GENERAL EVALUATION CRITERIAassets.pearsonschool.com/correlations/ADOPT_WV_CMP... · 5 INSTRUCTIONAL MATERIALS ADOPTION: 21st Century Learning EVALUATION CRITERIA The general evaluation

Prentice Hall Connected Mathematics 2, Grade 8 Module Bundlewith West Virginia Additional Lessons © 2010

C O R R E L A T E D T O

West Virginia 21st Century Mathematics Content Standards and Objectives for Grade 8

G r a d e 8

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PUBLISHER: Pearson Education, Inc., publishing as Prentice Hall SUBJECT: Mathematics SPECIFIC GRADE: 8 COURSE: Eighth Grade Mathematics TITLE: Prentice Hall Connected Mathematics 2, Grade 8 Module Bundle with West Virginia Additional Lessons COPYRIGHT DATE: 2010 SE ISBN: 0133731448 TE ISBN: 0133686159

GENERIC EVALUATION CRITERIA 2010-2015

Eighth Grade Mathematics

R-E-S-P-O-N-S-E Yes No N/A

CRITERIA

NOTES

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I. INTER-ETHNIC The instructional material meets the requirements of inter-ethnic: concepts, content and illustrations, as set by West Virginia Board of Education Policy (Adopted December 1970).

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II. EQUAL OPPORTUNITY The instructional material meets the requirements of equal opportunity: concept, content, illustration, heritage, roles contributions, experiences and achievements of males and females in American and other cultures, as set by West Virginia Board of Education Policy (Adopted May 1975).

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INSTRUCTIONAL MATERIALS ADOPTION: 21st CENTURY LEARNING EVALUATION CRITERIA

GENERAL EVALUATION CRITERIA 2010-2015

Eighth Grade Mathematics I

(IMR Committee) Responses (Vendor/Publisher)

SPECIFIC LOCATION OF CONTENT WITHIN PRODUCT I=In-depth

A=Adequate

M=Minimal

N=Nonexistent

I A M N

In addition to alignment of Content Standards and Objectives (CSOs), materials must also clearly connect to Learning for the 21st Century which includes opportunities for students to develop

A. Learning Skills

This criteria is addressed throughout the program. Sample citations follow: SE: Looking for Pythagoras Investigation 2: Squaring Off (20–22); Kaleidoscopes, Hubcaps, and Mirrors Investigation 2: Symmetry Transformations (27–35); Shapes of Algebra Investigation 2: Linear Equations and Inequalities (28–29) TG: Looking for Pythagoras Investigation 2:

• Thinking and Problem-Solving Skills/ Rigor and Depth of Content

Content is presented in a way that deepens student understanding through engagement in meaningful, challenging mathematics that builds on prior knowledge and promotes connections among mathematical concepts.

• Thinking and Problem-Solving Skills /Development of Conceptual

Understanding Learning opportunities require students to develop their own viable mathematical understandings and help them build connections between mathematical ideas.

• Information and Communication Skills/Mathematical Language

Appropriately introduce and reinforce in multiple ways all necessary terms and symbols.

• Personal and Work Place Productivity Skills

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Squaring Off (39–46); Kaleidoscopes, Hubcaps, and Mirrors Investigation 2: Symmetry Transformations (45–66); Shapes of Algebra Investigation 2: Linear Equations and Inequalities (47–50)

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B. 21st Century Tools

• Problem-solving tools (such as spreadsheets, decision support, design

tools) • Communication, information processing and research tools (such as word

processing, e-mail, groupware, presentation, Web development, Internet search tools)

• Personal development and productivity tools (such as e-learning, time

management/calendar, collaboration tools)

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INSTRUCTIONAL MATERIALS ADOPTION: 21st Century Learning EVALUATION CRITERIA

The general evaluation criteria apply to each grade level and are to be evaluated for each grade level unless otherwise specified. These criteria consist of information critical to the development of all grade levels. In reading the general evaluation criteria and subsequent specific grade level criteria, e.g. means “examples of” and i.e. means that “each of” those items must be addressed. Eighty percent of the combined general and specific criteria must be met with I (In-depth) or A (Adequate) in order to be recommended.

