correlated to the South Carolina Grade 6 Mathematics Standards 4/2001 2002
Introduction to Middle Grades MathThematics Books 1 3 The Middle Grades MathThematics program is a complete middle-grade mathematics curriculum designed to implement the National Council of Teachers of Mathematics Curriculum and the Evaluation Standards for School Mathematics. The following are some of the key features. Easy-to-follow lessons begin with a Setting the Stage feature that provides either a reading, a graph, an activity, or a game to introduce the section and motivate students. Each section uses Explorations that actively involve students in investigating math concepts, learning math skills, and solving problems in a variety of real-world contexts. Lab Sheets are provided for the teacher in the Resource Book Modules. A summary of Key Concepts helps students study and review the section while developing note-taking skills. Exercises, which include a Reflecting on the Section feature, develop numerical and problem-solving skills and the ability to write about and discuss mathematics. At the end of every section, Extra Skill Practice provides exercises that help the student assess understanding of important skills before starting the next section. Assessment opportunities include a Module Review and Assessment in the Pupil Edition and a Module Quiz and a Module Test (Forms A and B) in the Teacher s Resource Book. The Teacher s Resource Book also provides Standardized and Performance assessment options for each module, as well as Cumulative Tests on every two modules, a Mid-Year Test for Books 2 and 3, and an End-of-Year Test. Additional tests can be created using the Practice and Test Generator. Students who complete the Middle Grades MathThematics curriculum will have acquired the mathematical skills necessary to solve problems, to reason inductively and deductively, and to apply the numerical and spatial concepts necessary to function according to their needs in a technological society. Students will be independent learners, well prepared for both work and further experiences in mathematics. They will have the knowledge, ability, and confidence to explore mathematics at the secondary level. They will be experienced in working with extended projects, cooperative learning activities, technology, hands-on materials, applications, modeling, and new assessment techniques. Middle Grades MathThematics students learn to think mathematically, to become decision-makers, and to view mathematics as relevant to their lives.
Teachers are supported by a wealth of ancillary materials. A complete listing of available program components appears below. Middle Grades MathThematics Books 1 3 Components Pupil s Edition Annotated Teacher s Edition Teacher s Resource Package Annotated Teacher s Edition Resource Book Modules 1 8 Professional Development Handbook Other Ancillaries Student Manipulatives Kit Overhead Manipulatives Kit Spanish Resources (one for each grade: 6, 7, and 8) Multi-language Glossary Preparation for Middle School Math, PE (one for each grade: 6, 7, and 8) Preparation for Middle School Math, TE (one for each grade: 6, 7, and 8) Test and Practice Generator CD-ROM Personal Student Tutor CD-ROM
Design of the Teacher Resource Books Each Teacher s Resource Book for the Middle Grades MathThematics series include the following types of resources: Overviews Home Involvement Teaching Suggestions Labsheets Extended Exploration Guides Alternate Extended Exploration Warm-Up Exercises and Quick Quizzes Practice and Applications Study Guides Technology Activities Assessment Standardized Assessment Module Performance Assessment Answers Each Teacher s Resource Book has a dual numbering system. The first number represents the chapter with which the resource page is to be used, and the number following the dash sequences the resource page within that chapter. For example, The 3 in 3-18 means that the page is from the Chapter 3 part of the Teacher s Resource Book: Modules 3 and 4, and the 18 represents the page number within the Chapter 3 part of the Teacher s Resource Book. Certain pages within each Teacher s Resource Book begin with a letter code rather than a Chapter number: CT = Cumulative Test (at the end of all four resource books); MYT = Mid-Year-Test (at the end of the Teacher s Resource Book: Modules 3 and 4 for Books 2 and 3 ); EOYT = End-of-Year Test (at the end of the Teacher s Resource Book: Modules 7 and 8)
