correlated to the South Carolina Grade 7 Mathematics Standards 4/2001 1999
Introduction to PRE-ALGEBRA Passport to Algebra and Geometry Passport to Algebra and Geometry helps students gain an understanding of topics consistent with the Standards of the National Council of Teachers of Mathematics. The topics include algebra, data analysis and probability, geometry, integers, rational and real numbers, and measurement and number theory. Also included is concept development of ratios, proportions and percents. Technology is placed appropriately as a tool for learning. The following are some of the key features. Clear examples that model skills and problem-solving strategies provide students with a textbook that is easy to read and supports learning. The use of authentic data and connections to real-life contexts makes mathematics meaningful and relevant to students and gives them a foundation for success in future courses, particularly algebra and geometry. Exploratory Labs provide opportunities to investigate a variety of mathematical topics, make conjectures and develop a concrete understanding of abstract concepts. Standardized Test Practice, Portfolio Opportunities and Ongoing Assessment features in each lesson provide teachers with a variety of ways to assess student progress. Passport to Algebra and Geometry provides a nonthreatening development of abstract concepts that eases the transition to high school mathematics. Additionally, teachers will find comprehensive coverage of geomentry concepts, probability and statistics. Numerous assessment options are integrated thoughout the Passport to Algebra and Geometry. Opportunities for formal, alternative and performance-based assessment include review exercises in each lesson, daily cumulative reviews, writing questions, cooperative assessment, projects and technology activities. Teachers are supported by a wealth of ancillary materials. A complete listing of all program components is provided on the following page.
PRE-ALGEBRA Passport to Algebra and Geometry Components Pupil s Edtion Teacher s Edition Teacher s Resource Package Alternative Assessment Answer Masters Bridge Unit Complete Solution Manual Electronic Teacher Tools Enrichment Copymasters Formal Assessment Home and School Connection Lesson Plans Math Log Practice Workbook, Teacher s Edition Problem of the Day Reteaching Copymasters Teaching Tools: Transparencies and Copymasters Technology: Using Calculators and Computers Daily Cummulative Review Warm-up Exercises Warm-up Transparencies with Standardized Assessment Practice Other Ancillaries Practice Workbook (available in English or Spanish) Overhead Manipulatives Student Manipulatives Teacher Time-saver Transparencies Preparation for Middle School Math, PE Preparation for Middle School Math, TE Bridge Unit for Algebra and Geometry Spanish Resource Binder English-Spanish Problem Solving Transparencies Pasaporte al algebra y a la geometria Multi-Language Glossary Computer Test and Practice Generator CD-ROM (Mac/Windows) Middle School Tutorial Software Larson Interactive Real-Life Investigations CD-ROM (Mac/Windows) with Teacher s Guide
PRE-ALGEBRA Passport to Algebra and Geometry correlated to the SOUTH CAROLINA GRADE 7 MATHEMATICS STANDARDS Number and Operations Standard I. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Expectations: A. Work flexibly with fractions, decimals, and percents to solve problems. 1. Write and use the appropriate equivalent forms of whole numbers, fractions, decimals, and percents. PE/TE: 274, 276, 279, 280, 281, 282, 288, 290, 291, 292, 300, 301, 302, 303, 340-343, 357, 358, 725, 726, 728 Additional TE: 252A-F, 308A-F TRP: Alternative Assessment: Project pp. 25, 26, Partner Quiz p. 49; Bridge Unit: pp. 1, 15-21, 43; Daily Cumulative Review: 6.5, 6.6, 6.8, 7.7, pp. 24, 25, 30; Practice Workbook PE/TE: 6.5, 6.6, 6.8, 7.7, pp. 46, 47, 49, 57; Problem of the Day: 6.5, 6.6, 6.8, 7.7, pp. 17, 18, 21; Reteaching Copymasters: 6.5, 6.6, 6.8, 7.7, pp. 46, 47, 49, 57; 6.5, 6.6, 6.8, 7.7, pp. 46, 47, 49, 57 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 6-11 1
B. Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line. 1. Identify, represent, and find the approximate location of fractions, decimals, percents, and square roots of perfect squares on a number line and justify the reasoning used. PE/TE: 275, 415, 416, 417, 425, 451, 454, 730 Additional TE: 408A-F TRP: Alternative Assessment: Project p. 31; Bridge Unit: pp. 22, 29; Daily Cumulative Review: 9.2, p. 36; Practice Workbook PE/TE: 9.2, p. 69; Problem of the Day: 9.2, p. 25; Reteaching Copymasters: 9.2, p. 69; 9.2, p. 69 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 12, 18 2. Use order symbols to compare fractions, decimals, percents, and square roots of perfect squares and justify the reasoning used. PE/TE: 275, 276, 343 Additional TE: 252A-F, 308A-F TRP: Alternative Assessment: Project pp, 25, 26, Partner Quiz p. 49; Bridge Unit: pp. 27, 29, 35; Daily Cumulative Review: 6.5, 7.7, pp. 24, 30; Enrichment Copymasters: 6.5, pp. 31, 32; Practice Workbook PE/TE: 6.5, 7.7, pp. 46, 57; Problem of the Day: 6.5, 7.7, pp. 17, 21; Reteaching Copymasters: 6.5, 7.7, pp. 46, 57; 6.5, 7.7, pp. 46, 57 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 16, 18, 23 2
C. Develop meaning for percents greater than 100 and less than 1. 1. Use models to represent percents less than 1% and solve problems involving them. PE/TE: 340, 728 Additional TE: 308A-F TRP: Daily Cumulative Review: 7.7, p. 30; Practice Workbook PE/TE: 7.7, p. 57; Problem of the Day: 7.7, p. 21; Reteaching Copymasters: 7.7, p, 57; 7.7, p. 57 D. Understand and use ratios and proportions to represent quantitative relationships. 1. Create and write ratios and proportions from applied situations and explain the reasoning used. PE/TE: 362-365, 366-367, 369, 370, 371, 372-375, 376, 377, 379, 380, 381, 382, 384, 403, 404, 406, 728, 729, 752, 753 Additional TE: 360A-F TRP: Alternative Assessment: Project pp. 29, 30, Partner Quiz p. 51; Bridge Unit: pp. 65-71; Daily Cumulative Review: 8.1-8.5, pp. 32-35; Enrichment Copymasters: 8.3, pp. 39, 40; Practice Workbook PE/TE: 8.1-8.5, pp. 60-64; Problem of the Day: 8.1-8.5, pp. 22, 23; Reteaching Copymasters: 8.1-8.5, pp. 60-64; 8.1-8.5, pp. 60-64 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 48-70 3
E. Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation. 1. Translate a number written in exponential form, in scientific notation, and in calculator notation to standard form. PE/TE: 10, 12, 14, 20, 36, 44, 46, 284-287, 288-291, 292, 299, 301, 302, 303, 304, 307, 716, 726, 750 Additional TE: 1A-F, 252A TRP: Alternative Assessment: Project p. 15, Group and Individual pp. 69, 70; Bridge Unit: pp. 38, 39, 41, 42, 43; Daily Cumulative Review: 1.3, 6.7, 6.8, pp. 2, 25; Practice Workbook PE/TE: 1.3, 6.7, 6.8, pp. 3, 48, 49; Problem of the Day: 1.3, 6.7, 6.8, pp. 1, 18; Reteaching Copymasters: 1.3, 6.7, 6.8, pp. 3, 48, 49; 1.3, 6.7, 6.8, pp. 3, 48, 49 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 26, 27, 28, 29 F Use factors, multiples, prime factorization, and relatively prime numbers to solve problems. 1. Apply primes, composites, factors, multiples, and relatively prime numbers in a variety of applied and mathematical situations and explain the reasoning used. PE/TE: 258-259, 260-263, 264, 265, 266-269, 270-273, 274, 275, 276, 279, 299, 300, 302, 303, 725, 749 Additional TE: 252A-F TRP: Alternative Assessment: Project pp. 25, 26, Partner Quiz p. 49; Daily Cumulative Review: 6.2-6.5, pp. 22-24; Enrichment Copymasters: 6.2, 6.5, pp. 29-31; Practice Workbook PE/TE: 6.2-6.5, pp. 43-46; Problem of the Day: 6.2-6.5, pp. 16, 17; Reteaching Copymasters: 6.2-6.5, pp. 43-46; 6.2-6.5, pp. 43-46 4
G. Develop meaning for integers and represent and compare quantities with them. 1. Compare and order integers. PE/TE: 104, 106, 107, 130, 147, 150, 719 Additional TE: 102A-F TRP: Bridge Unit: p. 27; Daily Cumulative Review: 3.1, p. 10; Practice Workbook PE/TE: 3.1, p. 18; Problem of the Day: 3.1, p. 7; Reteaching Copymasters: 3.1, p. 18; 3.1, p. 18 Other Ancillaries: Preparation for Middle School Math, Grade 8: p. 16 Standard II. Understand meanings of operations and how they relate to one another. Expectations: A. Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers. 1. Explain the meaning and effects of arithmetic operations with integers. PE/TE: 108-109, 110-113, 114-117, 119, 120-123, 124-125, 126-129, 130, 132-135, 136, 137, 147, 148, 149, 150, 151, 719, 720, 748 Additional TE: 102A-F TRP: Alternative Assessment: Project p. 19, Partner Quiz p. 46; Bridge Unit: pp. 23, 24, 25, 27; Daily Cumulative Review: 3.2-3.6, pp. 10-12; Enrichment Copymasters: 3.4, 3.6, pp.12-15; Practice Workbook PE/TE: 3.2-3.6, pp. 19-23; Problem of the Day: 3.2-3.6, pp. 7, 8; Reteaching Copymasters: 3.2-3.6, pp. 19-23; 3.2-3.6, pp. 19-23 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 13, 14, 16 5
B. Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals. 1 Apply the associative, commutative, and distributive properties for operations on integers, fractions, and decimals. PE/TE: 52-55, 67, 97, 100, 717 Additional TE: 48A-F TRP: Bridge Unit: p.50; Daily Cumulative Review: 2.1, p.5; Enrichment Copymasters: 2.1, pp. 8, 9; Practice Workbook PE/TE: 2.1, p. 9; Problem of the Day: 2.1, p. 4; Reteaching Copymasters: 2.1, p. 9; 2.1, p. 9 Other Ancillaries: Preparation for Middle School Math, Grade 8: p. 35 C. Understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems. 1. Using models and numbers, explain the inverse relationships between squaring and finding square roots of perfect squares. PE/TE: 10-13, 44, 46, 716, 755 Additional TE: 1A-F TRP: Alternative Assessment: Project p. 15; Daily Cumulative Review: 1.3, p. 2; Practice Workbook PE/TE: 1.3, p. 3; Problem of the Day: 1.3, p. 1; Reteaching Copymasters: 1.3, p. 3; 1.3, p. 3 6
Standard III. Compute fluently and make reasonable estimates. Expectations: A. Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods. 1. Select appropriate methods and tools to solve problems applying all operations to fractions, decimals and integers. PE/TE: 8, 108-109, 110-113, 114-117, 119, 120-123, 124-125, 126-129, 130, 132-135, 136, 137, 147, 148, 149, 150, 151, 310-313, 314-315, 316-319, 320-323, 324-327, 328, 329, 330-333, 334, 355, 356, 358, 719, 720, 726, 727, 747, 748 Additional TE: 1A-F, 102A-F, 308A-F TRP: Alternative Assessment: Project pp. 19, 27, Partner Quiz p. 46, 50, Group and Individual pp. 71, 72; Bridge Unit: pp. 1, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 43; Daily Cumulative Review: 3.2-3.6, 7.1-7.5, pp. 10-12, 27-29; Enrichment Copymasters: 3.4, 3.6, 7.2, pp. 12-15, 35, 36; Practice Workbook PE/TE: 3.2-3.6, 7.1-7.5, pp. 19-23, 51-55; Problem of the Day: 3.2-3.6, 7.1-7.5, pp. 7, 8, 19, 20; Reteaching Copymasters: 3.2-3.6, 7.1-7.5, pp. 19-23, 51-55; 3.2-3.6, 7.1-7.5, pp. 19-23, 51-55 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 12, 13, 14, 15, 16, 19, 20, 21, 22, 23 7
B. Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use. 1. Use models and numbers to develop and analyze the algorithms for computing with integers. PE/TE: 108-109, 110-113, 114-117, 119, 120-123, 124-125, 126-129, 130, 132-135, 136, 137, 147, 148, 149, 150, 151, 719, 720, 748 Additional TE: 102A-F TRP: Alternative Assessment: Project p. 19, Partner Quiz p. 46; Bridge Unit: pp. 1, 23, 24, 25, 26, 27, 43; Daily Cumulative Review: 3.2-3.6, pp. 10-12; Enrichment Copymasters: 3.4, 3.6, pp.12-15; Practice Workbook PE/TE: 3.2-3.6, pp. 19-23; Problem of the Day: 3.2-3.6, pp. 7, 8; Reteaching Copymasters: 3.2-3.6, pp. 19-23; 3.2-3.6, pp. 19-23 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 13, 14, 15, 16 2. Add, subtract, multiply and divide integers to solve a variety of applied and mathematical problem situations. PE/TE: 108-109, 110-113, 114-117, 119, 120-123, 124-125, 126-129, 130, 132-135, 136, 137, 147, 148, 149, 150, 151, 719, 720, 748 Additional TE: 102A-F TRP: Alternative Assessment: Project p. 19, Partner Quiz p. 46; Bridge Unit: pp. 1, 23, 24, 25, 26, 27, 43; Daily Cumulative Review: 3.2-3.6, pp. 10-12; Enrichment Copymasters: 3.4, 3.6, pp.12-15; Practice Workbook PE/TE: 3.2-3.6, pp. 19-23; Problem of the Day: 3.2-3.6, pp. 7, 8; Reteaching Copymasters: 3.2-3.6, pp. 19-23; 3.2-3.6, pp. 19-23 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 13, 14, 15, 16 8
C. Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results. 1. Estimate the products and quotients of fractions and decimals, describe the method used, and determine the reasonableness of results. PE/TE: 75, 87, 345, 566, 567, 568, 570, 586, 587, 593, 596, 597, 601, 736, 737 Additional TE: 48A-F, 308A-F, 562A-F TRP: Alternative Assessment: Project p. 37; Bridge Unit: 1, 11, 12, 14, 18, 33, 34, 43; Daily Cumulative Review: 12.1, 12.5, pp. 50, 52; Enrichment Copymasters: 12.1, pp. 61, 62; Practice Workbook PE/TE: 12.1, 12.5, pp. 94, 98; Problem of the Day: 12.1, 12.5, pp. 34, 35; Reteaching Copymasters: 12.1, 12.5, pp. 94, 98; 12.1, 12.5, pp. 94, 98 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 3, 5, 9, 22 2. Estimate the sums and differences of integers, describe the method used, and determine the reasonableness of results. Related concepts are taught on the following pages: PE/TE: 87, 171 (#29), 176 (#18, 19) 9
D. Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios. 1 Explain the equivalent ratio method of solving problems involving proportions. PE/TE: 368-371, 372-375, 376-379, 380, 381, 382, 384, 385, 390, 403, 404, 406, 407, 728, 729, 752, 753 Additional TE: 360A-F TRP: Alternative Assessment: Project pp. 29, 30, Partner Quiz p. 51; Bridge Unit:pp. 65, 66, 67, 68, 69, 70, 71; Daily Cumulative Review: 8.2-8.5, pp. 32-34; Enrichment Copymasters: 8.3, pp. 39, 40; Practice Workbook PE/TE: 8.2-8.5, pp. 61-64; Problem of the Day: 8.2-8.5, pp. 22, 23; Reteaching Copymasters: 8.2-8.5, pp. 61-64; 8.2-8.5, pp. 61-64 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 48, 49, 50, 51, 52 10
6-8: Algebra Standard I. Understand patterns, relations, and functions. Expectations: A. Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules. 1. Describe, extend, analyze, and create a wide variety of patterns to investigate relationships and to solve problems. PE/TE: 2-5, 14, 20, 21, 22-25, 26-29, 30-31, 32-35, 36, 38-41, 42, 43, 44, 45, 46, 47, 57, 77, 82-86, 87, 88-91, 98, 99, 100, 101, 126, 136, 139, 141, 142-145, 149, 150, 151, 152, 183, 184, 185, 186, 187, 189, 191, 192-195, 199, 200, 201, 215, 236-239, 249, 250, 258-259, 283, 294-297, 301, 302, 303, 312, 318, 333, 348, 372-375, 376-379, 382, 384, 388, 391, 393, 395, 404, 406, 407, 418-419, 420-423, 424, 426-429, 431, 452, 454, 455, 473, 489, 492-493, 536-539, 540-541, 542-545, 546-549, 550, 551, 552-555, 559, 560, 569, 599, 602, 605, 609, 610, 618-621, 622-625, 626, 627, 629, 630, 631, 632, 638, 639, 643, 644, 645, 646-647, 648-651, 656-659, 661, 662, 663, 664, 665, 699, 707, 716, 717, 718, 719, 721, 722, 724, 726, 729, 731, 735, 736, 737, 738, 739 Additional TE: 1A-F, 48A-F, 102A-F, 154A-F, 202A-F, 252A-F, 308A-F, 360A-F, 408A-F, 458A-F, 510A-F, 562A-F, 616A-F, 666A-F TRP: Alternative Assessment: Project pp. 15, 16, 20-22, 24, 26, 29, 30, 31, 32, 35, 36, 40, Partner Quiz: pp. 51, 52, Group and Individual: pp. 55, 56, 59, 60; Bridge Unit: pp. 35, 36, 40, 41, 54, 86; Daily Cumulative Review: 1.1, 1.5-1.8, 2.7, 2.8, 3.8, 4.6-4.8, 5.7, 6.9, 8.3-8.5, 9.3, 9.4, 11.6, 11.7, 11.8, 11.9, 12.8, 13.1, 13.2, 13.6, 13.8, pp. 1, 3, 4, 8, 13, 16, 17, 21, 26, 33, 34, 37, 47, 48, 49, 53, 54, 56, 57; Enrichment Copymasters: 1.6-1.8, 3.8, 6.9, 8.3, 9.3, 11.6, 13.2, pp. 2-7, 16, 17, 33, 34, 39, 40, 47, 48, 59, 60, 67, 68; Practice Workbook PE/TE: 1.1, 1.5-1.8, 2.7, 2.8, 3.8, 4.6-4.8, 5.7, 6.9, 8.3-8.5, 9.3, 9.4, 11.6, 11.7, 11.8, 11.9, 12.8, 13.1, 13.2, 13.6, 13.8, pp.1, 5-8, 15, 16, 25, 31-33, 40, 50, 62-64, 70, 71, 90, 91, 92, 93, 101, 102, 103, 107, 109; Problem of the Day: 1.1, 1.5-1.8, 2.7, 2.8, 3.8, 4.6-4.8, 5.7, 6.9, 8.3-8.5, 9.3, 9.4, 11.6, 11.7, 11.8, 11.9, 12.8, 13.1, 13.2, 13.6, 13.8, pp, 1, 2, 3, 6, 9,11, 12, 15, 18, 22, 23, 25, 26, 32, 33, 36, 37, 38, 39; (Continued on next page) 11
Reteaching Copymasters: 1.1, 1.5-1.8, 2.7, 2.8, 3.8, 4.6-4.8, 5.7, 6.9, 8.3-8.5, 9.3, 9.4, 11.6, 11.7, 11.8, 11.9, 12.8, 13.1, 13.2, 13.6, 13.8, pp. 1, 5-8, 15, 16, 25, 31-33, 40, 50, 62-64, 70, 71, 90, 91, 92, 93, 101, 102, 103, 107, 109; 1.1, 1.5-1.8, 2.7, 2.8, 3.8, 4.6-4.8, 5.7, 6.9, 8.3-8.5, 9.3, 9.4, 11.6-11.9, 12.8, 13.1, 13.2, 13.6, 13.8, pp. 1, 5-8, 15, 16, 25, 31-33, 40, 50, 62-64, 70, 71, 90, 91, 92, 93, 101, 102, 103, 107, 109 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 23, 24, 28, 65 B. Relate and compare different forms of representations for a relationship. 