2010-2015 Eighth Grade Mathematics

(IMR Committee) Responses (Vendor/Publisher)

SPECIFIC LOCATION OF CONTENT WITHIN PRODUCT I=In-depth

A=Adequate

M=Minimal

N=Nonexistent

I A M N

For student mastery of content standards and objectives, the instructional materials will provide students with the opportunity to

4. Multimedia

Student Interactivity CD-ROM

1. offer appropriate multimedia (e.g., software, audio, visual, internet access) materials.

on-line www.PHSchool.com 2. provide a website which provides links to relevant sites as well as

lesson plans, student activities and parent resources.

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SE: Looking for Pythagoras Investigation 4: Using the Pythagorean Theorem (48); Frogs, Fleas, and Painted Cubes Investigation 1: Introduction to Quadratic Relationships (9–10); Investigation 3: Quadratic Patterns of Change (40–41); Shapes of Algebra Investigation 2: Linear Equations and Inequalities (29) TG: Thinking with Mathematical Models (10–12); Growing, Growing, Growing (14–16); Frogs, Fleas, and Painted Cubes (14–16), Investigation 1: Introduction to Quadratic Relationships (31–38); Investigation 3: Quadratic Patterns of Change (89–94); Shapes of Algebra Investigation 2: Linear Equations and Inequalities (47–50)

3. Integrate technology seamlessly when appropriate to model

mathematical situations, analyze data, calculate results, and solve problems.

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B. Scientifically-Based Research Strategies

This criteria is addressed throughout the program. Sample citations follow: SE: Thinking with Mathematical Models Investigation 3: Inverse Variation (48–51); Say It With Symbols Investigation 4: Looking Back at Functions (59), Investigation 5: Reasoning With Symbols (74–75) TG: Thinking with Mathematical Models Investigation 3: Inverse Variation (62–70); Say It With Symbols Investigation 4: Looking Back at Functions (103–106), Investigation 5: Reasoning With Symbols (119–122)

1. Consistently require students to link prior knowledge to new

information to construct their own viable understandings of mathematical ideas.

This criteria is addressed throughout the program. Sample citations follow: SE: Growing, Growing, Growing Investigation 4: Exponential Decay (51–52); Frogs, Fleas, and Painted Cubes Investigation 4: What Is a Quadratic Function? (62–63); Shapes of Algebra Investigation 5: Linear Inequalities (71–72) TG: Growing, Growing, Growing Investigation 4: Exponential Decay (89–92); Frogs, Fleas, and Painted Cubes Investigation 4: What Is a Quadratic Function? (137–143); Shapes of Algebra Investigation 5: Linear Inequalities (105–108)

2. Consistently provide opportunities for students to solve complex

problems that have multiple entry points and the possibility of multiple solution processes.

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This criteria is addressed throughout the program. Sample citations follow: SE: Thinking with Mathematical Models Investigation 2: Linear Models and Equations (42); Looking for Pythagoras Investigation 2: Squaring Off (20–22) TG: Thinking with Mathematical Models Investigation 2: Linear Models and Equations (59); Looking for Pythagoras Investigation 2: Squaring Off (39–46)

3. Consistently provide opportunities for students to communicate their

mathematical thinking processes to others orally, in writing, or pictorially.

This criteria is addressed throughout the program. Sample citations follow: SE: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns ( 8–9); Say It With Symbols Investigation 2: Combining Expressions (23–25), Investigation 5: Reasoning With Symbols (75); Samples and Populations Investigation 4: Relating Two Variables (62–68) TG: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns ( 21–24); Say It With Symbols Investigation 2: Combining Expressions (45–52), Investigation 5: Reasoning With Symbols (123–126); Samples and Populations Investigation 4: Relating Two Variables (62–68)

4. Routinely require students to develop and defend mathematical

conjectures, arguments, reasoning and proof.

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This criteria is addressed throughout the program. Sample citations follow: SE: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns ( 8–9); Growing, Growing, Growing Investigation 4: Exponential Decay (51–52) TG: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns ( 21–24); Growing, Growing, Growing Investigation 4: Exponential Decay (89–92)

5. Provide opportunities for the students to be involved in investigations

that enable them to make connections among mathematical ideas.

This criteria is addressed throughout the program. Sample citations follow: SE: Frogs, Fleas, and Painted Cubes Investigation 3: Quadratic Patterns of Change (42–43); Say It With Symbols Investigation 1: Equivalent Expressions (7); Shapes of Algebra Investigation 3: Equations With Two or More Variables (39–40) TG: Frogs, Fleas, and Painted Cubes Investigation 3: Quadratic Patterns of Change (95–100); Say It With Symbols Investigation 1: Equivalent Expressions (24–28); Shapes of Algebra Investigation 3: Equations With Two or More Variables (61–64)

6. Expect students to develop multiple representations of the

mathematics in order to depict reasoning used to explain real world phenomena or solutions to relevant problems and move fluently between those representations.