Math Thematics Book 1 correlated to the South Carolina Grade 6 Mathematics Standards Number and Operations Standard I. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. A. Work flexibly with fractions, decimals, and percents to solve problems. 1. Show the relationship among fractions, decimals, and percents. PE/TE: 135, 138, 139, 141, 174, 175, 176, 178, 181, 199, 200, 201, 202, 204, 206, 315, 316, 317, 376, 439-440, 444, 445, 446, 448, 450 RBM 1&2: 2-40, 2-42, 2-43, 2-65, 2-66, 2-77, 2-85, 2-100, 2-101 Assessment: 2-109, 2-111, 2-112 RBM 3&4: 3-18, 3-19, 3-20, 3-21, 3-32, 3-33, 3-34, 3-35, 3-37, 3-58, 3-59, 3-73, 3-74, 3-78, 3-81, 3-85, 3-86, 3-90, 3-92, 3-95, 3-96, 3-101 Assessment: 3-104, 3-105, 3-107 RBM 5&6: 5-11, 5-12, 5-64, 5-75, 5-76, 6-43, 6-44, 6-46, 6-47, 6-48, 6-54, 6-67, 6-75, 6-78, 6-94, 6-95 RBM 7&8: Assessment: CT-2, EOYT-1 Preparation for Middle School Math PE, Grade 6: 47-50, 51-54, 58, 59, 60 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 1
B. Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line. 1. Use order symbols to compare two fractions, two decimals, or two percents. PE/TE: 136-137, 138, 140, 141, 155, 175, 176, 178, 181, 310-320, 315-320, 376 RBM 1&2: 2-41, 2-42, 2-43, 2-86, 2-89, 2-100, 2-101 Assessment: 2-109, 2-111, 2-112, CT-2 RBM 3&4: 3-18, 3-19, 3-20, 3-21, 3-59, 3-78 Assessment: 3-104 RBM 5&6: 5-9, 5-10, 5-11, 5-12, 5-13, 5-15, 5-57, 5-63, 5-64, 5-72, 5-74, 5-75, 5-76 Assessment: 5-89 C. Develop meaning for percents greater than 100 and less than 1. 1. Use models to represent percents greater than 100% and solve problems involving them. PE/TE: 557-559, 561, 563, 586 RBM 7&8: 8-25, 8-26, 8-27, 8-28, 8-29, 8-48, 8-57, 8-65, 8-70, 8-76, 8-77, 8-78, 8-87, 8-88, 8-90 D. Understand and use ratios and proportions to represent quantitative relationships. 1. Connect the concept of ratio and fractions by determining the equivalence of two ratios. PE/TE: 381-387, 388, 414-415, 422, 450 RBM 5&6: 6-9, 6-10, 6-11, 6-12, 6-14, 6-29, 6-34, 6-62, 6-63, 6-65, 6-68, 6-69, 6-72, 6-77, 6-78, 6-79, 6-80, 6-88, 6-89 Assessment: 6-98, 6-99, 6-100, 6-101, 6-102, 6-103, CT-1 RBM 7&8: Assessment: EOYT-2 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 2
E. Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation. 1. Evaluate powers of ten up to 10 6. PE/TE: 255, 260, 262 RBM 3&4: 4-20, 4-23, 4-24 Assessment: 4-99 RBM 7&8: 8-18, 8-19, 8-20, 8-21, 8-22, 8-23 Assessment: CT-2 F. Use factors, multiples, prime factorization, and relatively prime numbers to solve problems. 1. Solve problems using prime factorization, common multiples, and common factors, and explain the reasoning used. PE/TE: 251-253, 256, 257, 258, 259, 260, 262, 267, 268, 269, 270, 272, 296, 300, 301, 303, 304, 306 RBM 3&4: 4-18, 4-19, 4-21, 4-22, 4-23, 4-24, 4-27, 4-28, 4-29, 4-31, 4-44, 4-45, 4-47, 4-48, 4-49, 4-53, 4-58, 4-65, 4-66, 4-69, 4-72, 4-73, 4-74, 4-78, 4-79, 4-84, 4-85, 4-86, 4-87, 4-88, 4-94, 4-95 Assessment: 4-99, 4-100, 4-102, 4-104, CT-2 Preparation for Middle School Math PE, Grade 6: 32-36, 37-41 G. Develop meaning for integers and represent and compare quantities with them. 1. Use integers to describe real world phenomena in order to develop their meaning. PE/TE: 510-512, 516, 517, 518, 519, 520, 521, 523 RBM 7&8: 7-41, 7-42, 7-44, 7-45, 7-46, 7-71, 7-79, 7-96, 7-97 Assessment: CT-1, CT-2 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 3
