south carolina grade 6 mathematics · pdf file• each section uses explorations that...

South CarolinaGrade 6

Mathematics Standards

correlated to the

4/20012002

Introduction

to

Middle Grades MathThematicsBooks 1–3

The Middle Grades MathThematics program is a complete middle-grade mathematicscurriculum designed to implement the National Council of Teachers of MathematicsCurriculum and the Evaluation Standards for School Mathematics. The following are someof the key features.

• Easy-to-follow lessons begin with a Setting the Stage feature that provides either areading, a graph, an activity, or a game to introduce the section and motivate students.

• Each section uses Explorations that actively involve students in investigating mathconcepts, 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 whiledeveloping note-taking skills.

• Exercises, which include a Reflecting on the Section feature, develop numerical andproblem-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 studentassess understanding of important skills before starting the next section.

• Assessment opportunities include a Module Review and Assessment in the PupilEdition and a Module Quiz and a Module Test (Forms A and B) in the Teacher’sResource Book. The Teacher’s Resource Book also provides Standardized andPerformance assessment options for each module, as well as Cumulative Tests onevery 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 haveacquired the mathematical skills necessary to solve problems, to reason inductively anddeductively, and to apply the numerical and spatial concepts necessary to functionaccording 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 theknowledge, ability, and confidence to explore mathematics at the secondary level. They willbe 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 becomedecision-makers, and to view mathematics as relevant to their lives.

Teachers are supported by a wealth of ancillary materials. A complete listing of availableprogram components appears below.

Middle Grades MathThematicsBooks 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 AncillariesStudent Manipulatives KitOverhead Manipulatives KitSpanish Resources

(one for each grade: 6, 7, and 8)Multi-language GlossaryPreparation 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-ROMPersonal Student Tutor CD-ROM

Design of the Teacher Resource Books

Each Teacher’s Resource Book for the Middle Grades MathThematics series includethe following types of resources:

OverviewsHome InvolvementTeaching SuggestionsLabsheetsExtended Exploration GuidesAlternate Extended ExplorationWarm-Up Exercises and Quick QuizzesPractice and ApplicationsStudy GuidesTechnology ActivitiesAssessmentStandardized AssessmentModule Performance AssessmentAnswers

Each Teacher’s Resource Book has a dual numbering system. The first numberrepresents the chapter with which the resource page is to be used, and the numberfollowing the dash sequences the resource page within that chapter. For example, The 3 in3-18 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 theTeacher’s Resource Book.

Certain pages within each Teacher’s Resource Book begin with a letter code rather than aChapter 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 4for Books 2 and 3 );EOYT = End-of-Year Test (at the end of the Teacher’s Resource Book: Modules 7and 8)

Math Thematics Book 1

correlated to the

South Carolina

Grade 6Mathematics Standards

Number and Operations

Standard I. Understand numbers, ways of representing numbers, relationships among numbers, andnumber systems.

Expectations:

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, 2-101Assessment: 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, 3-101Assessment: 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 theirapproximate 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, 2-101Assessment: 2-109, 2-111, 2-112, CT-2

RBM 3&4: 3-18, 3-19, 3-20, 3-21, 3-59, 3-78Assessment: 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, 5-75,5-76Assessment: 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, 6-89Assessment: 6-98, 6-99, 6-100, 6-101, 6-102, 6-103, CT-1

RBM 7&8: Assessment: EOYT-2

Math Thematics Book 1 correlated to theSouth Carolina Grade 6 Mathematics Standards


E. Develop an understanding of large numbers and recognize and appropriately useexponential, scientific, and calculator notation.

1. Evaluate powers of ten up to 106.

PE/TE: 255, 260, 262

RBM 3&4: 4-20, 4-23, 4-24Assessment: 4-99

RBM 7&8: 8-18, 8-19, 8-20, 8-21, 8-22, 8-23Assessment: CT-2

F. Use factors, multiples, prime factorization, and relatively prime numbers to solveproblems.

1. Solve problems using prime factorization, common multiples, and common factors, andexplain 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, 4-95Assessment: 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, 7-97Assessment: CT-1, CT-2



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 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, 2-104Assessment: 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, 4-90Assessment: 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, 5-86Assessment: 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, 8-72Assessment: 8-87, 8-88, 8-90, 8-92, CT-2, EOYT-1, EOYT-3



B. Use the associative and commutative properties of addition and multiplication and thedistributive property of multiplication over addition to simplify computations withintegers, fractions, and decimals.