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This criteria is addressed throughout the program. Sample citations follow: SE: Looking for Pythagoras Investigation 4: Using the Pythagorean Theorem (46–47); Say It With Symbols Investigation 5: Reasoning With Symbols (74–75) TG: Looking for Pythagoras Investigation 4: Using the Pythagorean Theorem (74–78); Say It With Symbols Investigation 5: Reasoning With Symbols (119–122)

7. Present varied teaching models with emphasis on differentiated

instruction in content, process, and product.

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C. Critical Thinking

This criteria is addressed throughout the program. Sample citations follow: SE: Samples and Populations Investigation 2: Choosing a Sample From a Population (29–30) TG: Samples and Populations Investigation 2: Choosing a Sample From a Population (59–62)

1. emphasize questioning models to promote higher order thinking skills

based on depth of knowledge.

This criteria is addressed throughout the program. Sample citations follow: SE: Looking for Pythagoras Investigation 3: The Pythagorean Theorem (31–34) TG: Looking for Pythagoras Investigation 3: The Pythagorean Theorem (52–60)

2. Consistently require students to discuss mathematics with each other and

with the teacher, make arguments, conjecture and reason, and justify/clarify their ideas in writing and orally in precise mathematical symbols and language.

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This criteria is addressed throughout the program. Sample citations follow: SE: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns ( 5–9); Shapes of Algebra Investigation 4: Solving Systems of Linear Equations Symbolically (52–53); Samples and Populations Investigation 3: Solving Real-World Problems (51–53) TG: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns ( 16–24); Shapes of Algebra Investigation 4: Solving Systems of Linear Equations Symbolically (76–80); Samples and Populations Investigation 3: Solving Real-World Problems (83–89)

3. Present real world application that is current, engaging, integrated

throughout the instruction, and promotes and develops critical thinking.

D. Life Skills

This criteria is addressed throughout the program. Sample citations follow: SE: Looking for Pythagoras Investigation 1: Coordinate Grids (5–10) TG: Looking for Pythagoras Investigation 1: Coordinate Grids (17–26)

1. address life skills (e.g., reading road maps, using reference tools,

researching, reading a newspaper, using want ads, completing an application, applying the interview process and goal setting).

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This criteria is addressed throughout the program. Sample citations follow: SE: Samples and Populations Investigation 1: Comparing Data Sets (16) TG: Samples and Populations Investigation 1: Comparing Data Sets (39–46)

2. address habits of mind activities (e.g., literacy skills, interpersonal

communications, problem solving and self-directional skills).

E. Classroom Management

This criteria is addressed throughout the program. Sample citations follow: SE: Kaleidoscopes, Hubcaps, and Mirrors Investigation 3: Exploring Congruence (51–53); Say It With Symbols Investigation 4: Looking Back at Functions (58) TG: Kaleidoscopes, Hubcaps, and Mirrors Investigation 3: Exploring Congruence (83–86); Say It With Symbols Investigation 4: Looking Back at Functions (99–102)

1. include opportunities for large group, small group, and independent

learning.

This criteria is addressed throughout the program. Sample citations follow: SE: Kaleidoscopes, Hubcaps, and Mirrors Investigation 3: Exploring Congruence (51–55) TG: Kaleidoscopes, Hubcaps, and Mirrors Investigation 3: Exploring Congruence (83–90)

2. Consistently require students to explore mathematical ideas,

individually and collaboratively, while integrating the process standards (see Section I of this rubric).

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CMP Special Needs Handbook 3. provide suggestions for differentiated instruction (e.g., practice

activities, learning stations, assessment, lesson plans).

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F. Instructional Materials This criteria is addressed throughout the program. Sample citations follow: SE: Looking for Pythagoras Investigation 4: Using the Pythagorean Theorem (46–49); Growing, Growing, Growing Investigation 5: Patterns with Exponents (60–63) TG: Looking for Pythagoras Investigation 4: Using the Pythagorean Theorem (74–90); Growing, Growing, Growing Investigation 5: Patterns with Exponents (99–112)

1. Are organized according to WV content standards or other increments

that allow students to investigate and explore major mathematical ideas; provide a variety of lessons, activities, and projects from which to choose; and emphasize connections between mathematical ideas.

