 2.2) PE/TE, p. 483;

(Gr. 6, AF 3.2) TE, p. 617See all references for MR 2.1-MR 2.7 below.



(Gr. 6, SDAP 1.1) PE/TE, p. 369 (Ex. 39)(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

See all references for MR 2.1-MR 2.7 below.

2.1 Use estimation to verify the reasonableness ofcalculated results.



(Gr. 6, AF 1.2) PE/TE, p. 198;(Gr. 6, NS 1.3) PE/TE, p. 294;(Gr. 6, NS 1.4) PE/TE, p. 307;



(Gr. 6, AF 2.1) TE, p. 532;(Gr. 6, MG 1.1) PE/TE, p. 554;

(Gr. 6, MG 1.3) PE/TE, p. 601;(Gr. 6, MG 1.3) TE, p. 616;

(Gr. 7, AF 3.3) PE/TE, p. 656



(Gr. 6, NS 1.2) PE/TE, p. 259 (Ex. 54);(Gr. 6, NS 1.4) PE/TE, p. 334 (Ex. 29);(Gr. 6, SDAP 2.3) PE/TE, p. 396 (Exs. 13-18);


(Gr. 6, AF 2.1) PE/TE, p. 524 (Ex. 46);(Gr. 6, MG 1.1) PE/TE, p. 553 (Ex. 28)

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



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


(Gr. 6, NS 1.1) TE, p. 53;(Gr. 6, NS 1.1) TE, p. 65;

(Gr. 6, NS 2.3) PE/TE, p. 134;(Gr. 6, AF 1.2) TE, p. 251;(Gr. 6, NS 1.4) TE, p. 336;

(Gr. 6, NS 1.4) PE/TE, p. 344;(Gr. 6, SDAP 3.4) TE, p. 433;


(Gr. 6, NS 1.2) TE, p. 500;(Gr. 6, AF 3.2) TE, p. 594;

(Gr. 6, MG 1.3) PE/TE, p. 602;(Gr. 6, AF 3.2) TE, p. 607;

(Gr. 6, AF 3.2) TE, p. 617;(Gr. 5, AF 1.4) TE, p. 658


(Gr. 6, NS 2.4) PE/TE, p. 12 (Exs. 31-34);(Gr. 6, NS 2.1) PE/TE, p. 73 (Ex. 48);

(Gr. 6, NS 1.3) PE/TE, p. 279 (Ex. 53);(Gr. 6, SDAP 3.4) PE/TE, p. 432 (Ex. 41);(Gr. 6, MG 2.2) PE/TE, p. 466 (Ex. 38);

(Gr. 6, MG 2.3) PE/TE, p. 487 (Ex. 43);(Gr. 6, AF 3.1) PE/TE, p. 546 (Ex. 35);

(Gr. 6, MG 1.3) PE/TE, p. 600 (Ex. 27);(Gr. 6, MG 1.3) PE/TE, p. 600 (Ex. 30)

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

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

Occurs throughout. Examples:(Gr. 6, NS 1.1) PE/TE, p. 62;

(Gr. 5, NS 2.1) TE, p. 124;(Gr. 6, SDAP 1.4) PE/TE, p. 370;

(Gr. 6, SDAP 2.3) PE/TE, p. 393;(Gr. 6, SDAP 2.5) TE, p. 400;

(Gr. 6, SDAP 2.5) TE, p. 410;(Gr. 6, AF 2.1) PE/TE, p. 571;

(Gr. 5, MG 2.3) TE, p. 617;(Gr. 5, AF 1.4)(Gr. 7, AF 3.3) PE/TE, p. 637;

(Gr. 7, AF 3.3) PE/TE, p. 641;(Gr. 5, AF 1.4) TE, p. 658


(Gr. 6, NS 1.3) PE/TE, p. 285 (Ex. 38);(Gr. 6, NS 1.4) PE/TE, p. 309 (Exs. 20-23);


(Gr. 6, AF 2.1) PE/TE, p. 525 (Ex. 57);(Gr. 6, AF 2.1) PE/TE, p. 531 (Ex. 45);

(Gr. 6, MG 1.2) PE/TE, p. 558 (Ex. 32);(Gr. 5, AF 1.4) PE/TE, p. 627 (Ex. 33)(Gr. 6, AF 2.0) CASRP, pp. 92-93



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


(Gr. 6, NS 1.1) PE/TE, p. 48;(Gr. 6, NS 2.2) PE/TE, p. 94;

(Gr. 6, NS 2.3) PE/TE, p. 153;(Gr. 6, AF 1.1) TE, p. 250;(Gr. 6, NS 1.4) TE, p. 347;

(Gr. 6, SDAP 2.3) TE, p. 400;(Gr. 6, SDAP 2.3) TE, p. 411;

(Gr. 6, SDAP 3.2) PE/TE, p. 421);(Gr. 6, SDAP 3.2) TE, p. 433;


(Gr. 6, SDAP 3.4) PE/TE, p. 456;(Gr. 6, AF 3.2) PE/TE, p. 587;

(Gr. 6, AF 3.2) PE/TE, p. 590;(Gr. 6, MG 1.3) TE, p. 607;(Gr. 7, AF 3.3) PE/TE, p. 657



(Gr. 6, SDAP 1.4) PE/TE, p. 377 (Ex. 23);(Gr. 6, SDAP 3.1) PE/TE, p. 438 (Ex. 26);(Gr. 6, MG 2.2) PE/TE, p. 465 (Exs. 22-23);

(Gr. 6, MG 2.3) PE/TE, p. 479 (Ex. 47);(Gr. 6, MG 2.3) PE/TE, p. 486 (Exs. 35-38);

(Gr. 6, NS 1.3) PE/TE, p. 498 (Ex. 20);(Gr. 6, MG 1.1) PE/TE, p. 546 (Ex. 35)

(Gr. 6, NS 2.2) CASRP, pp. 94-95

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.