1. Use different forms of representing information (e.g., graphical, symbolic and tabular). PE/TE: 21, 26, 30-31, 33, 34, 38, 41, 45, 61, 62, 65, 67, 69, 73, 75, 77, 81, 82-85, 87, 88, 90, 91, 93, 94, 95, 98, 99, 100, 101, 129, 133, 139, 140, 141, 143, 145, 159, 160, 161, 163, 165, 169, 171, 173, 174, 175, 176, 179, 180, 181, 182, 183, 184, 185, 186, 187, 189, 191, 199, 200, 201, 215, 236-239, 296, 348, 366, 369, 370, 372-375, 376-379, 381, 382, 384, 391, 396, 404, 406, 407, 413, 426-429, 439, 441, 443, 445, 448, 452, 454, 455, 492-493, 537, 542, 549, 551, 552-556, 561, 565, 587, 591, 602, 603, 605, 620, 622-625, 626, 627, 628-631, 632, 634-637, 638, 639, 640-641, 642-645, 646-647, 648-651, 652-655, 661, 662, 663, 664, 665, 691, 718, 719, 720, 721, 722, 724, 735, 736, 738, 739 Additional TE: 1A-F, 48A-F, 102A-F, 154A-F, 202A-F, 252A-F, 308A-F, 360A-F, 408A-F, 458A-F, 510A-F, 562A-F616A-F, 666A-F TRP: Alternative Assessment: Project pp.17, 18, 21, 22, 24, 29, 30, 32, 35, 36, 39, 40, Partner Quiz pp. 45, 47, 51, 56, Group and Individual: pp. 61, 62, 65, 66, 83, 84; Bridge Unit: pp. 54, 55, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 86, 93; Daily Cumulative Review: 2.3-2.5, 2.7-2.9, 3.7, 4.1-4.8, 5.7, 8.2-8.5, 9.4, 9.6, 9.7, 11.6, 11.7, 11.9, 12.8, 13.2-13.7, pp. 6-9, 13-17, 21, 32-34, 37-39, 47, 48, 49, 53-57; Enrichment Copymasters: 4.3, 8.3, 11.6, 13.2, 13.3 pp. 18-21, 39, 40, 59, 60, 67-71; Practice Workbook PE/TE: 2.3-2.5, 2.7-2.9, 3.7, 4.1-4.8, 5.7, 8.1-8.5, 9.4, 9.6, 9.7, 11.6, 11.7, 11.9, 12.8, 13.2-13.7, pp, 11-13, 15-17, 24, 26-33, 40, 61-64, 71, 73, 74, 90, 91, 93, 103-108; Problem of the Day: 2.3-2.5, 2.7-2.9, 3.7, 4.1-4.8, 5.7, 8.1-8.5, 9.4, 9.6, 9.7, 11.6, 11.7, 11.9, 12.8, 13.2-13.7, pp. 4, 5, 6, 9, 10, 11, 12, 15, 22, 23, 26, 27, 32, 33, 36, 37, 38, 39; (Continued on next page) 12
Reteaching Copymasters: 2.3-2.5, 2.7-2.9, 3.7, 4.1-4.8, 5.7, 8.1-8.5, 9.4, 9.6, 9.7, 11.6, 11.7, 11.9, 12.8, 13.2-13.7, pp. 11-13, 15-17, 24, 26-33, 40, 61-64, 71-74, 90, 91, 93, 101, 103-108; 2.3-2.5, 2.7-2.9, 3.7, 4.1-4.8, 5.7, 8.1-8.5, 9.4, 9.6, 9.7, 11.6, 11.7, 11.9, 12.8, 13.2-13.7, pp. 11-13, 15-17, 24, 26-33, 40, 61-64, 71-74, 90, 91, 93, 101, 103-108 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 39, 42, 43, 44, 46, 47, 49, 50, 51, 65, 71 C. Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. 1. Examine tables and graphs to determine if there is a constant rate of change between the quantities. PE/TE: 633, 634-637, 640-641, 642-645, 662, 664, 738, 739 Additional TE: 616A-F TRP: Alternative Assessment: Project pp. 39, 40, Partner Quiz p. 56; Bridge Unit: pp. 120, 122, 123; Daily Cumulative Review: 13.4, 13.5, pp. 55, 56; Practice Workbook PE/TE: 13.4, 13.5, pp. 105, 106; Problem of the Day: 13.5, 13.6, p. 38; Reteaching Copymasters: 13.4, 13.5, pp. 105, 106; 13.4, 13.5, pp. 105, 106 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 94, 95, 96 13
Standard II. Represent and analyze mathematical situations and structures using algebraic symbols. Expectations: A. Develop an initial conceptual understanding of different uses of variables. 1. Explain the use of a variable as a quantity that can change its value, as a quantity on which other values depend, and as generalization of patterns. PE/TE: 22-25, 33, 39, 41, 44, 46, 47, 53, 54, 55, 57, 59, 61, 63, 67, 69, 70, 73, 75, 78-81, 82-85, 86, 87, 88, 90, 91, 93, 94, 95, 98, 99, 100, 101, 127, 129, 131, 133, 139, 140, 141, 149, 157, 159, 160, 161, 163, 164, 165, 169, 171, 173, 175, 176, 179, 181, 183, 184, 185, 186, 187, 189, 191, 289, 294, 295, 296, 297, 372, 373, 374, 375, 376-379, 382, 404, 406, 407, 411, 412, 426, 427, 428, 439, 443, 452, 453, 512, 513, 542, 566, 567, 576, 577, 580, 586, 587, 592, 593, 596, 597, 603, 618, 619, 620, 621, 648, 650, 651, 657, 661, 663, 689, 691, 705, 716, 717-718, 720, 722, 726, 729, 739 Additional TE: 1A-F, 48A-F, 102A-F, 154A-F, 252A-F, 360A-F, 408A-F, 510A-F, 562A-F, 616A-F, 666A-F TRP: Alternative Assessment: Project pp. 17, 18, 20-22, Partner Quiz pp. 45, 51; Bridge Unit:pp. 2, 4, 50, 53, 54, 56, 71, 120, 121, 122, 123, 124; Daily Cumulative Review: 1.5, 2.6-2.9, 3.7, 4.6, 6.9, 8.3, 8.4, 13.6, pp. 3, 5-7, 13, 16, 26, 33, 56; Enrichment Copymasters: 2.6, 6.9,8.3, pp. 10, 11, 33, 34, 39, 40; Practice Workbook PE/TE: 1.5, 2.6-2.9, 3.7, 4.6, 6.9, 8.3, 8.4, 13.6, pp. 5, 10-14, 24, 31, 50, 62, 63, 107; Problem of the Day: 1.5, 2.6-2.9, 3.7, 4.6, 6.9, 8.3, 8.4, 13.6, pp. 2,4, 5, 9, 11, 18, 22, 23, 38; Reteaching Copymasters: 1.5, 2.6-2.9, 3.7, 4.6, 6.9, 8.3, 8.4, 13.6, pp. 5, 10-14, 24, 31, 50, 62, 63, 107; 1.5, 2.6-2.9, 3.7, 4.6, 6.9, 8.3, 8.4, 13.6, pp. 5, 10-14, 24, 31, 50, 62, 63, 107 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 35, 38, 94, 95, 40 14
B. Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope. 1. Analyze quantitative changes by comparing and contrasting numerical patterns in tables with their respective graphs in the coordinate plane. PE/TE: 623, 624, 625, 626, 639, 640-641, 646-647, 648, 649, 650, 651, 661, 663, 664, 665, 738, 739 Additional TE: 616A-F TRP: Bridge Unit: pp. 120, 122, 123, 124, 126; Daily Cumulative Review: 13.2, 13.6, pp. 54, 56; Enrichment Copymasters: 13.2, pp. 67, 68; Practice Workbook PE/TE: 13.2, 13.6, pp. 103, 107; Problem of the Day: 13.2, 13.3, pp. 37, 38; Reteaching Copymasters: 13.2, 13.6, pp. 103, 107; 13.2, 13.6, pp. 103, 107 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 94, 95, 96 2. State the coordinates of the x and y intercepts from a graph. PE/TE: 622, 627, 628-631, 639, 641, 738 Additional TE: 616A-F TRP: Bridge Unit: pp. 118, 119, 121, 122, 123, 124; Daily Cumulative Review: 13.3, p. 55; Enrichment Copymasters: 13.3, pp. 69-71; Practice Workbook PE/TE: 13.3, p. 104; Problem of the Day: 13.3, p. 37; Reteaching Copymasters: 13.3, p. 104; 13.3, p. 104 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 92, 93, 95, 96 15
C. Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships. 1. Use variables to describe numerical expressions and relationships. PE/TE: 22-25, 33, 39, 41, 44, 46, 47, 53, 54, 55, 57, 59, 61, 63, 67, 69, 70, 73, 75, 78-81, 82-85, 86, 87, 88, 90, 91, 93, 94, 95, 98, 99, 100, 101, 127, 129, 131, 133, 139, 140, 141, 149, 157, 159, 160, 161, 163, 164, 165, 169, 171, 173, 175, 176, 179, 181, 183, 184, 185, 186, 187, 189, 191, 289, 294, 295, 296, 297, 372, 373, 374, 375, 376-379, 382, 404, 406, 407, 411, 412, 426, 427, 428, 439, 443, 452, 453, 512, 513, 542, 566, 567, 576, 577, 580, 586, 587, 592, 593, 596, 597, 603, 618, 619, 620, 621, 648, 650, 651, 657, 661, 663, 689, 691, 705, 716, 717-718, 720, 722, 726, 729, 739 Additional TE: 1A-F, 48A-F, 102A-F, 154A-F, 252A-F, 360A-F, 408A-F, 510A-F, 562A-F, 616A-F, 666A-F TRP: Alternative Assessment: Project pp. 17, 18, 20-22, Partner Quiz pp. 45, 51; Bridge Unit: pp. 2, 44-49, 55, 56, 58, 59, 60, 62, 64, 66, 67, 68, 71; Daily Cumulative Review: 1.5, 2.6-2.9, 3.7, 4.6, 6.9, 8.3, 8.4, 13.6, pp. 3, 5-7, 13, 16, 26, 33, 56; Enrichment Copymasters: 2.6, 6.9, 8.3, pp. 10, 11, 33, 34, 39, 40; Practice Workbook PE/TE: 1.5, 2.6-2.9, 3.7, 4.6, 6.9, 8.3, 8.4, 13.6, pp. 5, 10-14, 24, 31, 50, 62, 63, 107; Problem of the Day: 1.5, 2.6-2.9, 3.7, 4.6, 6.9, 8.3, 8.4, 13.6, pp. 2, 4, 5, 9, 11, 18, 22, 23, 38; Reteaching Copymasters: 1.5, 2.6-2.9, 3.7, 4.6, 6.9, 8.3, 8.4, 13.6, pp. 5, 10-14, 24, 31, 50, 62, 63, 107; 1.5, 2.6-2.9, 3.7, 4.6, 6.9, 8.3, 8.4, 13.6, pp. 5, 10-14, 24, 31, 50, 62, 63, 107 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 30-34, 39, 40, 42, 43, 44, 47, 49, 50 16
D. Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations. 1. Recognize and apply the additive and multiplicative inverses. PE/TE: 66, 67, 72, 73, 82, 83, 88, 92, 93, 98, 99, 138, 149, 158, 159, 162, 168, 169, 172, 173, 178, 179, 183, 197, 198, 368, 369, 377, 382, 403, 404, 438, 439, 442, 453, 542, 718, 719, 720, 721, 722, 728, 729, 735 Additional TE: 48A-F, 102A-F, 154A-F, 360A-F, 408A-F, 510A-F TRP: Alternative Assessment:Project pp. 17, 18, 20, 21, 32, 35, 36, Partner Quiz p. 47, Group and Individual pp. 61, 62; Bridge Unit: pp. 57, 58, 59, 60, 61, 66; Daily Cumulative Review: 2.4-2.9, 3.7, 4.1-4.5, 8.2-8.4, 9.6, 9.7, 11.7, pp.6-9, 13-16, 38, 39, 48; Enrichment Copymasters: 4.3, 4.4, 8.3, pp. 18-21, 39, 40; Practice Workbook PE/TE: 2.4-2.9, 3.7, 4.1-4.5, 8.2-8.4, 9.6, 9.7, 11.7, pp. 12, 13, 15-17, 24, 26-30, 61-63, 73, 74, 91; Problem of the Day: 2.4-2.9, 3.7, 4.1-4.5, 8.2-8.4, 9.6, 9.7, 11.7, pp, 5, 6, 9-11, 22, 23, 26, 27, 33; Reteaching Copymasters: 2.4-2.9, 3.7, 4.1-4.5, 8.2-8.4, 9.6, 9.7, 11.7, pp. 12, 13, 15-17, 24, 26-30, 61-63, 73, 74, 91; 2.4-2.9, 3.7, 4.1-4.4, 4.5, 8.2-8.4, 9.6, 9.7, 11.7, pp. 12, 13, 15-17, 24, 26-30, 61-63, 73, 74, 91 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 41, 42, 43, 44, 45, 49 2. Use models and numbers to solve one-step linear equations and inequalities in one variable. PE/TE: 60-63, 64-65, 66-69, 70, 71, 72-75, 82-85, 86, 88, 90, 91, 92-95, 97, 98, 99, 100, 101, 112, 113, 128, 130, 134, 138, 140, 149, 150, 312, 328, 438-441, 718, 719, 720, 731, 751 Additional TE: 48A-F, 102A-F, 308A-F, 408A-F TRP: Alternative Assessment: Project pp. 17, 18, Partner Quiz p. 45, Group and Individual pp. 61, 62; Bridge Unit: pp. 2, 57-64; Daily Cumulative Review: 2.3-2.9, 9.6, pp. 6-9, 38; Practice Workbook PE/TE: 2.3-2.9, 9.6, pp. 11-13, 15-17, 73; Problem of the Day: 2.3-2.9, 9.6, pp. 4, 5, 6, 26; Reteaching Copymasters: 2.3-2.9, 9.6, pp. 11-13, 15-17, 73; 2.3-2.9, 9.6, pp. 11-13, 15-17, 73 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 41-47 17
Standard III. Use mathematical models to represent and understand quantitative relationships. Expectations: A. Model and solve contextualized problems using various representations, such as graphs, tables, and equations. 1. Use graphs, tables, and equations to solve applied problems involving tips, discounts, sales tax and simple interest. PE/TE: 348, 350-353, 357, 377, 383, 384, 385, 390, 404, 729 Additional TE: 308A-F, 360A-F TRP: Alternative Assessment: Project pp. 28, 30, Partner Quiz p. 51; Daily Cumulative Review: 7.9, 8.4, 8.5, pp. 31, 33, 34; Practice Workbook PE/TE: 7.9, 8.4, 8.5, pp. 59, 63, 64; Problem of the Day: 7.9, 8.4, 8.5, pp. 21, 23; Reteaching Copymasters: 7.9, 8.4, 8.5, pp. 59, 63, 64; 7.9, 8.3, 8.4, pp. 59, 63, 64 Standard IV. Analyze change in various contexts. Expectations: A. Use graphs to analyze the nature of changes in quantities in linear relationships. 1. Describe a linear relationship as positive or negative from a graph. PE/TE: 634-637, 639, 662, 664, 738 Additional TE: 616A-F TRP: Alternative Assessment: Partner Quiz p. 56; Daily Cumulative Review: 13.4, p. 55; Practice Workbook PE/TE:13.4, p. 105; Problem of the Day: 13.4, p. 38; Reteaching Copymasters: 13.4, p. 105; 13.4, p. 105 18
Geometry Standard I. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. Expectations: A. Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties. 1. Classify polygons as regular or non-regular and investigate relationships between the number of diagonals and the number of sides of a regular polygon. PE/TE: 32-35, 478-481, 483, 484-487, 492-493, 506, 507, 508, 717, 733, 744 Additional TE: 1A-F, 458A-F TRP: Alternative Assessment: Group and Individual pp. 59, 60; Daily Cumulative Review: 1.7, 10.5, 10.6, pp. 4, 42; Enrichment Copymasters: 1.7, pp. 4, 5; Practice Workbook PE/TE: 1.7, 10.5, 10.6, pp. 7, 80, 81; Problem of the Day: 1.7, 10.5, 10.6, pp. 3, 29; Reteaching Copymasters: 1.7, 10.5, 10.6, pp. 7, 80, 81; 1.7, 10.5, 10.6, pp. 7, 80, 81 B. Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects. 1. Describe relationships between the edge lengths, and volume of similar prisms. PE/TE: 602-605, 609, 610, 611, 737 Additional TE: 562A-F TRP: Daily Cumulative Review:12.8, p.53; Practice Workbook PE/TE: 12.8, p. 101; Problem of the Day: 12.8, p. 36; Reteaching Copymasters: 12.8, p. 101; 12.8, p. 101 19
C. Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship. 1. Compare and contrast attributes of similar figures and the attributes of congruent figures. PE/TE: 516-519, 520, 521, 522-525, 526-530, 531-533, 534, 535, 536-539, 540-541, 542-545, 557, 558, 559, 560, 561, 734, 735 Additional TE: 510A-F TRP: Alternative Assessment: Project: pp 35, 36, Partner Quiz: p. 54, Group and Individual: pp. 79, 80; Daily Cumulative Review: 11.2-11.7, pp. 45-48; Enrichment Copymasters: 11.5, 11.6, pp. 57-60; Practice Workbook PE/TE: 11.2-11.7, pp. 86-91; Problem of the Day: 11.2-11.7, pp. 31, 32, 33; Reteaching Copymasters: 11.2-11.7, pp. 86-91; 11.2-11.7, pp. 86-91 20