This criteria is addressed throughout the program. Sample citations follow: SE: Growing, Growing, Growing Investigation 5: Patterns with Exponents (60–63); Frogs, Fleas, and Painted Cubes Investigation 4: What Is a Quadratic Function? (62–63) SE: Growing, Growing, Growing Investigation 5: Patterns with Exponents (99–112); Frogs, Fleas, and Painted Cubes Investigation 4: What Is a Quadratic Function? (137–143)

2. Consistently integrate tasks that engage students and invite them to

speculate and hypothesize, are open-ended, and require them to determine appropriate strategies.

TG: Every Problem in each Investigation provides questions to develop understanding

3. Provide teachers with guiding questions to aid students’ development

of mathematical discourse to further mathematical understanding.

ExamView ™ , Teacher Express™ CD-ROM, LessonLab Online Courses

4. Provide additional resources that are organized in a way that is easy

to access and use.

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5. Include various instructional models to address varied learning styles

of students.

Differentiated Instruction provided in every section of ACE Answers for all Investigations; Special Needs Handbook

6. Provide extensive and varied opportunities to differentiate individual

needs for skill-building.

Differentiated Instruction provided in every section of ACE Answers for all Investigations; Special Needs Handbook

7. Provide supplemental materials for intervention and enrichment.


8. Provide teachers with support to properly integrate the process

standards using the available resources.

TG: Thinking with Mathematical Models (4–5); Looking for Pythagoras (4–9); Growing, Growing, Growing (4–10); Frogs, Fleas, and Painted Cubes (4–10); Kaleidoscopes, Hubcaps, and Mirrors (4–10); Say It With Symbols (4–12); Shapes of Algebra (4–10); Samples and Populations (6–11)

9. Include a teacher resource that builds content knowledge for the

teacher.

This criteria is addressed throughout the program. Sample citations follow: SE: Say It With Symbols Investigation 1: Equivalent Expressions (9–11), Investigation 4: Looking Back at Functions (57–59) TG: Say It With Symbols Investigation 1: Equivalent Expressions (33–36), Investigation 4: Looking Back at Functions (105–108)

10. Spiral previously taught skills and strategies with new content.

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G. Assessment TG: Thinking with Mathematical Models (13); Looking for Pythagoras (14); Growing, Growing, Growing (17); Frogs, Fleas, and Painted Cubes (17); Kaleidoscopes, Hubcaps, and Mirrors (16); Say It With Symbols (17); Shapes of Algebra (15); Samples and Populations (17)

1. provide assessment formats commensurate with WV assessment

programs (e.g., WESTEST, NAEP, State Writing Assessment, informal assessments, PLAN, EXPLORE, ACT and SAT).

TG: Thinking with Mathematical Models (13); Looking for Pythagoras (14); Growing, Growing, Growing (17); Frogs, Fleas, and Painted Cubes (17); Kaleidoscopes, Hubcaps, and Mirrors (16); Say It With Symbols (17); Shapes of Algebra (15); Samples and Populations (17)

2. provide opportunities for assessment based on performance-based

measures, open-ended questioning, portfolio evaluation, rubrics and multimedia simulations.


3. provide benchmark and ongoing progress monitoring.

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SE: Growing, Growing, Growing (74–75); Kaleidoscopes, Hubcaps, and Mirrors (96–100); Say It With Symbols (85–86); Samples and Populations (81–82) TG: Growing, Growing, Growing (119–120); Kaleidoscopes, Hubcaps, and Mirrors (136–138); Say It With Symbols (133–137); Samples and Populations (111–112)

4. provide rubric-based differentiated assessment.

TG: Thinking with Mathematical Models (10–13); Looking for Pythagoras (14); Growing, Growing, Growing (17); Frogs, Fleas, and Painted Cubes (17); Kaleidoscopes, Hubcaps, and Mirrors (16); Say It With Symbols (17); Shapes of Algebra (15); Samples and Populations (17)

5. provide an electronic system for managing assessment data to

facilitate the implementation of tiered instruction

TG: Thinking with Mathematical Models (13); Looking for Pythagoras (13–14); Growing, Growing, Growing (14–17); Frogs, Fleas, and Painted Cubes (14–17); Kaleidoscopes, Hubcaps, and Mirrors (14–16); Say It With Symbols (16–17); Shapes of Algebra (14–15); Samples and Populations (17)

6. integrate student self-assessment for and of learning by providing

tools and organizers that are linked to clearly identified learning goals.