Standard II. Understand meanings of operations and how they relate to one another. A. Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers. 1. Explain the meaning and effects of adding, subtracting, multiplying and dividing. PE/TE: 142-151, 155, 207-210, 212, 213, 214, 216, 217, 221-222, 223, 225, 226, 228, 231, 264-272, 273-275, 278, 279, 280, 281, 292, 306, 307, 332-339, 341-352, 355-357, 359, 360, 362, 363, 364-374, 376, 377, 526-538, 586, 592, 593, 594, 595 RBM 1&2: 2-45, 2-46, 2-47, 2-48, 2-49, 2-78, 2-87, 2-89, 2-102, 2-103, 2-104 Assessment: 2-109, 2-111, CT-1, CT-2 RBM 3&4: 3-37, 3-38, 3-39, 3-40, 3-41, 3-42, 3-45, 3-46, 3-47, 3-48, 3-49, 3-61, 3-62, 3-64, 3-74, 3-75, 3-82, 3-83, 3-84, 3-86, 3-97, 3-98, 3-100, 3-101, 4-26, 4-27, 4-28, 4-29, 4-31, 4-32, 4-34, 4-35, 4-54, 4-55, 4-66, 4-67, 4-74, 4-75, 4-79, 4-80, 4-86, 4-87, 4-88, 4-89, 4-90 Assessment: 3-106, 3-108, 3-109, 4-99, 4-100, 4-101, 4-102, 4-103, 4-104, CT-2 RBM 5&6: 5-22, 5-23, 5-24, 5-25, 5-27, 5-28, 5-29, 5-30, 5-31, 5-32, 5-34, 5-35, 5-36, 5-37, 5-38, 5-39, 5-41, 5-42, 5-43, 5-44, 5-45, 5-46, 5-49, 5-51, 5-59, 5-60, 5-61, 5-62, 5-66, 5-67, 5-68, 5-69, 5-70, 5-71, 5-72, 5-73, 5-79, 5-80, 5-81, 5-82, 5-83, 5-84, 5-85, 5-86 Assessment: 5-89, 5-90, 5-91, 5-92, 5-93, 5-94, CT-1 RBM 7&8: 8-9, 8-10, 8-11, 8-12, 8-13, 8-14, 8-16, 8-43, 8-55, 8-60, 8-61, 8-62, 8-69, 8-71, 8-72 Assessment: 8-87, 8-88, 8-90, 8-92, CT-2, EOYT-1, EOYT-3 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 4
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 commutative, associative, and distributive properties to simplify computations with whole numbers, fractions, and decimals. PE/TE: 53, 356, 358, 359, 377, 537 RBM 1&2: 1-37 Assessment: CT-1 RBM 5&6: 5-36, 5-37, 5-83, 5-84 RBM 7&8: 8-14 Assessment: CT-2, EOYT-1, EOYT-3 Standard III. Compute fluently and make reasonable estimates. 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 requiring the addition and subtraction of fractions and decimals. PE/TE: 142-151, 155, 332-339, 341-352, 361, 376, 377, 592, 593, 594 RBM 1&2: 2-45, 2-46, 2-47, 2-48, 2-49, 2-78, 2-87, 2-89, 2-102, 2-103, 2-104 Assessment: 2-109, 2-111, 2-112, CT-2 RBM 5&6: 5-22, 5-23, 5-24, 5-25, 5-27, 5-28, 5-29, 5-30, 5-31, 5-32, 5-34, 5-49, 5-59, 5-60, 5-66, 5-67, 5-68, 5-72, 5-73, 5-79, 5-80, 5-81, 5-82 Assessment: 5-89, 5-90, 5-91, 5-92, 5-93, 5-94, CT-1 RBM 7&8: Assessment: EOYT-1 Preparation for Middle School Math PE, Grade 6: 7, 8, 9, 10 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 5
B. Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use. 1. Divide commonly used fractions (including decimals) using models. PE/TE: 207-210, 213, 214, 217, 221-222, 223, 225, 228, 231, 364-374, 377 RBM 3&4: 3-37, 3-38, 3-39, 3-40, 3-41, 3-42, 3-45, 3-46, 3-47, 3-49, 3-61, 3-62, 3-64, 3-74, 3-75, 3-82, 3-84, 3-86, 3-97, 3-98, 3-100, 3-101 Assessment: 3-106, 3-108, 3-109 RBM 5&6: 5-41, 5-42, 5-43, 5-44, 5-45, 5-46, 5-51, 5-62, 5-70, 5-71, 5-73, 5-85, 5-86 Assessment: 5-91, 5-93, 5-94 2. Use models and numbers to develop and analyze algorithms with fractions and decimals. PE/TE: 142-151, 155, 207-210, 212, 213, 214, 216, 217, 221-222, 223, 225, 226, 228, 231, 264-272, 273-275, 278, 279, 280, 281, 292, 306, 307, 332-339, 341-352, 355-357, 359, 360, 362, 363, 364-374, 376, 377 RBM 1&2: 2-45, 2-46, 2-47, 2-48, 2-49, 2-78, 2-87, 2-89, 2-102, 2-103, 2-104 Assessment: 2-109, 2-111, CT-2 RBM 3&4: 3-37, 3-38, 3-39, 3-40, 3-41, 3-42, 3-45, 3-46, 3-47, 3-48, 3-49, 3-61, 3-62, 3-64, 3-74, 3-75, 3-82, 3-83, 3-84, 3-86, 3-97, 3-98, 3-100, 3-101, 4-26, 4-27, 4-28, 4-29, 4-31, 4-32, 4-34, 4-35, 4-54, 4-55, 4-66, 4-67, 4-74, 4-75, 4-79, 4-80, 4-86, 4-87, 4-88, 4-89, 4-90 Assessment: 3-106, 3-108, 3-109, 4-99, 4-100, 4-101, 4-102, 4-103, 4-104 RBM 5&6: 5-22, 5-23, 5-24, 5-25, 5-27, 5-28, 5-29, 5-30, 5-31, 5-32, 5-34, 5-35, 5-36, 5-37, 5-38, 5-39, 5-41, 5-42, 5-43, 5-44, 5-45, 5-46, 5-49, 5-51, 5-59, 5-60, 5-61, 5-62, 5-66, 5-67, 5-68, 5-69, 5-70, 5-71, 5-72, 5-73, 5-79, 5-80, 5-81, 5-82, 5-83, 5-84, 5-85, 5-86 Assessment: 5-89, 5-90, 5-91, 5-92, 5-93, 5-94, CT-1, CT-2 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 6