Standard II. Specify locations and describe spatial relationships using coordinate geometry and other representational systems. Expectations: A. Use coordinate geometry to represent and examine the properties of geometric shapes. 1. Identify and graph ordered pairs in the four quadrants of a coordinate plane. PE/TE: 142-145, 149, 150, 721 Additional TE: 102A-F TRP: Alternative Assessment: Project p. 20, Group and Individual pp. 63, 64; Bridge Unit: pp. 4, 104, 105, 110, 111, 112, 113, 115, 116, 117, 118, 119, 124; Daily Cumulative Review: 3.8, p. 13; Enrichment Copymasters: 3.8, pp. 16, 17; Practice Workbook PE/TE: 3.8, p. 25; Problem of the Day: 3.8, p. 9; Reteaching Copymasters: 3.8, p. 25; 3.8, p. 25 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 80, 81, 85, 86, 87, 88, 90, 91, 92, 93 21
B. Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides 1. State relationships among the coordinates of the vertices of rectangles, squares, parallelograms, trapezoids, and rhombuses oriented horizontally. PE/TE: 525, 527, 528, 531, 532, 533, 535, 539, 658 Additional TE: 510A-F TRP: Alternative Assessment: Project p. 40, Partner Quiz p. 54; Bridge Unit: pp. 4, 111, 113, 116, 117, 124; Daily Cumulative Review: 11.3-11.5, 13.8, pp. 46, 47, 57; Enrichment Copymasters: 11.5, pp. 57, 58; Practice Workbook PE/TE: 11.3-11.5, 13.8, pp. 87-89, 109; Problem of the Day: 11.3-11.5, 13.8, pp. 31, 32, 39; Reteaching Copymasters: 11.3-11.5, 13.8, pp. 87-89, 109; 11.3-11.5, 13.8, pp. 87-89, 109 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 86, 88, 90, 91 Standard III. Apply transformations and use symmetry to analyze mathematical situations. Expectations: A. Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling. 1. Describe the transformation used to move a polygon in one quadrant to another quadrant in the coordinate plane. PE/TE: 522-525, 526-529, 530-533, 535, 558, 560, 561, 734, 735, 758 Additional TE: 510A-F TRP: Alternative Assessment: Partner Quiz p. 54; Daily Cumulative Review: 11.3-11.5, pp. 46, 47; Enrichment Copymasters: 11.5, pp. 57, 58; Practice Workbook PE/TE: 11.3-11.5, pp. 87-89; Problem of the Day: 11.3-11.5, pp. 31, 32; Reteaching Copymasters: 11.3-11.5, pp. 87-89; 11.3-11.5, pp. 87-89 22
B. Examine the congruence, similarity, and line or rotational symmetry of objects using transformations. 1. Determine the type of symmetry (point or line) found in a reflection or a rotation. PE/TE: 522-525, 526-529, 535, 558, 560, 734, 735 Additional TE: 510A-F TRP: Daily Cumulative Review: 11.3, 11.4, p. 46; Practice Workbook PE/TE: 11.3, 11.4, pp. 87, 88; Problem of the Day: 11.3, 11.4, pp. 31, 32; Reteaching Copymasters: 11.3, 11.4, pp. 87, 88; 11.3, 11.4, pp. 87, 88 Standard IV. Use visualization, spatial reasoning, and geometry modeling to solve problems. Expectations: A. Draw geometric objects with specified properties, such as side lengths or angle measures. 1. Draw two-dimensional objects from a geometric description and write a description of geometric properties for a given object. PE/TE: 35, 142, 170, 194, 418-419, 422, 428, 446, 476, 480, 496, 519, 520, 521, 524, 525, 527, 528, 529, 530, 531, 532, 535, 537, 539, 558, 560, 734, 735, 758 Additional TE: 1A-F, 102A-F, 154A-F, 408A-F, 458A-F, 510A-F TRP: Alternative Assessment: Partner Quiz p. 54; Bridge Unit: p. 12; Daily Cumulative Review: 11.3-11.6, pp. 46-47; Enrichment Copymasters: 11.4, 11.5, pp. 57-59; Practice Workbook PE/TE: 11.3-11.6, pp. 87-90; Problem of the Day: 11.3-11.6, pp. 31, 32; Reteaching Copymasters: 11.3-11.6, pp. 87-90; 11.3-11.6, pp. 87-90 23
B. Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume. 1. Construct nets for 3-dimensional figures. PE/TE: 571, 572, 574, 607, 611 Additional TE: 562A-F TRP: Alternative Assessment: Group and Individual pp. 81, 82; Bridge Unit: p. 78; Daily Cumulative Review: 12.2, p. 50; Enrichment Copymasters: 12.2, pp. 63, 64; Practice Workbook PE/TE: 12.2, p. 95; Problem of the Day: 12.2, p. 34; Reteaching Copymasters: 12.2, p. 95; 12.2, p. 95 Other Ancillaries: Preparation for Middle School Math, Grade 8: p. 58 2. Compare and contrast the number of faces, vertices, and edges of 3-dimensional figures. PE/TE: 572, 574, 585, 607, 610 Additional TE: 562A-F TRP: Alternative Assessment: Group and Individual pp. 80, 81; Daily Cumulative Review: 12.2, p. 50; Enrichment Copymasters: 12.2, pp. 63, 64; Practice Workbook PE/TE: 12.2, p. 95; Problem of the Day: 12.2, p. 34; Reteaching Copymasters: 12.2, p. 95; 12.2, p. 95 C. Use visual tools such as networks to represent and solve problems. 1. Given a network with up to six vertices, determine the number of paths. Related concepts are taught on the following pages: PE/TE: 33, 35, 492-493, 744 Additional TE: 1A-F, 458A-F 24
E. Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life. 1. Identify transformations in tessellations, use transformations to draw tessellations, and describe relationships among figures that tessellate. Prerequisite concepts are taught on the following pages: PE/TE: 522-525, 526-529, 530-533, 535, 558, 560, 561, 734, 735, 758 Additional TE: 510A-F TRP: Alternative Assessment: Partner Quiz p. 54; Daily Cumulative Review: 11.3-11.5; pp. 46, 47, Enrichment Copymasters: 11.5, pp. 57, 58; Practice Workbook PE/TE: 11.3-11.5, pp. 87-89; Problem of the Day: 11.3-11.5, pp. 31, 32; Reteaching Copymasters: 11.3-11.5, pp. 87-89; 11.3-11.5, pp. 87-89 25
Measurement Standard I. Understand measurable attributes of objects and the units, systems, and processes of measurement. Expectations: A. Understand both metric and customary systems of measurement. 1. Explain the relationship between the metric system and the base ten number system. PE/TE: 764 B. Understand relationships among units and convert from one unit to another within the same system. 1. Compare and convert units of measure for length, weight/mass, and volume within the U.S. customary system and within the metric system. PE/TE: 587, 600, 621, 639, 763, 764 2. Add and subtract mixed units of measure and express answers in appropriate form. Related concepts are taught on the following pages: PE/TE: 313 (#35), 319 (#32, 33), 577 (Ex. 2), 763, 764 26
C. Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. 1. Use appropriate units of measure to label surface area and volume. PE/TE: 576-579, 580-583, 584, 585, 586-589, 592-595, 596-599, 608, 609, 610, 611, 736, 737 Additional TE: 562A-F TRP: Alternative Assessment: Project pp. 37, 38, Partner Quiz p. 55; Bridge Unit: pp. 3, 4, 88, 89, 90, 91, 92, 93, 94, 98, 99, 100, 102, 103; Daily Cumulative Review: 12.3-12.7, pp. 51-53; Enrichment Copymasters: 12.3, pp. 65, 66; Practice Workbook PE/TE: 12.3-12.7, pp. 96-100; Problem of the Day: 12.3-12.7, pp. 34, 35, 36; Reteaching Copymasters: 12.3-12.7, pp. 96-100; 12.3-12.7, pp. 96-100 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 67, 68, 69, 70, 71, 72, 76, 77, 79 Standard II. Apply appropriate techniques, tools, and formulas to determine measurements. Expectations: A. Use common benchmarks to select appropriate methods for estimating measurements. 1. Use appropriate methods to approximate the surface area and volume of an irregular figure. PE/TE: 593, 595 Additional TE: 562A-F TRP: Daily Cumulative Review: 12.6, p. 52; Practice Workbook PE/TE: 12.6, p. 99; Problem of the Day: 12.6, p. 35; Reteaching Copymasters: 12.6, p. 99; 12.6, p. 99 27
B. Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision. 1. Analyze a variety of measurement situations to determine the necessary degree of accuracy and precision. PE/TE: 345, 418-419, 464-467, 468, 492-493, 499, 505, 508, 521, 540-541, 564-565, 587, 590-591, 646-647, 732 Additional TE: 308A-F, 408A-F, 458A-F, 510A-F, 562A-F TRP: Bridge Unit: pp. 68, 93, 101; Daily Cumulative Review: 10.2, p. 40; Practice Workbook PE/TE: 10.2, p. 77; Problem of the Day: 10.2, p. 28; Reteaching Copymasters: 10.2, p. 77; 10.2, p. 77 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 71, 78 C. Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes. 1. Use measurements and formulas to solve real-world and mathematical problems. PE/TE: 192-195, 199, 200, 420, 423, 426-429, 430, 431, 436, 437, 452, 454, 455, 492-493, 494-497, 499, 501, 512-515, 542, 544, 545, 553, 554, 555, 557, 560, 564-565, 566-569, 570, 576-579, 580-583, 584, 585, 586-589, 590-591, 592-595, 596-599, 600, 603, 604, 605, 607, 608, 609, 610, 611, 656, 663, 664, 722, 731, 733, 734, 735, 736, 737, 739, 752, 754, 755, 756 Additional TE: 154A-F, 408A-F, 458A-F, 510A-F, 562A-F, 616A-F TRP: Alternative Assessment: Project pp. 31, 32, 35-38, 40, Partner Quiz pp. 52, 55, Group and Individual pp. 65, 66; Bridge Unit: pp. 3, 4, 80-102, 103; Daily Cumulative Review: 4.8, 9.3, 9.4, 10.8, 11.1, 11.7, 11.9, 12.1, 12.3-12.8, 13.8, pp. 17, 37, 43, 45, 48-53, 57; Enrichment Copymasters: 9.3, 11.1, 12.1, 12.3 pp. 47, 48, 54-56, 61, 62, 65, 66; Practice Workbook PE/TE: 4.8, 9.3, 9.4, 10.8, 11.1, 11.7, 11.9, 12.1, 12.3-12.8, 13.8, pp. 33, 70, 71, 83, 85, 91, 93, 94, 96-101, 109; Problem of the Day: 4.8, 9.3, 9.4, 10.8, 11.1, 11.7, 11.9, 12.1, 12.3-12.8, 13.8, pp. 12, 25, 26, 30, 31, 33-36, 39; (Continued on next page) 28
Reteaching Copymasters: 4.8, 9.3, 9.4, 10.8, 11.1, 11.7, 11.9, 12.1, 12.3-12.8, 13.8, pp. 33, 70, 71, 83, 85, 91, 93, 94, 96-101, 109; 4.8, 9.3, 9.4, 10.8, 11.1, 11.7, 11.9, 12.1, 12.3-12.8, 13.8, pp. 33, 70, 71, 83, 85, 91, 93, 94, 96-101, 109 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 60-79 2. Using concrete materials or computer models, derive approximations for pi from measurements for circumference and diameter. PE/TE: 564-565 Additional TE: 562A-F 3. Create and solve problems by finding the circumference and/or area of a circle when given the diameter or radius. PE/TE: 564-565, 566-569, 570, 736 Additional TE: 562A-F TRP: Alternative Assessment: Project p. 37; Bridge Unit: pp. 4, 95, 96, 97, 98, 100, 101, 102, 103, Enrichment Copymasters: 12.1, pp. 61, 62; Practice Workbook PE/TE: 12.1, p. 94; Problem of the Day: 12.1, p. 34; Reteaching Copymasters: 12.1, p. 94; 12.1, p. 94 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 73, 74, 75, 76, 78, 79 29
D. Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders. 1. Investigate and describe the relationship between the area of the base and the volume of a prism, pyramid or cylinder. PE/TE: 580-583, 585, 586-589, 592-595, 608, 610, 611, 737 Additional TE: 562A-F TRP: Alternative Assessment: Partner Quiz p. 55; Bridge Unit: pp. 3, 91, 92, 93, 94, 103; Daily Cumulative Review: 12.4-12.6, pp. 51, 52; Practice Workbook PE/TE: 12.4-12.6, pp. 97-99; Problem of the Day: 12.4-12.6, p. 35; Reteaching Copymasters: 12.4-12.6, pp. 97-99; 12.4-12.6, pp. 97-99 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 70, 71, 72 E. Solve problems involving scale factors, using ratio and proportion. 1. Determine the unit rate. PE/TE: 362, 364, 365, 403 Additional TE: 360A-F TRP: Alternative Assessment: Project p. 29; Daily Cumulative Review: 8.1, p. 32; Practice Workbook PE/TE: 8.1, p. 60; Problem of the Day: 8.1, p. 22; Reteaching Copymasters: 8.1, p. 60; 8.1, p. 60 30
F. Solve simple problems involving rates and derived measurements for such attributes as velocity and density. 1. Apply rates to solve problems in real world situations. PE/TE: 23, 44, 73, 81, 95, 327, 331, 362, 364, 365, 371, 374, 386-389, 390, 403, 405, 621 Additional TE: 308A-F, 360A-F TRP: Alternative Assessment: Project p. 29; Bridge Unit pp. 66, 67, 68; Daily Cumulative Review: 8.1, p.32; Practice Workbook PE/TE: 8.1, p. 60; Problem of the Day: 8.1, p. 22; Reteaching Copymasters: 8.1, p. 60; 8.1, p. 60 Other Ancillaries: Preparation for Middle School Math, Grade 8: pp. 49, 50 31