(Gr. 6, AF 1.3) PE/TE, p. 175;

(Gr. 6, AF 1.3) TE, p. 191;(Gr. 6, NS 1.3) TE, p. 273;(Gr. 6, SDAP 2.5) TE, p. 400;


(Gr. 6, MG 1.3) TE, p. 607


(Gr. 6, NS 2.4) PE/TE, p. 25 (Ex. 41);

(Gr. 6, AF 1.4) PE/TE, p. 165 (Exs. 65-68);(Gr. 6, AF 1.3) PE/TE, p. 172 (Ex. 51);(Gr. 6, AF 1.2) PE/TE, p. 209 (Ex. 17);


(Gr. 6, NS 1.4) PE/TE, p. 323 (Exs. 46-49);(Gr. 6, SDAP 2.3) PE/TE, p. 391 (Ex. 22);

(Gr. 6, AF 3.2) PE/TE, p. 585 (Ex. 33)(Gr. 6, AF 3.2; Gr. 6, MG 1.1) CASRP,pp. 96-97



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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:(Gr. 4 NS 1.5) PE/TE, p. 6;




(Gr. 6, MG 1.2) PE/TE, p. 571



(Gr. 6, NS 1.4) PE/TE, p. 328 (Exs. 20-21);(Gr. 6, SDAP 2.1) PE/TE, p. 356 (Exs. 3-6);(Gr. 6, SDAP 3.2) PE/TE, p. 426 (Ex. 26);

(Gr. 6, NS 1.3) PE/TE, p. 499 (Ex. 21);(Gr. 6, MG 1.2) PE/TE, p. 553 (Ex. 26)

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

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


(Gr. 6, NS 2.1) PE/TE, p. 96;

(Gr. 6, NS 2.3) PE/TE, p. 144;(Gr. 6, AF 1.3) TE, p. 179;

(Gr. 6, AF 1.1) TE, p. 240;(Gr. 6, SDAP 2.5) PE/TE, p. 408;(Gr. 6, SDAP 3.5) TE, p. 447;

(Gr. 6, AF 2.1) PE/TE, p. 526


(Gr. 6, AF 3.2) PE/TE, p. 58 (Ex. 10);

(Gr. 6, AF 1.2) PE/TE, p. 206 (Ex. 47);(Gr. 6, NS 1.3) PE/TE, p. 283 (Exs. 11-14);

(Gr. 6, NS 1.4) PE/TE, p. 317 (Ex. 91);(Gr. 6, SDAP 1.1) PE/TE, p. 369 (Ex. 39);(Gr. 6, SDAP 3.2) PE/TE, p. 424 (Ex. 11);

(Gr. 6, MG 2.2) PE/TE, p. 465 (Exs. 22-23);PE/TE, p. 518 (Ex. 29);

(Gr. 6, AF 3.2) PE/TE, p. 586 (Ex. 39);(Gr. 6, AF 3.1) PE/TE, p. 592 (Exs. 13-16)

(Gr. 6, AF 2.0) CASRP, p. 100-101

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


(Gr. 6, NS 1.1) PE/TE, pp. 47-52;

(Gr. 6, NS 1.1) PE/TE, pp. 56-61;(Gr. 6, NS 2.1) TE, p. 125;(Gr. 6, AF 1.3) PE/TE, p. 249;

(Gr. 6, SDAP 2.2) TE, p. 378;(Gr. 6, MG 2.3) PE/TE, p. 480;

(Gr. 6, AF 2.1) PE/TE, p. 520;(Gr. 6, AF 3.2) PE/TE, p. 595

See all references for MR 3.1-MR 3.3 below.


(Gr. 6, AF 1.3) PE/TE, p. 172 (Exs. 55-57);

(Gr. 6, SDAP 1.4) PE/TE,p. 369 (Ex. 32);(Gr. 6, MG 2.3) PE/TE, p. 485 (Ex. 9)

(Gr. 6, NS 1.4; Gr. 6, AF 2.1; Gr. 6, SDAP 3.2)CASRP,pp. 102-107See all references for MR 3.1-MR 3.3 below.



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

Occurs throughout. Examples:(Gr. 6, NS 2.4) TE, p. 53;

(Gr. 6, NS 2.1) TE, p. 114;(Gr. 6, AF 1.3) PE/TE, p. 189;

(Gr. 6, NS 1.4) PE/TE, p. 345;(Gr. 6, SDAP 2.2) TE, p. 378;

(Gr. 6, SDAP 2.1) TE, p. 410;(Gr. 6, AF 2.1) PE/TE, p. 520;

(Gr. 6, MG 1.2) PE/TE, p. 569

Occurs throughout. Examples:(Gr. 6, AF 1.2) PE/TE, p. 205 (Exs. 29-30);



(Gr. 6, SDAP 3.3) PE/TE, p. 418 (Ex. 23);(Gr. 6, MG 2.3) PE/TE, p. 485 (Ex. 9);

(Gr. 6, MG 2.3) PE/TE, p. 478 (Exs. 39-42);(Gr. 6, MG 1.2) PE/TE, p. 494 (Ex. 29);(Gr. 6, AF 2.1) TE, p. 532 (Ex. 46);

(Gr. 5, MG 2.3) PE/TE, p. 578 (Exs. 15-18)(Gr. 6, NS 1.4) CASRP, pp. 102-103

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



(Gr. 6, AF 1.3) PE/TE, p. 249;(Gr. 6, AF 3.2) TE, p. 250;(Gr. 6, MG 2.3) PE/TE, p. 480;

(Gr. 6, AF 2.1) PE/TE, p. 517;(Gr. 6, AF 2.1) TE, p. 570;


(Gr. 7, AF 3.3) TE, p. 648;(Gr. 7, AF 3.3) PE/TE, p. 659



PE/TE, p. 177 (Ex. 52);(Gr. 6, AF 1.2) PE/TE, p. 199 (Exs. 23-24);(Gr. 6, NS 1.2) PE/TE, p. 257 (Ex. 38);


(Gr. 6, AF 2.1) PE/TE, p. 529 (Ex. 30);(Gr. 6, AF 3.2) PE/TE, p. 593 (Ex. 25)

(Gr. 6, AF 2.1) CASRP, p. 104-105



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

Occurs throughout. Examples:(Gr. 6, NS 2.4) TE, p. 26 ;


(Gr. 6, AF 1.2) TE, p. 218;(Gr. 6, NS 1.3) PE/TE, p. 295;

(Gr. 6, AF 3.2) TE, p. 560;(Gr. 6, AF 3.2) PE/TE, p. 595

Occurs throughout. Examples:(Gr. 5, NS 1.4) PE/TE, p. 9(Ex. 57);

(Gr. 6, NS 2.1) PE/TE, p. 91 (Exs. 28-30);(Gr. 6, AF 1.3) PE/TE, p. 172 (Exs. 55-57);

(Gr. 6, AF 1.1) PE/TE, p. 231 (Ex. 66);(Gr. 6, NS 1.3) PE/TE, p. 284 (Ex. 24);


(Gr. 6, SDAP 1.3) PE/TE, p. 375 (Ex. 13);(Gr. 6, SDAP 3.4) PE/TE, p. 431 (Exs. 28-30);

(Gr. 6, MG 2.1) PE/TE, p. 466 (Exs. 29-31);(Gr. 6, AF 3.2) PE/TE, p. 585 (Ex. 31)(Gr. 6, SDAP 3.2) CASRP, pp. 106-107


Course 2



STANDARDS MAP for a Basic Grade-Level ProgramGrade 7 – Mathematics

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NUMBER SENSE

1.0 Students know the properties of, andcompute with, rational numbers expressed ina variety of forms:

PE/TE: pp. 5 (Example 2), 113-117, 137-141,142-149, 160-165, 167-171, 172-178, 201-205, 225-230 (See Example 1 and relatedexercises.)