3. Add, subtract, multiply and divide fractions (including decimals) to solve a variety of applied and mathematical problem situations. PE/TE: 142-151, 155, 207-210, 212, 213, 214, 216, 217, 221-222, 223, 225, 227, 226, 228, 231, 264-272, 273-275, 278, 279, 280, 281, 292, 306, 307, 332-339, 341-352, 355-357, 359, 360, 362, 363, 364-374, 376, 377 RBM 1&2: 2-45, 2-46, 2-47, 2-48, 2-49, 2-78, 2-87, 2-89, 2-102, 2-103, 2-104 Assessment: 2-109, 2-111 RBM 3&4: 3-37, 3-38, 3-39, 3-40, 3-41, 3-42, 3-45, 3-46, 3-47, 3-48, 3-49, 3-61, 3-62, 3-64, 3-74, 3-75, 3-82, 3-83, 3-84, 3-86, 3-97, 3-98, 3-100, 3-101, 4-26, 4-27, 4-28, 4-29, 4-31, 4-32, 4-34, 4-35, 4-54, 4-55, 4-66, 4-67, 4-74, 4-75, 4-79, 4-80, 4-86, 4-87, 4-88, 4-89, 4-90 Assessment: 3-106, 3-108, 3-109, 4-99, 4-100, 4-101, 4-102, 4-103, 4-104, CT-1 RBM 5&6: 5-22, 5-23, 5-24, 5-25, 5-27, 5-28, 5-29, 5-30, 5-31, 5-32, 5-34, 5-35, 5-36, 5-37, 5-38, 5-39, 5-41, 5-42, 5-43, 5-44, 5-45, 5-46, 5-49, 5-51, 5-59, 5-60, 5-61, 5-62, 5-66, 5-67, 5-68, 5-69, 5-70, 5-71, 5-72, 5-73, 5-79, 5-80, 5-81, 5-82, 5-83, 5-84, 5-85, 5-86 Assessment: 5-89, 5-90, 5-91, 5-92, 5-93, 5-94, CT-1 C. Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results. 1. Estimate the sums and differences of fractions, describe the method used, and determine the reasonableness of results. PE/TE: 342, 343, 347, 348, 349 RBM 5&6: 5-28, 5-30, 5-31, 5-49, 5-67, 5-73, 5-81, 5-82 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 7
6-8: Algebra Standard I. Understand patterns, relations, and functions. A. Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules. 1. Describe, extend, and write rules for a wide variety of patterns. PE/TE: 2-12, 26, 27, 33-34, 35, 37, 55, 62, 68, 69, 71, 76, 77, 93, 163-164, 165, 170, 179, 230, 254, 255, 260, 261, 266-267, 282-284, 287, 288, 289, 291, 293, 295, 313, 390, 391, 392, 393, 394, 395, 396, 402-404, 406, 408, 409, 410, 411, 415, 416-417, 418, 419, 420, 421, 422, 427-428, 431, 433, 434, 447, 450, 451, 544, 555, 556, 559, 605 RBM 1&2: 1-9, 1-10, 1-11, 1-12, 1-13, 1-15, 1-22, 1-26, 1-27, 1-28, 1-38, 1-43, 1-47, 1-48, 1-56, 1-67, 1-73, 1-74, 1-82, 1-84, 1-85, 1-91, 1-98, 1-99, 2-54 Assessment: 1-100, 1-101, 1-103, 1-105, CT-1 RBM 3&4: 3-11, 3-12, 3-16, 3-20, 3-77, 3-88, 4-20, 4-23, 4-27, 4-37, 4-39, 4-40, 4-41, 4-42, 4-44, 4-47, 4-57, 4-58, 4-68, 4-69, 4-76, 4-80, 4-92, 4-93 Assessment: 3-105, 3-107, 3-109, 4-99, 4-100, 4-101, 4-103, 4-104 RBM 5&6: 5-10, 6-15, 6-16, 6-17, 6-19, 6-22, 6-23, 6-24, 6-25, 6-26, 6-28, 6-29, 6-30, 6-31, 6-32, 6-34, 6-36, 6-37, 6-38, 6-39, 6-40, 6-47, 6-65, 6-66, 6-69, 6-70, 6-71, 6-72, 6-73, 6-74, 6-77, 6-78, 6-81, 6-82, 6-83, 6-84, 6-86, 6-87, 6-88, 6-89, 6-90, 6-91, 6-92,6-93, 6-96, 6-97 Assessment: 6-98, 6-99, 6-100, 6-101, 6-102, 6-103 RBM 7&8: 8-19, 8-25, 8-26, 8-27, 8-57, 8-64, 8-70, 8-76, 8-77, 8-78 Assessment: 8-87, EOYT-1 Preparation for Middle School Math PE, Grade 6: 11-16, 27-31, 75 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 8
Standard II. Represent and analyze mathematical situations and structures using algebraic symbols. A. Develop an initial conceptual understanding of different uses of variables. 1. Use order of operations to evaluate numerical expressions. PE/TE: 48-51, 53, 54, 55, 56, 62, 77 RBM 1&2: 1-35, 1-36, 1-37, 1-38, 1-40, 1-70, 1-79, 1-83, 1-92, 1-93 Assessment: 1-102, 1-104, 1-105, CT-1 RBM 7&8: Assessment: EOYT-1 B. Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope. 1. Write simple equations and inequalities accurately to represent relationships. PE/TE: 287, 288, 289, 291, 293, 415, 416-417, 419, 420, 421, 422, 427-428, 431, 433, 437, 447, 451 RBM 3&4: 4-39, 4-40, 4-41, 4-42, 4-80, 4-92, 4-93 Assessment: 4-101, 4-103, 4-104 RBM 5&6: 6-29, 6-30, 6-31, 6-32, 6-34, 6-36, 6-37, 6-38, 6-39, 6-41, 6-47,6-72, 6-74, 6-88, 6-89, 6-90, 6-91, 6-92, 6-93 D. Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations. 1. Use commutative, associative and distributive properties to examine equivalence of a variety of simple algebraic expressions. PE/TE: 53, 356, 358, 359, 377, 537 RBM 1&2: 1-37 RBM 5&6: 5-36, 5-83, 5-84 RBM 7&8: 8-14 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 9