1. Apply the commutative, associative, and distributive properties to simplify computationswith whole numbers, fractions, and decimals.

PE/TE: 53, 356, 358, 359, 377, 537

RBM 1&2: 1-37Assessment: CT-1

RBM 5&6: 5-36, 5-37, 5-83, 5-84RBM 7&8: 8-14

Assessment: CT-2, EOYT-1, EOYT-3

Standard III. Compute fluently and make reasonable estimates.

Expectations:

A. Select appropriate methods and tools for computing with fractions and decimals fromamong mental computation, estimation, calculators or computers, and paper andpencil, depending on the situation, and apply the selected methods.

1. Select appropriate methods and tools to solve problems requiring the addition andsubtraction 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, 2-104Assessment: 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, 5-82Assessment: 5-89, 5-90, 5-91, 5-92, 5-93, 5-94, CT-1


Preparation for Middle School Math PE, Grade 6: 7, 8, 9, 10



B. Develop and analyze algorithms for computing with fractions, decimals, and integersand 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, 3-101Assessment: 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, 5-85,5-86Assessment: 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, 2-104Assessment: 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, 4-90Assessment: 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, 5-86Assessment: 5-89, 5-90, 5-91, 5-92, 5-93, 5-94, CT-1, CT-2



3. Add, subtract, multiply and divide fractions (including decimals) to solve a variety ofapplied 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, 2-104Assessment: 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, 4-90Assessment: 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, 5-86Assessment: 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 computationsand judge the reasonableness of the results.

1. Estimate the sums and differences of fractions, describe the method used, and determinethe 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



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, 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, 2-54Assessment: 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, 4-93Assessment: 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, 6-97Assessment: 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, 8-78Assessment: 8-87, EOYT-1

Preparation for Middle School Math PE, Grade 6: 11-16, 27-31, 75



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. 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, 1-93Assessment: 1-102, 1-104, 1-105, CT-1


B. Explore relationships between symbolic expressions and graphs of lines, payingparticular 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, 4-93Assessment: 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 solvelinear equations.

1. Use commutative, associative and distributive properties to examine equivalence of avariety of simple algebraic expressions.

PE/TE: 53, 356, 358, 359, 377, 537

RBM 1&2: 1-37RBM 5&6: 5-36, 5-83, 5-84RBM 7&8: 8-14



Standard III. Use mathematical models to represent and understand quantitative relationships.

Expectations:

A. Model and solve contextualized problems using various representations, such asgraphs, 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, 1-99Assessment: 1-100

RBM 3&4: 4-20, 4-39, 4-40, 4-61Assessment: 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, 6-97Assessment: 6-98, 6-99, 6-101

Preparation for Middle School Math PE, Grade 6: 75



Geometry

Standard I. Analyze characteristics and properties of two- and three-dimensional geometric shapesand develop mathematical arguments about geometric relationships.

Expectations:

A. Precisely describe, classify, and understand relationships among types of two- andthree-dimensional objects using their defining properties.

1. Compare and contrast prisms, cylinders and pyramids with the polygons or circles thatconstitute 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, 7-88Assessment: 7-101, 7-102, 7-104, CT-1

B. Understand relationships among the angles, side lengths, perimeters, areas, andvolumes of similar objects.

1. Describe relationships among angles, side lengths, perimeters, and areas of similarpolygons.

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, 6-93Assessment: 6-99, 6-100, 6-101, 6-102, 6-103, CT-1, CT-2

C. Create and critique inductive and deductive arguments concerning geometric ideasand 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




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, 2-106Assessment: 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, 6-93Assessment: 6-99, 6-100, 6-101, 6-102, 6-103

Standard II. Specify locations and describe spatial relationships using coordinate geometry and otherrepresentational systems.

Expectations:

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 orvertically, use the first quadrant of the rectangular coordinate system to locate the othervertex.

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, 4-93Assessment: 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 regularpolygons or those with pairs of parallel or perpendicular sides

1. Plot the vertices of squares and rectangles and determine the relationship among thecoordinates.

PE/TE: 290 (#15, 16)

RBM 3&4: 4-41



Standard III. Apply transformations and use symmetry to analyze mathematical situations.

Expectations:

A. Describe sizes, positions, and orientations of shapes under informal transformationssuch as flips, turns, slides, and scaling.