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

PE/TE: pp. 63-65, 122-124, 182-186, 234-236CASRP: pp. 2-18


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

PE/TE: pp. 12-16, 80-84, 126-129, 133-136,156, 157-159 (Exs. 25-28, 30-36, 45), 196-200, 201-205, 238-241, 395 (Example 3),396-398 (Exs. 28-31, 42-44, 46-49)

PE/TE: pp. 29, 60, 63, 67, 96, 119, 122, 125,154, 179, 180, 182, 187 (Exs. 3-6), 211, 232,234-235, 237 (Exs. 9-14)CASRP: pp. 2-3,138-140

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

PE/TE: pp. 5-8, 18-23, 24-28, 30-35, 36-40,41-45, 68-71, 85-89, 90-95, 97-104, 105,106-112, 126-129, 137-141, 142-149, 206-210

PE/TE: pp. 29, 59, 60, 63-65, 67, 96, 118, 119,122-124, 125, 154, 180, 183, 187, 211, 232,237

CASRP: pp. 4-6, 141-142, 144-145

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

PE/TE: pp. 5 (Example 2), 8 (Exs.12-23), 79(Ex. 44), 87 (Example 4), 88 (Exs. 16-27),113-117, 137-141, 144-145 (Examples 1, 2,3), 146-147 (Exs. 3-22, 27-35, 43-46), 150-153, 155-159, 165 (Ex. 37), 168-171

PE/TE: pp. 118, 119, 125, 154, 179, 180, 184,187CASRP: pp. 7-8, 135, 139-140, 143-145

1.4 Differentiate between rational and irrationalnumbers.

PE/TE: pp. 225-230 (See Example 1 andrelated exercises.)

PE/TE: pp. 231, 232, 236, 237 (Exs. 30-33)

CASRP: pp. 9-10, 137, 139-140

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

PE/TE: pp. 113-117, 225 (Example 1), 227-229 (Exs. 3-14, 45-50, 52-60)

PE/TE: pp. 118, 119, 124, 125 (Exs. 19-22)

CASRP: pp. 11-12, 135, 139-140



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1.6 Calculate the percentage of increases anddecreases of a quantity.

PE/TE: pp. 167-171, 188-191 PE/TE: pp. 180, 185, 187 (Exs. 23-25)

CASRP: pp. 13-15,143-145

1.7 Solve problems that involve discounts, markups,commissions, and profit and compute simpleand compound interest.

PE/TE: pp. 160-165, 166, 172-178, 188-191 PE/TE: pp. 179, 180, 185-186, 187 (Exs. 28-30)CASRP: pp. 16-18, 143-145

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

PE/TE: pp. 12-16 (See Examples 2 and 3and related exercises.), 91-95, 206-210, 212-218, 386-391, 392-398


PE/TE: pp. 63, 235-236

CASRP: pp. 19-28See all references for NS2.1-NS2.5 below.

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

PE/TE: pp. 195-200, 206-210, 386 (Example1), 389-391, 393 (Example 1), 396-398

PE/TE: pp. 211, 232, 237, 427 (Exs. 3-6, 13-14)CASRP: pp. 19-20

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

PE/TE: pp. 91-95 PE/TE: pp. 96, 119, 125 (Ex. 13)

CASRP: pp. 21-22, 141, 144-145

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

PE/TE: pp. 386-391, 392-398, 428-431 PE/TE: pp. 232, 406, 422, 427

CASRP: pp. 23-24, 146, 149-150

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: pp. 212-218, 219-223, 224, 238-241 PE/TE: pp. 231, 232, 235-236, 237

CASRP: pp. 25-26, 136, 139-140

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: pp. 12-16 (See Examples 2 and 3and related exercises.), 17, 26 (Example 4),27 (Exs. 24-27)

PE/TE: pp. 29, 60, 63, 67 (Exs. 12-13)

CASRP: pp. 27-28, 136, 139-140



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ALGEBRA AND FUNCTIONS

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

PE/TE: pp. 41-45, 46-51, 247-251, 252-255,407-412See all references for AF1.1-AF1.5 below.

PE/TE: pp. 62, 65-66, 302-303, 305-306, 375-376, 426CASRP: pp. 29-40

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

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

PE/TE: pp. 247-251, 257-262 (See Example4 and related exercises.), 264 (Example 3),266-267 (Exs. 41-49), 270-275 (See Example2 and related exercises.), 282-287, 288-292(See Example 3 and related exercises.), 293-297 (See Example 3 and related exercises.),

308-311, 354-359 (See Example 3 andrelated exercises.), 360-367 (See Examples2, 4 and related exercises.), 368, 378-381

PE/TE: pp. 268, 299, 300, 302-303, 305-306,307, 369, 375-376, 377 (Exs. 23-24)CASRP: pp. 29-31, 151, 154-155

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

PE/TE: pp. 5-11 (See Examples 4-5 andrelated exercises.), 34 (Exs. 43-44), 247-251

PE/TE: pp. 29, 62, 307 (Ex. 7), 340CASRP: pp. 32-33, 147, 149-150

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

PE/TE: pp. 18-23, 31-35, 41-45, 46-51, 85-89, 91-95, 98-104, 105, 106-111, 252-255

PE/TE: pp. 59, 60, 65-66, 67, 118, 119, 268,300, 303, 307

CASRP: pp. 34-35, 147-150

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

PE/TE: pp. 5-10 (See Example 4-5 andrelated exercises.), 252-255, 256-262, 263-267, 269-275, 276, 282-287, 288-292, 293-298, 336 (text), 689-692

PE/TE: pp. 60, 67, 268, 299, 300, 302, 307

CASRP: pp. 36-37, 147, 149-151, 154-155,157, 160-161

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

PE/TE: pp. 407-412 PE/TE: pp. 421, 422, 426, 427

CASRP: pp. 38-40, 156, 160-161



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

PE/TE: pp. 195-200, 385-391, 392-398, 399-404


PE/TE: pp. 234-235, 424-425

CASRP: pp. 41-44See all references for AF2.1-AF2.2 below.