Data Analysis and Probability Standard I. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them. Expectations: A. Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population. 1. Given a problem situation involving two populations, collect, analyze and interpret data. PE/TE: 239 (#23), 241, 675 (#15), 685 (#25) Additional TE: 202A-F, 666A-F TRP: Alternative Assessment: Project pp. 24, 41, Partner Quiz p. 57; Bridge Unit: p. 20; Daily Cumulative Review: 5.7, 14.2, 14.4, pp. 21, 58, 59; Practice Workbook PE/TE: 5.7, 14.2, 14.4, pp. 40, 111, 113; Problem of the Day: 5.7, 14.2, 14.4, pp. 15, 40, 41; Reteaching Copymasters: 5.7, 14.2, 14.4, pp. 40, 111, 113; 5.7, 14.2, 14.4, pp. 40, 111, 113 Other Ancillaries: Preparation for Middle School Math, Grade 8: p. 10 32
B. Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatter plots. 1. Organize, display and interpret data in a variety of ways including box-and-whisker plots. PE/TE: 676-679, 681, 686, 687, 710, 712, 713, 740 Additional TE: 666A-F TRP: Daily Cumulative Review: 14.3, p. 59; Practice Workbook PE/TE: 14.3, p. 112; Problem of the Day: 14.3, p. 40; Reteaching Copymasters: 14.3, p. 112; 14.3, p. 112 Other examples of graphical representations of data can be found on the following pages: PE/TE: 204-207, 208-211, 213, 214-217, 218-219, 220-223, 225, 230-233, 235, 236-239, 247, 248, 249, 250, 251, 345, 347, 358, 672-675, 709, 723, 724, 729, 761, 762 Additional TE: 202A-F, 204-207, 208-211, 213, 214-217, 218-219, 220-223, 225, 230-233, 235, 236-239, 247, 248, 249, 250, 251, 308A-F, 345, 347, 358, 666A-F, 672-675, 709, 723, 724, 729, 761, 762 TRP: Alternative Assessment: Project pp. 23, 24, Partner Quiz p. 48; Bridge Unit: p. 20; Daily Cumulative Review: 5.1-5.4, 5.6, 5.7, 14.2, pp. 18-21, 58; Enrichment Copymasters: 5.1, 5.4, pp. 22-28; Practice Workbook PE/TE: 5.1-5.4, 5.6, 5.7, 14.2, pp. 34-37, 39, 40, 111; Problem of the Day: 5.1-5.4, 5.6, 5.7, 14.2, pp. 13, 14, 15; Reteaching Copymasters: 5.1-5.4, 5.6, 5.7, 14.2, pp. 34-37, 39, 40, 111; 5.1-5.4, 5.6, 5.7, 14.2, pp. 34-37, 39, 40, 111 Other Ancillaries: Preparation for Middle School Math, Grade 8: p. 10 33
2. Construct circle graphs and interpret the meaning. PE/TE: 345, 347, 358, 762 Additional TE: 308A-F TRP: Daily Cumulative Review: 7.8, p. 30; Practice Workbook PE/TE: 7.8, p. 58; Problem of the Day: 7.8, p. 21; Reteaching Copymasters: 7.8, p. 58; 7.8, p. 58 Standard II. Select and use appropriate statistical methods to analyze data. Expectations: A. Find, use, and interpret measures of center and spread, including mean and interquartile range. 1. Compute, describe, and interpret the interquartile range. PE/TE: 676-679, 681, 686, 687, 710, 712, 740 Additional TE: 666A-F TRP: Daily Cumulative Review: 14.3, p. 59; Practice Workbook PE/TE: 14.3, p. 112; Problem of the Day: 14.3, p. 40; Reteaching Copymasters: 14.3, p. 112; 14.3, p. 112 34
B. Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots. 1. Describe the relationship between a data set and its corresponding box plot or circle graph. PE/TE: 345, 347, 358, 407, 676-679, 680, 681, 686, 687, 710, 712, 713, 740, 762 Additional TE: 308A-F, 666A-F TRP: Daily Cumulative Review: 14.3, p. 59; Practice Workbook PE/TE: 14.3, p. 112; Problem of the Day: 14.3, p. 40; Reteaching Copymasters: 14.3, p. 112; 14.3, p. 112 Standard III. Develop and evaluate inferences and predictions that are based on data. Expectations: A. Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken. 1. Make inferences and predictions based on the analysis of sample data. PE/TE: 211, 235, 236-239, 240-241, 243, 244, 245, 249, 647, 649, 650, 651 Additional TE: 202A-F, 616A-F TRP: Alternative Assessment: Project p. 24; Bridge Unit: p. 20; Daily Cumulative Review: 5.7, 5.8, 13.6, pp. 21, 56; Practice Workbook PE/TE: 5.7, 5.8, 13.6, pp. 40, 41, 107; Problem of the Day: 5.7, 5.8, 13.6, pp. 15, 38; Reteaching Copymasters: 5.7, 5.8, 13.6, pp. 40, 41, 107; 5.7, 5.8, 13.6, pp. 40, 41, 107 Other Ancillaries: Preparation for Middle School Math, Grade 8: p. 10 35
Standard IV. Understand and apply basic concepts of probability Expectations: A. Understand and use appropriate terminology to describe complementary and mutually exclusive events. 1. Identify and describe mutually exclusive events. Related concepts are taught on the following pages: PE/TE: 399, 400, 401, 405, 730 Additional TE: 360A-F TRP: Alternative Assessment: Project p. 30; Daily Cumulative Review: 8.8, p. 35; Enrichment Copymasters: 8.8, pp. 43, 44; Practice Workbook PE/TE: 8.8, p. 67; Problem of the Day: 8.8, p. 24; Reteaching Copymasters: 8.8, p. 67; 8.8, p. 67 B. Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations. 1. Investigate and describe the difference between the probability of an event found through simulation versus the theoretical probability of that same event. PE/TE: 240-241, 242-245, 249, 250, 251, 398-401, 405, 724, 730 Additional TE: 202A-F, 360A-F TRP: Alternative Assessment: Project pp. 21, 30; Daily Cumulative Review: 5.8, 8.8, pp. 21, 35; Enrichment Copymasters: 8.8, pp. 43, 44; Practice Workbook PE/TE: 5.8, 8.8, pp. 41, 67; Problem of the Day: 5.8, 8.8, pp. 15, 24; Reteaching Copymasters: 5.8, 8.8, pp. 41, 67; 5.8, 8.8, pp. 41, 67 36
C. Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models. 1. Determine the number of possible outcomes in a multi-stage event using the fundamental counting principle or other techniques. PE/TE: 392-395, 405, 406, 407, 730, 759 Additional TE: 360A-F TRP: Alternative Assessment: Group and Individual, pp.73, 74; Daily Cumulative Review: 8.7, p. 35; Practice Workbook PE/TE: 8.7, p. 66; Problem of the Day: 8.7, p. 24; Reteaching Copymasters: 8.7, p. 66; 8.7, p. 66 2. Compute the probability of two independent events. PE/TE: 399, 400, 401, 405, 730 Additional TE: 360A-F TRP: Alternative Assessment: Project p. 30; Daily Cumulative Review: 8.8, p. 35; Enrichment Copymasters: 8.8, pp. 43, 44; Practice Workbook PE/TE: 8.8, p. 67; Problem of the Day: 8.8, p. 24; Reteaching Copymasters: 8.8, p. 67; 8.8, p. 67 37