1. Describe the transformation used to move a polygon from one location to another in thefirst 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, 2-106Assessment: 2-109, CT-2

B. Examine the congruence, similarity, and line or rotational symmetry of objects usingtransformations.

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, 2-106Assessment: 2-109, CT-2



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 anglemeasures.

1. Use symbols for parallel lines and perpendicular lines to describe polygons and figureswhere 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, 2-12Assessment: 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 andsolve 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 themathematics 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, 6-47RBM 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, 7-38Assessment: CT-2

Preparation for Middle School Math PE, Grade 6: 72, 73, 74, 76, 77, 78, 79,80, 81



Measurement

Standard I. Understand measurable attributes of objects and the units, systems, and processes ofmeasurement.

Expectations:

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, and360 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: 1-18RBM 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, 4-41RBM 5&6: 6-38, 6-40, 6-41, 6-53, 6-66, 6-73, 6-74, 6-78, 6-92

Assessment: 6-100, 6-102RBM 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, 7-95Assessment: 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



Standard II. Apply appropriate techniques, tools, and formulas to determine measurements.

Expectations:

A. Use common benchmarks to select appropriate methods for estimating measurements.

1. Estimate and then determine length, weight/mass, area, and volume/capacity, usingstandard 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, 3-89RBM 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, 5-84RBM 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, 8-78Assessment: 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, 7-81Assessment: 7-101, 7-106

Preparation for Middle School Math PE, Grade 6: 80, 81



B. Select and apply techniques and tools to accurately find length, area, volume, andangle measures to appropriate levels of precision.

1. Select and use appropriate tools and units to measure to the degree of accuracy requiredin 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, 3-109RBM 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, 6-93Assessment: 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, 8-78Assessment: 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 oftriangles, parallelograms, trapezoids, and circles and develop strategies to find thearea of more-complex shapes.

1. Investigate and describe the relationship between areas of rectangles and triangles orother 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, 4-42Assessment: 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, 7-85Assessment: 7-101, 7-102, 7-104, 7-106, CT-2



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, 4-42Assessment: 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, 7-85Assessment: 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, 6-93Assessment: 6-102, 6-103, CT-2



Data Analysis and Probability

Standard I. Formulate questions that can be addressed with data and collect, organize, and displayrelevant data to answer them.

Expectations:

A. Formulate questions, design studies, and collect data about a characteristic shared bytwo 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, 4-83Assessment: 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, 8-80Assessment: EOYT-2



B. Select, create, and use appropriate graphical representations of data, includinghistograms, 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, 3-101Assessment: 3-106, 3-108, 3-109, 3-110, 4-9, CT-2

RBM 7&8: 8-39Assessment: 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, 3-103Assessment: 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, 6-96Assessment: 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, 8-83,8-86Assessment: 8-89, 8-91



Standard II.Select and use appropriate statistical methods to analyze data.

Expectations:

A. Find, use, and interpret measures of center and spread, including mean andinterquartile range.

1. Create and solve problems involving the mean, median, mode, and range of a set ofdata.

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, 3-95,3-96Assessment: 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, 8-84Assessment: EOYT-2

B. Discuss and understand the correspondence between data sets and their graphicalrepresentations, 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, 3-101Assessment: 3-106, 3-108, 3-109, 3-110, CT-2


2. Describe the relationship between a data set and its corresponding histogram or stem-and-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, 3-101Assessment: 3-106, 3-108, 3-109, 3-110, CT-2




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 conjecturesabout 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: 4-10RBM 5&6: 6-25

Standard IV.Understand and apply basic concepts of probability

Expectations:

A. Understand and use appropriate terminology to describe complementary and mutuallyexclusive events.

1. Identify and describe complementary events.

PE/TE: 243 (#4b, 4c), 568 (#8)

RBM 3&4: 4-13RBM 7&8: 8-83



B. Use proportionality and a basic understanding of probability to make and testconjectures 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, 4-98Assessment: 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, 6-95Assessment: 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, 8-84Assessment: 8-89, 8-91, 8-92

2. Determine and interpret the probability of an event occurring from a given samplespace.

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, 4-98Assessment: 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, 6-95Assessment: 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, 8-84Assessment: 8-89, 8-91, 8-92, CT-2, EOYT-2

C. Compute probabilities for simple compound events, using such methods as organizedlists, 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




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