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: pp. 5-10, 31 (Example 2), 33 (Exs.25-32), 147 (Exs. 26, 38-39), 195-200, 206-210, 385-391, 392-398

PE/TE: pp. 67 (Exs. 6-8), 211, 232, 234-235,237, 406, 422, 424-425, 427

CASRP: pp. 41-42

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: pp. 399-404, 405 PE/TE: pp. 406, 422, 425, 427

CASRP: pp. 43-44, 148-150

3.0 Students graph and interpret linear and somenonlinear functions:

PE/TE: pp. 333-339, 341-347, 348-353 (SeeExample 3 and related exercises.), 413-420,589-596 (See Example 5 and relatedexercises.)


PE/TE: pp. 373-374, 426

CASRP: pp. 45-54


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

and use in solving problems.PE/TE: pp. 413-420 PE/TE: pp. 421, 422, 426, 427 (Exs. 30-32)

CASRP: pp. 45-46, 159-161

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 heightand an equilateral triangle base of varyinglengths).

PE/TE: pp. 589-596 (See Example 5 andrelated exercises.), 602 (Exs. 38-40), 610(Ex. 28)

CASRP: pp. 47-48, 159-161



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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: pp. 320-326, 327-332 (See Examples2, 4 and related exercises.), 333-339, 341-347, 378-381

PE/TE: pp. 340, 370, 373-374, 377

CASRP: pp. 49-51, 158, 160-161

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 understandthat the slope of the line equals the quantities.

PE/TE: pp. 348-353 (See Example 3 andrelated exercises.)

PE/TE: p. 377

CASRP: pp. 52-54, 157, 160-161

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

PE/TE: pp. 258 (Example 2), 269-275, 290(Exs. 11-26), 293-298, 348-353


PE/TE: pp. 304, 306, 372CASRP: pp. 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: pp. 269-275, 276, 293-298 PE/TE: pp. 299, 300, 304, 306, 307 (Exs. 14,27-28), 308-311CASRP: pp. 55-57, 152, 154-155

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

PE/TE: pp. 52-54, 57 (Exs. 19, 24), 263-267,274 (Exs. 35, 37), 281 (Ex. 33), 292 (Ex. 42),315-319, 339 (Exs. 35-36), 348-353

PE/TE: pp. 268, 304, 340, 369, 372, 375, 377(Ex. 23)CASRP: pp. 58-59, 154-155



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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: pp. 437-442, 443-448, 449-453, 540-545See all references for MG1.1-MG1.3 below.

PE/TE: pp. 502, 503, 552CASRP: pp. 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: pp. 136 (Ex. 41), 138 (Example 3),140 (Exs. 30, 33), 147-148 (Exs. 47, 53, 55-56), 437-442, 449-453, 484 (Exs. 39-41),508-511

PE/TE: pp. 462, 500, 502, 507

CASRP: pp. 60-61, 162, 166-167

1.2 Construct and read drawings and models madeto scale.

PE/TE: pp. 540-545, 546 PE/TE: pp. 547, 548, 552, 553 (Ex. 16)

CASRP: pp. 62-63, 163, 166-167

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: pp. 443-448, 449-453 PE/TE: pp. 462, 503, 507

CASRP: pp. 64-65, 164, 166-167

2.0 Students compute the perimeter, area, andvolume of common geometric objects anduse the results to find measures of lesscommon objects. They know how perimeter,area, and volume are affected by changes ofscale:

PE/TE: pp. 489-495 (See Example 6 andrelated exercises.), 573-579, 580-586, 588-596, 598-603 (See Example 2 and relatedexercises.), 604-611See all references for MG2.1-MG2.4 below.

PE/TE: pp. 505-506, 616-618

CASRP: pp. 66-75See all references for MG2.1-MG2.4 below.

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

PE/TE: pp. 48 (Example 1), 51 (Ex.38), 463-467, 475 (Ex. 30), 477-485 (See Activity,Examples 3,4, 5 and related exercises.), 489-495, 498, 508-511, 573-579, 580-586, 588-596, 598-603, 620-623, 742

PE/TE: pp. 499, 500, 505-506, 507, 587, 612,613, 616-618, 619CASRP: pp. 66-68, 165-167, 174, 177-178

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

PE/TE: pp. 478-485, 488, 489-495 (SeeExample 6 and related exercises.), 580-586(See Example 3 and related exercises.)

PE/TE: pp. 499, 507 (Exs. 18, 20), 613, 619

CASRP: pp. 69-70, 165-167, 175, 177-178



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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: pp. 574 (Example 2), 577 (Exs. 6, 9-13), 584 (Ex. 13-14), 588, 604-611

PE/TE: pp. 612, 613, 618, 619 (Ex. 14)

CASRP: pp. 71-73, 174, 177-178

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 ft.2] = [144 in.2], 1 cubic inch is approximately16.38 cubic centimeters or [1 in.3] = [16.38 cm3]).

PE/TE: pp. 484 (Exs. 39-41), 576 (Example4), 593 (Exs. 21-23), 598-603 (See Example2 and related exercises.)

PE/TE: p. 57 (Ex. 17, 19)CASRP: pp. 74-75, 162, 166-167

3.0 Students know the Pythagorean theorem anddeepen their understanding of plane andsolid geometric shapes by constructingfigures that meet given conditions and byidentifying attributes of figures:

PE/TE: pp. 454-461, 463-469, 470-476, 478-487, 489-497, 515-521, 522-527 (SeeExercises 2,3 and Activity and relatedexercises.), 528-533, 561-565, 566-571 (SeeExamples 2,3 and related exercises.), 573-579, 580-586See all references for MG3.1-MG3.6 below.

PE/TE: pp. 504, 505, 551-552, 615-616

CASRP: pp. 76-90See all references for MG3.1-MG3.6 below.

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: pp. 454-461, 463-469, 478-487, 489-497

PE/TE: pp. 462, 500, 504

CASRP: pp. 76-78, 168, 172-173

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

PE/TE: pp. 522-527 (See Exercises 2,3 andActivity and related exercises.), 528-533,535-539, 554-557

PE/TE: pp. 534, 547, 548, 551-552, 553

CASRP: pp. 79-80, 171, 172-173

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 thelengths of other line segments and, in somesituations, empirically verify the Pythagoreantheorem by direct measurement.

PE/TE: pp. 470-476 PE/TE: pp. 499, 505, 507

CASRP: pp. 81-82, 171, 172-173



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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 ofthe two figures.