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7. Integrate formal and informal means of assessment in the materials

for diagnostic, formative, and summative purposes.


8. include various types of assessments: performance tasks, multiple

choice, short answer, and free response.

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H. Process Standards

Mathematical Reflections are found at the end of each Investigation SE: Frogs, Fleas, and Painted Cubes Investigation 4: What Is a Quadratic Function? (62–63) TG: Frogs, Fleas, and Painted Cubes Investigation 4: What Is a Quadratic Function? (137–143)

1. Problem Solving: Provide frequent opportunities for students to

formulate, grapple with, and solve complex problems that require a significant amount of effort and have multiple viable solution paths.

This criteria is addressed throughout the program. Sample citations follow: SE: Looking for Pythagoras Investigation 2: Squaring Off (20–22); Say It With Symbols Investigation 4: Looking Back at Functions (57–59) TG: Looking for Pythagoras Investigation 2: Squaring Off (39–46); Say It With Symbols Investigation 4: Looking Back at Functions (101–108)

2. Communication: Routinely challenge students to communicate their

thinking to others orally, in writing, and/or pictorially, using precise mathematical language.

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This criteria is addressed throughout the program. Sample citations follow: SE: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns ( 8–9); Looking for Pythagoras Investigation 3: The Pythagorean Theorem (31–34); Samples and Populations Investigation 4: Relating Two Variables (62–68) TG: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns ( 21–24); Looking for Pythagoras Investigation 3: The Pythagorean Theorem (52–60); Samples and Populations Investigation 4: Relating Two Variables (62–68)

3. Reasoning and Proof: Provide frequent opportunities for students to

complete mathematical investigations with and without technology; develop conjectures, mathematical arguments and proofs to confirm those conjectures.

This criteria is addressed throughout the program. Sample citations follow: SE: Growing, Growing, Growing Investigation 4: Exponential Decay (49–55); Kaleidoscopes, Hubcaps, and Mirrors Investigation 4: Applying Congruence and Symmetry (66–67) TG: Growing, Growing, Growing Investigation 4: Exponential Decay (85–92) ); Kaleidoscopes, Hubcaps, and Mirrors Investigation 4: Applying Congruence and Symmetry (97–102)

4. Connections with Mathematics: Consistently establish connections,

and provide opportunities for students to establish connections, among mathematical concepts and their real-world applications.

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This criteria is addressed throughout the program. Sample citations follow: SE: Frogs, Fleas, and Painted Cubes Investigation 3: Quadratic Patterns of Change (42–43); Say It With Symbols Investigation 1: Equivalent Expressions (7); Shapes of Algebra Investigation 3: Equations With Two or More Variables (39–40) TG: Frogs, Fleas, and Painted Cubes Investigation 3: Quadratic Patterns of Change (95–100); Say It With Symbols Investigation 1: Equivalent Expressions (24–28); Shapes of Algebra Investigation 3: Equations With Two or More Variables (61–64)

5. Representations: Provide frequent opportunities for students to

develop multiple representations of the mathematics in order to depict reasoning used to explain real world phenomena or solutions to relevant problems and move fluently between those representations.

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SPECIFIC EVALUATION CRITERIA Eighth Grade Mathematics

Eighth grade objectives provide an alternative course for students who do not take Algebra I in the eighth grade. In addition to

reinforcing the concepts presented in seventh grade, this course extends problem solving to a more sophisticated level. Linear equations, systems of linear equations, proportional reasoning and rate of change are emphasized in the Algebra strand in preparation for the formal Algebra I course. Lessons involving cooperative learning, manipulatives, or technology strengthen understanding of concepts while fostering communication and reasoning skills. Calculator use is emphasized for all mathematical tasks including assessment. The West Virginia Standards for 21st Century Learning include the following components: 21st Century Content Standards and Objectives and 21st Century Learning Skills and Technology Tools. All West Virginia teachers are responsible for classroom instruction that integrates learning skills, technology tools and content standards and objectives.

Standard 1: Number and Operations Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will

• demonstrate understanding of numbers, ways of representing numbers, and relationships among numbers and number systems,

• demonstrate meanings of operations and how they relate to one another, and • compute fluently and make reasonable estimates.