Standard III. Use mathematical models to represent and understand quantitative relationships. A. Model and solve contextualized problems using various representations, such as graphs, tables, and equations. 1. Use graphs and tables to solve applied problems. PE/TE: 10 (#9), 27, 33, 34, 37 (#9), 68, 71, 77 (#32), 93, 254, 255, 287, 289, 391, 393, 394, 395, 396, 402-403, 404, 406, 408, 409, 411, 450 RBM 1&2: 1-13, 1-22, 1-26, 1-27, 1-28, 1-47, 1-67, 1-74, 1-81, 1-82, 1-84, 1-91, 1-98, 1-99 Assessment: 1-100 RBM 3&4: 4-20, 4-39, 4-40, 4-61 Assessment: CT-1, CT-2 RBM 5&6: 6-15, 6-16, 6-17, 6-19, 6-23, 6-24, 6-25, 6-26, 6-49, 6-50, 6-51, 6-69, 6-71, 6-82, 6-83, 6-84, 6-86, 6-87, 6-96, 6-97 Assessment: 6-98, 6-99, 6-101 Preparation for Middle School Math PE, Grade 6: 75 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 10
Geometry Standard I. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. A. Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties. 1. Compare and contrast prisms, cylinders and pyramids with the polygons or circles that constitute their faces. PE/TE: 469, 470, 471, 472, 473, 475, 476, 478, 479, 482, 485, 502, 504, 506, 522 RBM 7&8: 7-17, 7-18, 7-19, 7-20, 7-21, 7-23, 7-25, 7-26, 7-36, 7-37, 7-38, 7-50, 7-51, 7-52, 7-74, 7-86, 7-87, 7-88 Assessment: 7-101, 7-102, 7-104, CT-1 B. Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects. 1. Describe relationships among angles, side lengths, perimeters, and areas of similar polygons. PE/TE: 423, 424-426, 428, 430, 431, 432, 433, 437, 451 RBM 5&6: 6-35, 6-36, 6-37, 6-38, 6-39, 6-41, 6-66, 6-73, 6-78, 6-91, 6-93 Assessment: 6-99, 6-100, 6-101, 6-102, 6-103, CT-1, CT-2 C. Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship. 1. Identify and describe point and line symmetry in two-dimensional shapes. PE/TE: 85, 86, 87, 88, 89, 90, 91, 92, 154 RBM 1&2: 2-11, 2-12, 2-13, 2-14, 2-15, 2-52, 2-73, 2-80, 2-88, 2-91, 2-92 Assessment: 2-108, 2-110, CT-2 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 11
2. Distinguish between similarity and congruence. PE/TE: 85, 88, 98, 99, 100, 103, 106, 120-123, 124-130, 132, 140, 423, 424-426, 428, 430, 431, 432, 433, 437, 447, 451 RBM 1&2: 2-11, 2-12, 2-19, 2-20, 2-21, 2-24, 2-32, 2-33, 2-34, 2-35, 2-36, 2-37, 2-39, 2-43, 2-52, 2-61, 2-62, 2-63, 2-64, 2-76, 2-81, 2-84, 2-89, 2-97, 2-98, 2-105, 2-106 Assessment: 2-109 RBM 5&6: 6-35, 6-36, 6-37, 6-38, 6-39, 6-41, 6-66, 6-73, 6-78, 6-91, 6-93 Assessment: 6-99, 6-100, 6-101, 6-102, 6-103 Standard II. Specify locations and describe spatial relationships using coordinate geometry and other representational systems. A. Use coordinate geometry to represent and examine the properties of geometric shapes. 1. Given the coordinates of three vertices of a rectangle or square oriented horizontally or vertically, use the first quadrant of the rectangular coordinate system to locate the other vertex. Prerequisite concepts are taught on the following pages: PE/TE: 283-284, 288, 289, 290, 293, 514, 515, 516, 518, 519, 520, 523 RBM 3&4: 4-37, 4-38, 4-40, 4-41, 4-57, 4-68, 4-76, 4-91, 4-92, 4-93 Assessment: 4-101, 4-103, 4-105 RBM 7&8: 7-43, 7-44, 7-45, 7-46, 7-59, 7-80, 7-96, 7-98 B. Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides 1. Plot the vertices of squares and rectangles and determine the relationship among the coordinates. PE/TE: 290 (#15, 16) RBM 3&4: 4-41 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 12