PE/TE: pp. 515-521, 554-557 PE/TE: pp. 534, 548, 550, 553

CASRP: pp. 83-85, 170, 172-173

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

PE/TE: pp. 566-571 (See Example 4 andrelated exercises.), 572, 573-579, 580-586,597

PE/TE: pp

614, 623CASRP: pp. 86-87, 175, 177-178

3.6 Identify elements of three-dimensional geometricobjects (e.g., diagonals of rectangular solids)and describe how two or more objects arerelated in space (e.g., skew lines, the possibleways three planes might intersect).

PE/TE: pp. 561-565, 566-571 (See Examples2,3 and related exercises.), 620-623

PE/TE: pp. 587, 615-616, 619CASRP: pp. 88-90, 176-178



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STATISTICS, DATA ANALYSIS, ANDPROBABILITY

1.0 Students collect, organize, and representdata sets that have one or more variablesand identify relationships among variableswithin a data set by hand and through theuse of an electronic spreadsheet softwareprogram:

PE/TE: pp. 650-654, 655-659, 660-667 (SeeExamples 1-2 and related exercises.)See all references for SDAP1.1-SDAP1.3below.

PE/TE: pp. 675-678

CASRP: pp. 91-97

See all references for SDAP1.1-SDAP1.3below.

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

PE/TE: pp. 636-642, 643-648, 650-654, 655-659, 660-669, 680-683

PE/TE: pp. 649, 671, 672, 675-677, 679 (Exs.3-4, 10)

CASRP: pp. 91-93, 179, 182-183

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

PE/TE: pp. 407 (Example 1), 410 (Exs. 3-8),660-667 (See Examples 1-2 and relatedexercises.), 670

PE/TE: pp. 671, 672, 678, 679 (Ex. 11)

CASRP: pp. 94-95, 180, 182-183

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

PE/TE: pp. 632 (Example 2), 633-634 (Exs.5-9, 14-16, 24), 655-659 (See Example 1 andrelated exercises.)

PE/TE: pp. 671, 672, 679 (Ex. 9)CASRP: pp. 96-97, 181-183



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MATHEMATICAL REASONING

1.0 Students make decisions about how toapproach problems:

Occurs throughout. Examples:(Gr. 7, NS 1.2) PE/TE, p. 24;

(Gr. 7, NS 1.2) PE/TE, p. 30;(Gr. 7, NS 1.0) PE/TE, p. 52-58;

(Gr. 7, AF 1.3) TE, p. 59;(Gr. 7, NS 1.2) PE/TE, p. 127;

(Gr. 7, NS 1.7) PE/TE, p. 166;(Gr. 7, NS 1.2) TE, p. 191

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


(Gr. 7, AF1.3) PE/TE, p. 109 (Ex. 53);(Gr. 7, NS 2.4) PE/TE, p. 218 (Ex. 60)

(Gr. 7, NS 1.2; Gr. 7, MG 1.1; Gr. 7, MG 2.1)CASRP, pp. 98-104See all references for MR1.1-MR1.3 below.

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




(Gr. 7, NS 1.1) TE, p. 190;(Gr. 7 NS 2.1) PE/TE, p. 195;

(Gr. 7, NS 1.1) PE/TE, p. 196;(Gr. 7, NS 1.1) TE, p. 241;(Gr. 7, AF 1.1) PE/TE, p. 268;


(Gr. 7, MG 1.1) TE, p. 462;(Gr. 7, MG 1.3) TE, p. 510;

(Gr. 7, MG 3.4) TE, p. 534




(Gr. 7, MG 2.1) PE/TE, p. 585 (Ex. 29)(Gr. 7, NS 1.2) CASRP, pp. 98-100



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



(Gr. 7, NS 1.2) TE, p. 118;(Gr. 7, NS 2.1) TE, p. 211;(Gr. 7, AF 3.3) PE/TE, p. 341;

(Gr. 7, MG 3.3) PE/TE, p. 470;(Gr. 7, MG 2.3) TE, p. 612



(Gr. 7, NS1.2) PE/TE, p. 39 (Ex. 50);(Gr. 7, AF 1.3) PE/TE, p. 45 (Ex. 48);(Gr. 6, NS 2.4) PE/TE, p. 79 (Ex. 49);

(Gr. 7, AF1.3) PE/TE, p. 109 (Ex. 53)(Gr. 7, MG 1.1) CASRP, pp. 101-102

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



(Gr. 7, NS 1.2) TE, p. 191;(Gr. 7, AF 2.1) TE, p. 406;

(Gr. 7, MG 2.1) PE/TE, p. 477;(Gr. 7, MG 2.1) TE, p. 511;(Gr. 7, MG 1.2) PE/TE, p. 546;

(Gr. 7, MG 2.2) PE/TE, p. 583;(Gr. 7, MG 2.1) TE, p. 622



(Gr. 7, NS 1.2) PE/TE, p. 56 (Ex. 11);(Gr. 7, MG 2.2) PE/TE, p. 584 (Exs. 13-15)

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

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


(Gr. 7, AF 4.2) PE/TE, pp. 52-58;(Gr. 7, NS 1.2) PE/TE, p. 59;

(Gr. 7, AF 4.2) PE/TE, pp. 66-67;(Gr. 7, NS 1.2) PE/TE, p. 92;

(Gr. 7, NS 1.1) PE/TE, p. 126;(Gr. 7, NS 1.1) TE, p. 129;(Gr. 7, AF 3.3) PE/TE, p. 341;

(Gr. 7, NS 2.3) TE, p. 406;(Gr. 7, MG 2.2) PE/TE, p. 488




(Gr. 7, MG 1.3) PE/TE, p. 448 (Ex. 43);(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, SDAP 1.1;Gr. 7, SDAP 1.2) CASRP, pp. 105-121




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2.1 Use estimation to verify the reasonableness ofcalculated results.



(Gr. 7, NS 1.2) PE/TE, p. 137 (Example 1);(Gr. 7, NS 1.2) PE/TE, p. 144 (Example 1);(Gr. 7, NS 1.2) PE/TE, p. 145 (Example 2);


(Gr. 7, MG 2.1; Gr. 7, MG 3.1) PE/TE, p. 490;(Gr. 7, MG 1.1) PE/TE p. 509;

(Gr. 7, MG 1.2) TE, p. 547;(Gr. 7, MG 2.1) PE/TE, p. 600;

(Gr. 7, MG 2.1) PE/TE, p. 620



(Gr. 7, NS 1.2) PE/TE, p. 147 (Ex. 47);(Gr. 7, NS 1.2) PE/TE, p. 148 (Ex. 51);(Gr. 7, MG 1.3) PE/TE, p. 452 (Ex. 33)

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

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

Occurs throughout. Examples.

(Gr. 7, NS 1.5) TE, p. 118;(Gr. 7, AF 3.3) TE, p. 381;

(Gr. 7, MG 2.2) PE/TE p. 488;(Gr. 7, MG 2.1) TE, p. 499;

(Gr. 7, MG 1.1; Gr. 7, MG 2.1, Gr. 7, MG 2.2;Gr. 7, MG 3.1) PE/TE, p. 501;(Gr. 7, AF 1.3) PE/TE, p. 699;

(Gr. 7, MG 2.1) TE, p. 721


(Gr. 7, MG 1.3) PE/TE, p. 448 (Ex. 43);(Gr. 7, MG 2.1) PE/TE, p. 467 (Ex. 26);

(Gr. 7, MG 2.2) PE/TE, p. 485 (Ex. 57)(Gr. 7, MG 2.1) CASRP, pp. 107-108

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


(Gr. 7, NS 1.2) TE, p. 96;

(Gr. 7, NS 1.2) TE, p. 154;(Gr. 7, NS 2.4) TE, p. 231;

(Gr. 7, AF 3.3) TE, p. 340;(Gr. 7, AF 3.3) PE/TE, p. 341;(Gr. 7, SDAP 1.2) PE/TE, p. 666 (Extension);

(Gr. 7, AF 3.3) PE/TE, p. 344;(Gr. 7, AF 3.1) PE/TE, p. 414;

(Gr. 7, AF 3.1) TE, p. 421;(Gr. 7, AF 1.5) TE, p. 431


(Gr. 7, AF 3.3) PE/TE, p. 325 (Ex. 43);

(Gr. 7, AF 3.3) PE/TE, p. 346 (Ex. 38);(Gr. 7, SDAP 1.2) PE/TE, p. 666 (Exs. 31-32);

(Gr. 7, SDAP 1.2) PE/TE, p. 670 (Ex. 3)(Gr. 7, SDAP 1.1; Gr. 7, SDAP 1.2) CASRP,pp. 109-110



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


(Gr. 7, AF 1.3) PE/TE, p. 19 (Example 3);(Gr. 7, NS 1.2) PE/TE, p. 30;

(Gr. 7, AF 1.3) PE/TE, p. 33 (Example 4);(Gr. 7, NS 1.1) TE, p. 129;(Gr. 7, AF 1.1) TE, p. 369;


(Gr. 7, MG 2.1) PE/TE, p. 463;(Gr. 7, MG 2.1) PE/TE, p. 477;

(Gr. 7, SDAP 1.2) TE, p. 671;(Gr. 7, SDAP 1.2) TE, p. 683


(Gr. 7, AF 1.3) PE/TE, p. 21 (Exs. 14-28);(Gr. 7, AF 1.3) PE/TE, p. 33 (Exs. 3-22);

(Gr. 7, AF 4.1) PE/TE, p. 273 (Exs. 22-23);(Gr. 7, AF 3.3) PE/TE, p. 338 (Ex. 19)(Gr. 7, AF 1.0) CASRP, pp. 111-112

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


(Gr. 7, NS 1.2) PE/TE, p. 30;(Gr. 7, NS 1.1) TE, p. 70;(Gr. 7, NS 1.2) PE/TE, p. 90;

(Gr. 7, NS 1.2) PE/TE, p. 97;(Gr. 7, NS 1.1; Gr. 7, NS 1.2; Gr. 7, NS 1.3)PE/TE, p. 120;


(Gr. 7, AF 1.1) TE, p. 369;(Gr. 7, NS 2.3; Gr. 7, AF 1.5; Gr. 7, AF 2.1;Gr. 7, AF 3.1) PE/TE, p. 423;

(Gr. 7, MG 3.1) TE, p. 462;(Gr. 7, MG 3.2) TE, p. 534;

(Gr. 7, MG 3.2) PE/TE, p. 557;(Gr. 7, SDAP 1.1) TE, p. 649


(Gr. 7, AF 3.3) PE/TE, p. 325 (Ex. 45);(Gr. 7, AF 3.3) PE/TE, p. 347 (Exs. 41, 44);(Gr. 7, AF 1.5) PE/TE, p. 411 (Ex. 23);

(Gr. 7, AF 1.5) PE/TE, p. 412 (Ex. 31)(Gr. 7, NS 1.0) CASRP, pp. 113-115



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


(Gr. 7, NS 2.5) TE, p. 71;(Gr. 7, NS 1.1) TE, p. 240;

(Gr. 7, AF 1.1) TE, p. 299;(Gr. 7, AF 1.1) TE, p. 310;(Gr. 7, AF 3.3) PE/TE, p. 320;


(Gr. 7, AF 1.5) TE, p. 421;(Gr. 7, MG 3.4) PE/TE, p. 517 (Example 2);

(Gr. 7, MG 3.2) TE, p. 547;(Gr. 7, SDAP 1.1) PE/TE, p. 651;

(Gr. 7, AF 1.1) TE, p. 720


(Gr. 7, AF 3.3) PE/TE, p. 332 (Exs. 43-44);(Gr. 7, NS 2.3; Gr. 7, AF 2.1) PE/TE, p. 391(Exs. 54, 58);

(Gr. 7, NS 2.3; Gr. 7, AF 2.1) PE/TE, p. 398(Ex. 50)(Gr. 7, NS 1.0) CASRP, pp. 116-117

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



(Gr. 7, NS 1.2) TE, p. 154;(Gr. 7, MG 3.3) PE/TE, p. 472 (Example 2);

(Gr. 7, MG 2.1) TE, p. 587;(Gr. 7, MG 2.1) TE, p. 612



(Gr. 7, MG 3.3) PE/TE, p. 475 (Exs. 35, 37)(Gr. 7, NS 1.0) CASRP, pp. 118-119



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


(Gr. 7, AF 1.2) TE, p. 29;(Gr. 7, NS 1.0) PE/TE, pp. 52-58;

(Gr. 7, NS 1.2) PE/TE, p. 69;(Gr. 7, NS 1.6; Gr. 7, NS 1.7) PE/TE, pp.188-189;

(Gr. 7, AF 2.1) TE, p. 211;(Gr. 7, AF 4.2) TE, p. 268;

(Gr. 7, AF 1.1) TE, p. 299;(Gr. 7, AF 3.3) PE/TE, p. 329 (Example 4);(Gr. 7, AF 1.1) PE/TE, p. 356 (Example 4);