Standard III. Apply transformations and use symmetry to analyze mathematical situations. 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 from one location to another in the first quadrant. PE/TE: 120-130, 131, 132, 140, 155 RBM 1&2: 2-32, 2-33, 2-34, 2-35, 2-36, 2-37, 2-39, 2-61, 2-62, 2-63, 2-64, 2-67, 2-76, 2-84, 2-89, 2-97, 2-98, 2-105, 2-106 Assessment: 2-109, CT-2 B. Examine the congruence, similarity, and line or rotational symmetry of objects using transformations. 1. Apply a transformation to a polygon and describe how it has changed. PE/TE: 120-130, 131, 132, 140, 155 RBM 1&2: 2-32, 2-33, 2-34, 2-35, 2-36, 2-37, 2-39, 2-61, 2-62, 2-63, 2-64, 2-67, 2-76, 2-84, 2-89, 2-97, 2-98, 2-105, 2-106 Assessment: 2-109, CT-2 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 13
Standard IV. Use visualization, spatial reasoning, and geometry modeling to solve problems. A. Draw geometric objects with specified properties, such as side lengths or angle measures. 1. Use symbols for parallel lines and perpendicular lines to describe polygons and figures where appropriate. PE/TE: 19, 20, 23, 25, 38, 82-83, 87, 458 RBM 1&2: 1-18, 1-19, 1-20, 1-29, 1-87, 1-100, 2-10, 2-12 Assessment: 1-100, CT-2 RBM 7&8: 7-11 Preparation for Middle School Math PE, Grade 6: 61, 62, 63, 64 B. Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume. 1. Given the top, side, and front views, construct a 3-dimensional model using cubes. PE/TE: 468, 469, 470 RBM 7&8: 7-17, 7-18 E. Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life. 1. Identify and apply geometric concepts in a variety of practical contexts. PE/TE: 428, 429, 430, 435, 436, 446, 456, 457, 459, 462, 470, 474, 475, 479, 480, 482, 485, 487, 489, 490, 492, 493, 494, 495, 499, 502, 505, 506, 640 RBM 5&6: 6-37, 6-38, 6-41, 6-47 RBM 7&8: 7-10, 7-11, 7-13, 7-18, 7-20, 7-23, 7-24, 7-25, 7-26, 7-28, 7-29, 7-30, 7-31, 7-32, 7-34, 7-36, 7-37, 7-38 Assessment: CT-2 Preparation for Middle School Math PE, Grade 6: 72, 73, 74, 76, 77, 78, 79, 80, 81 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 14
Measurement Standard I. Understand measurable attributes of objects and the units, systems, and processes of measurement. C. Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. 1. Estimate angle measure using 45 degrees, 90 degrees, 180 degrees, 270 degrees, and 360 degrees as referents and use the appropriate tools to measure any angle. PE/TE: 19, 25, 28, 76, 429-430, 431, 434, 435, 436, 437, 451 RBM 1&2: 1-18 RBM 5&6: 6-38, 6-40, 6-41, 6-53, 6-66, 6-74, 6-78, 6-92, 6-93 Assessment: 6-100, 6-102, CT-2 Preparation for Middle School Math PE, Grade 6: 67-71 2. Use appropriate units of measure to label angles, perimeter, and area. PE/TE: 287, 288, 290, 291, 293, 429-430, 431, 434, 435, 436, 437, 451, 454-465, 466, 490-492, 493, 494, 497, 499-501, 505, 507, 508, 519, 523 RBM 3&4: 4-39, 4-40, 4-41 RBM 5&6: 6-38, 6-40, 6-41, 6-53, 6-66, 6-73, 6-74, 6-78, 6-92 Assessment: 6-100, 6-102 RBM 7&8: 7-9, 7-10, 7-11, 7-12, 7-13, 7-14, 7-16, 7-30, 7-34, 7-35, 7-37, 7-47, 7-48, 7-49, 7-63, 7-66, 7-67, 7-69, 7-70, 7-72, 7-73, 7-76, 7-77, 7-81, 7-83, 7-84, 7-85, 7-91, 7-92, 7-93, 7-94, 7-95 Assessment: 7-101, 7-102, 7-103, 7-104, 7-105, 7-106, CT-1, CT-2, EOYT-3 Preparation for Middle School Math PE, Grade 6: 67-71, 72-76, 77-81 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 15
Standard II. Apply appropriate techniques, tools, and formulas to determine measurements. A. Use common benchmarks to select appropriate methods for estimating measurements. 1. Estimate and then determine length, weight/mass, area, and volume/capacity, using standard and nonstandard units of measure. PE/TE: 161-164, 165, 167, 168, 170, 178, 230, 321-329, 330, 331,338, 353, 354-355, 358, 359, 362, 363, 376, 377, 454-465, 468-470, 473, 474, 475, 476, 478, 479-486, 487, 490-492, 493, 494, 495, 496, 497, 499-501, 502-503, 504, 505, 506, 507, 508, 519, 522, 523, 555-557, 559, 560, 562, 563, 564, 586, 599, 600, 605 RBM 3&4: 3-10, 3-11, 3-12, 3-13, 3-14, 3-20, 3-76, 3-77, 3-87, 3-88, 3-89 RBM 5&6: 5-15, 5-16, 5-17, 5-18, 5-19, 5-20, 5-26, 5-34, 5-35, 5-37, 5-39, 5-58, 5-61, 5-65, 5-69, 5-73, 5-77, 5-78, 5-83, 5-84 RBM 7&8: 7-9, 7-10, 7-11, 7-12, 7-13, 7-14, 7-17, 7-18, 7-19, 7-20, 7-21, 7-23, 7-24, 7-25, 7-26, 7-28, 7-30, 7-31, 7-32, 7-33, 7-34, 7-35, 7-36, 7-37, 7-38, 7-40, 7-45, 