(Gr. 7, AF 4.1) PE/TE, p. 378;(Gr. 7, NS 2.3; Gr. 7, AF 1.0) PE/TE, pp. 428-429;

(Gr. 7, MG 1.1) PE/TE, p. 450 (Example 2);(Gr. 7, MG 3.3) PE/TE, p. 473;

(Gr. 7, MG 3.3) TE, p. 499;(Gr. 7, SDAP 1.1) TE, p. 649


(Gr. 7, AF 4.2) PE/TE, p. 319 (Ex. 41);(Gr. 7, AF 1.1) PE/TE, p. 359 (Exs. 49, 51);

(Gr. 7, MG 1.1) PE/TE, p 452 (Ex. 33)(Gr. 7, NS 1.0) CASRP, pp. 120-121

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


(Gr. 7, AF 1.3) PE/TE, pp. 46-47;(Gr. 7, NS 1.0) PE/TE, p. 52-58;

(Gr. 7, NS 1.7) PE/TE, p. 188;(Gr. 7, MG 2.2) PE/TE, p. 488;(Gr. 7, MG 3.2) PE/TE, p. 536;

(Gr. 7, MG 1.2) TE, p. 557;(Gr. 7, MG 3.6) TE, p. 587




(Gr. 7, MG 1.3) PE/TE, p. 452 (Ex. 33)(Gr. 7, AF 1.0; Gr. 7, AF 1.1; Gr. 7, MG 2.1)CASRP, pp. 122-127




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


(Gr. 7, NS 1.7) PE/TE, p. 188;(Gr. 7, AF 1.1) PE/TE, p. 309;

(Gr. 7, AF 1.1) PE/TE, p. 378;(Gr. 7, MG 2.1) PE/TE, p. 508;(Gr. 7, MG 3.2) PE/TE, p. 536;

(Gr. 7, MG 2.2) TE, p. 623;(Gr. 7, SDAP 1.3) TE, p. 671



(Gr. 7, MG 1.3) PE/TE, p. 452 (Ex. 33)(Gr. 7, MG 2.1) CASRP, pp. 122-123

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




(Gr. 7, AF 1.4) PE/TE, p. 256;(Gr. 7, MG 1.2) TE, p. 557



(Gr. 7, AF 1.4) PE/TE, p. 287 (Ex. 49);(Gr. 7, AF 4.1) PE/TE, p. 297 (Ex. 37)

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

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

Occurs throughout. Examples:(Gr. 7, AF 1.3) PE/TE, pp. 46-47;

(Gr. 7, NS 1.7) TE, p. 179;(Gr. 7, AF 2.1) PE/TE, p. 387;

(Gr. 7, MG 2.2) PE/TE, p. 488;(Gr. 7, MG 2.1) PE/TE, p. 588;

(Gr. 7, MG 3.5) PE/TE, p. 597;(Gr. 7, SDAP 1.3) TE, p. 683

Occurs throughout. Examples:(Gr. 7, AF 1.3) PE/TE, p. 47 (Ex. 15);

(Gr. 7, MG 2.1) PE/TE, p. 595 (Exs. 36-37);(Gr. 7, MG 2.3) PE/TE, p. 610 (Ex. 27)

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


Algebra 1



STANDARDS MAP for a Basic Grade-Level Program

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 arithmetic operationswhere applicable:

PE/TE: pp. 60-66, 67-71, 73-79, 81-86, 88-93, 95-101 (See Examples 3-5 and relatedexercises.), 102-108, 118-121, 483-490

PE/TE: 80, 110, 113-115, 117, 505, 509, 511

CASRP: pp. 2-4, 91, 94-95

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

PE/TE: pp. 56 (Example 6), 57 (Exs. 38-44),64-65 (Exs. 50-51), 70 (Exs. 41, 44), 78(Exs. 50-51), 85 (Ex. 44), 92 (Ex. 52), 94, 98(Example 5), 99 (Exs. 33-36), 103-104(Examples 3-4), 106 (Exs. 19-30)

PE/TE: 110, 117

CASRP: pp. 5-6, 91, 94-95

2.0 Students understand and use such operations astaking the opposite, finding the reciprocal, takinga root, and raising to a fractional power. Theyunderstand and use the rules of exponents.

PE/TE: pp. 53-59 (See Examples 4-5 andrelated exercises.), 67-71, 88-93, 95-101,459-466, 467-473, 474-480, 482-490, 498-503, 512-515, 633-639

PE/TE: 109, 110, 112-113, 116, 117, 481, 504,505, 507-510, 511

CASRP: pp. 7-9, 92, 94-95

3.0 Students solve equations and inequalitiesinvolving absolute values.

PE/TE: pp. 220-225, 226-231, 240-243 PE/TE: 232, 233, 237-238, 239

CASRP: pp. 10-12, 93-95

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

PE/TE: pp. 139-144, 182-185, 202-207,210-218

PE/TE: 154, 175, 178, 181, 219, 236-237, 239

CASRP: pp. 13-14, 96, 98-99

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

PE/TE: pp. 139-144, 145-152, 202-207, 208,210-217, 240-243

PE/TE: 154, 175, 179, 181, 182-185, 219, 233,236-237, 239CASRP: pp. 15-17, 97-99



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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: pp. 264-272, 273-279, 290-296,297-303, 314-317, 424-432, 450-453

PE/TE: 280, 306, 307, 310-312, 313, 441, 442,448, 449

CASRP: pp. 18-21, 104, 106-107

7.0 Students verify that a point lies on a line, given anequation of the line. Students are able to derivelinear equations by using the point-slope formula.

PE/TE: pp. 264-271 (See Example 3 andrelated exercises.),340-346, 347-352, 368-371

PE/TE: 322-328, 329-336, 339, 361, 362, 364-366, 367CASRP: pp. 22-23, 105-107

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: pp. 293 (Example 5), 294-296(Exs. 24-30, 36), 354-360, 368-371

PE/TE: 361, 362, 366, 367CASRP: pp. 24-26, 108, 111-112

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 inequalities intwo variables and to sketch the solution sets.

PE/TE: pp. 375-382, 383-388, 389, 390-397,398-404, 405-411, 413-417, 433-440, 450-453

PE/TE: 412, 441, 442, 444-448, 449

CASRP: pp. 27-30, 109-112

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

PE/TE: pp. 519-526, 527-533, 534-539,540-547, 563-564

PE/TE: 548, 587, 588, 590-592, 595

CASRP: pp. 31-35, 113-114, 116-117



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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: pp. 549-554, 555-562, 565-572,573-578, 579-586, 596-599, 640-641, 688-694, 696-703

PE/TE: 587, 588, 593-594, 595

CASRP: pp. 36-39, 113-114, 115-117

12.0 Students simplify fractions with polynomials in thenumerator and denominator by factoring both andreducing them to the lowest terms.

PE/TE: pp. 688-695, 696-703, 734-737 PE/TE: 704, 727, 730, 733

CASRP: pp. 40-41, 123, 126-127

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

PE/TE: pp. 696-703, 705-712, 713-718,719-720

PE/TE: 704, 726, 727, 730-731, 733

CASRP: pp. 42-44, 124, 126-127

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

PE/TE: pp. 549-554, 556-562 (SeeExamples 4-5 and related exercises.),566-572 (See Examples 4-5 and relatedexercises.), 573-578 (See Examples 4-5 andrelated exercises.), 579-586 (See Examples5-6 and related exercises.), 596-599, 640,642-648

PE/TE: 587, 588, 592, 595, 663, 664, 669, 671

CASRP: pp. 45-47, 115-117

15.0 Students apply algebraic techniques to solve rateproblems, work problems, and percent mixtureproblems.

PE/TE: pp. 413-417, 418-423, 683(Example 6), 686 (Exs. 60-61), 708, 710-711(Exs. 44-50), 721-725, 734-737

PE/TE: 441, 447, 449, 704, 726, 727, 729,732, 733CASRP: pp. 48-50, 125-127



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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: pp. 249-255, 256-263, 266-267(Examples 5-7), 268-271 (Exs. 36-60, 62),275, 278-279 (Exs. 53, 55-56)

PE/TE: 280, 307, 313

CASRP: pp. 51-52, 128, 130-131

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: pp. 249-254, 257-263, 267, 270(Exs. 53-56), 608 (Example 5), 610 (Exs.42-44, 46)

PE/TE: 280, 309-310, 313, 632

CASRP: pp. 53-55, 129-131

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

PE/TE: pp. 249-254, 257-263 PE/TE: 280, 313CASRP: pp. 56-57, 128, 130-131

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

PE/TE: pp. 649-655, 656-662 PE/TE: 663, 664, 670, 671

CASRP: pp. 58-59, 118, 121-122

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

PE/TE: pp. 649-655, 657-662, 672-675 PE/TE: 663, 664, 670, 671

CASRP: pp. 60-61, 118, 121-122

21.0 Students graph quadratic functions and know thattheir roots are the x-intercepts.

PE/TE: pp. 605-611, 612-617, 618-623,624-631, 657-662

PE/TE: 632, 664, 666-668, 671

CASRP: pp. 62-65, 119, 121-122

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: pp. 618-623, 624-631, 654 (Ex. 57),656-662

PE/TE: 632, 663, 664, 670, 671CASRP: pp. 66-67, 119, 121-122

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

PE/TE: pp. 549-554 (See Example 5 andrelated exercises.), 558 (Example 5),568-569 (Examples 4-5), 575 (Example 5),582, 608 (Example 5), 614 (Example 4),620 (Example 5), 627 (Example 6), 633-639(See Example 5 and related exercises.),640-641, 645, 659, 672-675

PE/TE: 561-562 (Exs. 64-72), 571-572 (Exs.53-60), 577-578 (Exs. 40-47), 585, 587, 588,595, 610-611 (Exs. 42-49), 616-617 (Exs. 39-44), 622-623 (Exs. 36-41), 629-630 (Exs. 52-58, 60-63), 632, 647-648 (Exs. 46-52, 55), 654(Ex. 63), 661-662 (Exs. 38-44), 663, 669, 671CASRP: pp. 68-69, 120-122



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24.0 Students use and know simple aspects of alogical argument:

PE/TE:, pp. 102-108, 147 (Example 3),203 (Example 3), 503 (Ex. 46), 532 (Ex. 44),584 (Example and Exs. 64-66), 649See also references for 24.1, 24.2, 24.3below.

PE/TE: 80, 109, 110, 117

CASRP: pp. 70-75, 100, 102-103

24.1 Students explain the difference between inductiveand deductive reasoning and identify and provideexamples of each.

PE/TE: pp. 102-108, 109, 482 PE/TE: 80, 109, 116

CASRP: pp. 70-71, 100, 102-103

24.2 Students identify the hypothesis and conclusionin logical deduction.

PE/TE: pp. 53-59 (See Example 6 andrelated exercises.), 94, 98 (Example 5), 99(Exs. 33-36), 353

PE/TE: 80, 117

CASRP: pp. 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: pp. 53-59, 94, 98 (Example 5), 99(Exs. 33-36), 107 (Ex. 34), 353, 480(Exs. 54-56)

PE/TE: 80, 110, 116 (Ex. 63), 117, 120

CASRP: pp. 74-75, 100, 102-103

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

PE/TE: pp. 77 (Exs. 29-38), 102-108, 147(Example 3), 203 (Example 3), 464(Exs. 52-53), 471 (Ex. 48), 503 (Ex. 46)See also references for 25.1, 25.2, 25.3below.

PE/TE: 110, 117, 120

CASRP: pp. 76-81, 101-103



Publisher Citations

StandardNo.


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

PE/TE: pp. 56 (Example 6), 57 (Exs. 38-43),65 (Exs. 51-52), 70 (Exs. 42-44), 78 (Ex.51), 92 (Exs. 51-52), 94, 98 (Example 5), 99(Exs. 33-36, 38), 103-108, 149 (Ex. 17), 165(Ex. 39), 171 (Ex. 39), 215 (Exs. 32-35), 480(Exs. 54-56), 482, 483-490 (See Exampleand related exercises on page 488.),579-586 (See Example and relatedexercises on p. 584.), 649, 653 (Ex. 55),655 (Ex. 67)

PE/TE: 110, 120, 121, 505

CASRP: pp. 76-77, 101-103

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: pp. 81-86, 91 (Exs. 42-43), 103-104,106-108 (Exs. 16-17, 35-39), 573-578

PE/TE: 121

CASRP: pp. 78-79, 101-103

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

PE/TE: pp. 102-108 (See Exs. 19-30.), 623(Ex. 47), 662 (Ex. 50), 768 (Ex. 30)

PE/TE: 117, 121

CASRP: pp. 80-81, 101-103

CA 2395/2007

2007CC2

McDougal Littell California · PDF fileCalifornia Math: Course 1 Course 2 Algebra 1. ... for...

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