7-54, 7-66, 7-67, 7-68, 7-69, 7-70, 7-72, 7-73, 7-74, 7-75, 7-76, 7-77, 7-78, 7-81, 7-82, 7-83, 7-84, 7-85, 7-86, 7-87, 7-88, 7-89, 7-90, 7-91, 7-92, 7-93, 7-94, 7-95, 7-98, 7-99, 7-100, 8-26, 8-27, 8-28, 8-29, 8-31, 8-52, 8-57, 8-64, 8-70, 8-76, 8-77, 8-78 Assessment: 7-101, 7-102, 7-103, 7-104, 7-105, 7-106, 7-107, 8-87, 8-88, 8-90, 8-92 Preparation for Middle School Math PE, Grade 6: 72-76, 77-81 2. Estimate and justify estimates of perimeter and area of irregular shapes. PE/TE: 464 RBM 7&8: 7-14, 7-66, 7-73, 7-81 Assessment: 7-101, 7-106 Preparation for Middle School Math PE, Grade 6: 80, 81 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 16
B. Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision. 1. Select and use appropriate tools and units to measure to the degree of accuracy required in a particular situation. PE/TE: 24, 121, 161, 162, 322, 328, 331, 337, 342, 344, 365, 376, 387, 398, 400, 401, 412, 429, 430, 431, 434, 435, 436, 437, 451, 455, 458, 459, 463, 476, 481, 490, 519, 522, 546, 555, 556 RBM 1&2: 1-21, 2-32; RBM 3&4: 3-10, 3-11, 3-76, 3-87, 3-89 Assessment: 3-104, 3-105, 3-107, 3-109 RBM 5&6: 5-16, 5-19, 5-20, 5-24, 5-26, 5-29, 5-41, 5-65, 5-77, 5-78, 6-12, 6-20, 6-21, 6-28, 6-37, 6-38, 6-40, 6-41, 6-53, 6-66, 6-74, 6-78, 6-92, 6-93 Assessment: 6-100, 6-102 RBM 7&8: 7-9, 7-11, 7-13, 7-21, 7-24, 7-30, 7-45, 7-72, 7-73, 7-83, 7-84, 8-20, 8-25, 8-26, 8-64, 8-76, 8-77, 8-78 Assessment: 8-87, 8-90, 8-92 Preparation for Middle School Math PE, Grade 6: 67-71, 72-76, 77-81 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. Investigate and describe the relationship between areas of rectangles and triangles or other quadrilaterals. PE/TE: 287, 288, 290, 291, 293, 455, 456, 457-458, 459-460, 461, 462, 463, 465, 522 RBM 3&4: 4-39, 4-40, 4-41, 4-42 Assessment: 4-103 RBM 7&8: 7-9, 7-10, 7-11, 7-12, 7-13, 7-14, 7-66, 7-67, 7-70, 7-72, 7-73, 7-81, 7-83, 7-84, 7-85 Assessment: 7-101, 7-102, 7-104, 7-106, CT-2 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 17
2. Develop and apply the formulas for the area of triangles and parallelograms. PE/TE: 287, 288, 290, 291, 293, 455, 456, 457-458, 459-460, 461, 462, 463, 465, 522 RBM 3&4: 4-39, 4-40, 4-41, 4-42 Assessment: 4-103 RBM 7&8: 7-9, 7-10, 7-11, 7-12, 7-13, 7-14, 7-66, 7-67, 7-70, 7-72, 7-73, 7-81, 7-83, 7-84, 7-85 Assessment: 7-101, 7-102, 7-104, 7-106, CT-1 Preparation for Middle School Math PE, Grade 6: 77-81 E. Solve problems involving scale factors, using ratio and proportion. 1. Use a scale to find distance. PE/TE: 427-428, 431, 433, 434, 435, 436, 437, 451 RBM 5&6: 6-36, 6-37, 6-38, 6-39, 6-40, 6-41, 6-66, 6-74, 6-78, 6-91, 6-92, 6-93 Assessment: 6-102, 6-103, CT-2 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 18
Data Analysis and Probability Standard I. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them. 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 one population, collect, analyze, and interpret data. PE/TE: 157, 180, 192, 216, 229, 235-237, 238, 239-240, 245, 378, 387, 398-403, 404, 405, 406, 408, 410, 436, 449, 490-492, 566-567 RBM 3&4: 3-21, 3-28, 3-42, 3-49, 4-9, 4-10, 4-11, 4-12, 4-14, 4-50, 4-64, 4-70, 4-71, 4-78, 4-81, 4-82, 4-83 Assessment: CT-1, CT-2 RBM 5&6: 6-12, 6-20, 6-21, 6-22, 6-23, 6-24, 6-25, 6-26, 6-41, 6-48, 6-50, 6-51, 6-70, 6-71, 6-85, 6-86, 6-87 RBM 7&8: 7-30, 7-76, 7-91, 7-92, 8-32, 8-66, 8-79, 8-80 Assessment: EOYT-2 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 19
B. Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatter plots. 1. Organize and display data in a variety of ways including frequency tables, histograms, and stem-and-leaf plots. PE/TE: 187, 191, 194, 196, 199, 200, 201, 215, 219-220, 223, 224, 225, 226, 227, 228, 229, 231, 235, 578, 603 RBM 3&4: 3-25, 3-27, 3-30, 3-31, 3-32, 3-33, 3-44, 3-41, 3-45, 3-46, 3-47, 3-48, 3-49, 3-75, 3-84, 3-86, 3-99, 3-100, 3-101 Assessment: 3-106, 3-108, 3-109, 3-110, 4-9, CT-2 RBM 7&8: 8-39 Assessment: EOYT-2 Other examples of graphical representations of data can be found on the following pages: PE/TE: 182-185, 186-192, 193, 229, 230, 402-403, 404, 406, 408, 409, 410, 411, 539-541, 547, 548, 549, 553, 602, 603 RBM 3&4: 3-23, 3-24, 3-25, 3-26, 3-27, 3-28, 3-49, 3-72, 3-79, 3-80, 3-93, 3-94, 3-101, 3-102, 3-103 Assessment: 3-104, 3-105, 3-109, 3-110 RBM 5&6: 6-22, 6-23, 6-24, 6-25, 6-26, 6-51, 6-71, 6-84, 6-86, 6-87, 6-96 Assessment: 6-98, 6-99, 6-101 RBM 7&8: 8-16, 8-17, 8-20, 8-21, 8-49, 8-62, 8-67, 8-73, 8-74, 8-75, 8-82, 8-83, 8-86 Assessment: 8-89, 8-91 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 20
Standard II. Select and use appropriate statistical methods to analyze data. A. Find, use, and interpret measures of center and spread, including mean and interquartile range. 1. Create and solve problems involving the mean, median, mode, and range of a set of data. PE/TE: 195-198, 199-201, 202, 203, 204, 205, 206, 216, 231, 577-578, 579, 581, 582, 584, 587 RBM 3&4: 3-30, 3-31, 3-32, 3-33, 3-34, 3-35, 3-37, 3-42, 3-73, 3-81, 3-86, 3-95, 3-96 Assessment: 3-105, 3-106, 3-108, 3-108, 3-109, 3-110, CT-1, CT-2 RBM 7&8: 8-38, 3-39, 8-40, 8-41, 8-42, 8-68, 8-82, 8-84 Assessment: EOYT-2 B. Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots. 1. Interpret histograms and stem-and-leaf plots. PE/TE: 219-220, 223, 224, 225, 226, 227, 228, 229, 231, 578 RBM 3&4: 3-44, 3-45, 3-46, 3-47, 3-48, 3-49, 3-63, 3-84, 3-99, 3-100, 3-101 Assessment: 3-106, 3-108, 3-109, 3-110, CT-2 RBM 7&8: Assessment: EOYT-2 2. Describe the relationship between a data set and its corresponding histogram or stemand-leaf plot. PE/TE: 219-220, 223, 224, 225, 226, 227, 228, 229, 231, 578 RBM 3&4: 3-44, 3-45, 3-46, 3-47, 3-48, 3-49, 3-63, 3-84, 3-99, 3-100, 3-101 Assessment: 3-106, 3-108, 3-109, 3-110, CT-2 RBM 7&8: Assessment: EOYT-2 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 21
Standard III. Develop and evaluate inferences and predictions that are based on data. A. Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken. 1. Analyze and list the differences between two data sets. PE/TE: 236, 237, 408 (#15) RBM 3&4: 4-10 RBM 5&6: 6-25 Standard IV. Understand and apply basic concepts of probability A. Understand and use appropriate terminology to describe complementary and mutually exclusive events. 1. Identify and describe complementary events. PE/TE: 243 (#4b, 4c), 568 (#8) RBM 3&4: 4-13 RBM 7&8: 8-83 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 22
B. Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations. 1. Create a sample space for one- or two-stage events and represent it in the form of a list, chart, picture, or tree diagram. PE/TE: 235-237, 239, 242, 243, 244, 245, 246, 306, 441-443, 444, 446, 447, 448, 451, 566-567 RBM 3&4: 4-9, 4-10, 4-11, 4-12, 4-13, 4-14, 4-16, 4-50, 4-64, 4-70, 4-71, 4-79, 4-81, 4-82, 4-83, 4-97, 4-98 Assessment: 4-99, 4-100, 4-102, 4-104, 4-105 RBM 5&6: 6-44, 6-45, 6-46, 6-47, 6-48, 6-55, 6-56, 6-67, 6-76, 6-78, 6-94, 6-95 Assessment: 6-100, 6-102, 6-103, CT-2 RBM 7&8: 8-32, 8-33, 8-34, 8-36, 8-58, 8-66, 8-70, 8-79, 8-80, 8-84 Assessment: 8-89, 8-91, 8-92 2. Determine and interpret the probability of an event occurring from a given sample space. PE/TE: 234-246, 260, 306, 441-443, 444, 446, 447, 448, 451, 566-567, 568, 570, 572, 587 RBM 3&4: 4-9, 4-10, 4-11, 4-12, 4-13, 4-14, 4-16, 4-50, 4-64, 4-70, 4-71, 4-79, 4-81, 4-82, 4-83, 4-97, 4-98 Assessment: 4-99, 4-100, 4-102, 4-104, 4-105, CT-2 RBM 5&6: 6-44, 6-45, 6-46, 6-47, 6-48, 6-55, 6-56, 6-67, 6-76, 6-78, 6-94, 6-95 Assessment: 6-100, 6-102, 6-103, CT-2 RBM 7&8: 8-32, 8-33, 8-34, 8-36, 8-58, 8-66, 8-70, 8-79, 8-80, 8-84 Assessment: 8-89, 8-91, 8-92, CT-2, EOYT-2 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 two-stage events, making a tree diagram, or using models. PE/TE: 441-443, 444, 446, 447, 448, 451 RBM 5&6: 6-44, 6-45, 6-46, 6-47, 6-48, 6-55, 6-56, 6-67, 6-76, 6-94, 6-95 Assessment: 6-100, 6-102, CT-2 PE: Pupil s Edition; TE: Teacher s Edition; RBM: Resource Book Modules 23