Standard 2: Algebra Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will

• demonstrate understanding of patterns, relations and functions, • represent and analyze mathematical situations and structures using algebraic symbols, • use mathematical models to represent and understand quantitative relationships, and • analyze change in various contexts.

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Standard 3: Geometry Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will

• analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships,

• specify locations and describe spatial relationships using coordinate geometry and other representational systems, • apply transformations and use symmetry to analyze mathematical situations, and • solve problems using visualization, spatial reasoning, and geometric modeling.

Standard 4: Measurement Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will

• demonstrate understanding of measurable attributes of objects and the units, systems, and processes of measurement, and

• apply appropriate techniques, tools and formulas to determine measurements. Standard 5: Data Analysis and Probability Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will

• formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them, • select and use appropriate statistical methods to analyze data, • develop and evaluate inferences and predictions that are based on models, and • apply and demonstrate an understanding of basic concepts of probability.

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(IMR Committee) Responses

(Vendor/Publisher) SPECIFIC LOCATION OF

CONTENT WITHIN PRODUCT I=In-depth

A=Adequate

M=Minimal

N=Nonexistent I A M N

For student mastery of content standards and objectives, the instructional materials will …

A. Number and Operations

SE: Looking for Pythagoras Investigation 2: Squaring Off (26, 28, 29), Investigation 3: The Pythagorean Theorem (43–44), Investigation 4: Using the Pythagorean Theorem (46–48, 57–60, 62); Growing, Growing, Growing Investigation 3: Growth Factors and Growth Rates (35–36) TG: Looking for Pythagoras Investigation 2: Squaring Off (48–50), Investigation 3: The Pythagorean Theorem (71), Investigation 4: Using the Pythagorean Theorem (74–78, 92–95); Growing, Growing, Growing Investigation 3: Growth Factors and Growth Rates (67–70)

1. provide opportunities to analyze, describe and compare

the characteristics of rational and irrational numbers.

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SE: Looking for Pythagoras Investigation 2: Squaring Off (20–22, 27), Investigation 3: The Pythagorean Theorem (35), Investigation 4: Using the Pythagorean Theorem (46–52, 57–59); Growing, Growing, Growing Investigation 1: Exponential Growth (5–9, 12, 17), Investigation 2: Examining Growth Patterns (28), Investigation 3: Growth Factors and Growth Rates (34), Investigation 4: Exponential Decay (55), Investigation 5: Patterns with Exponents (59–62, 66–71); Say It With Symbols Investigation 5: Reasoning With Symbols (75) TG: Looking for Pythagoras Investigation 2: Squaring Off (39–46, 49), Investigation 3: The Pythagorean Theorem (61–64), Investigation 4: Using the Pythagorean Theorem (74–90, 92–93); Growing, Growing, Growing Investigation 1: Exponential Growth (20–34, 42), Investigation 2: Examining Growth Patterns (58),Investigation 3: Growth Factors and Growth Rates (62–66), Investigation 4: Exponential Decay (96), Investigation 5: Patterns with Exponents (99–112, 114–115); Say It With Symbols Investigation 5: Reasoning With Symbols (123–126)

2. provide examples and opportunities to analyze and solve

application problems with • powers, • squares, • square roots, • scientific notation, and

verify solutions using estimation techniques.

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SE: Thinking with Mathematical Models Investigation 2: Linear Models and Equations (30–31); Looking for Pythagoras Investigation 1: Coordinate Grids (10); Growing, Growing, Growing Investigation 2: Examining Growth Patterns (31), Investigation 3: Growth Factors and Growth Rates (35–37, 41–44), Investigation 4: Exponential Decay (49–51); Say It With Symbols Investigation 2: Combining Expressions (34); Samples and Populations Investigation 2: Choosing a Sample From a Population (26–29) TG: Thinking with Mathematical Models Investigation 2: Linear Models and Equations (47–50); Looking for Pythagoras Investigation 1: Coordinate Grids (25–28); Growing, Growing, Growing Investigation 2: Examining Growth Patterns (58), Investigation 3: Growth Factors and Growth Rates (67–74, 76–77), Investigation 4: Exponential Decay (85–88); Say It With Symbols Investigation 2: Combining Expressions (62); Samples and Populations Investigation 2: Choosing a Sample From a Population (54–58)

3. provide examples and opportunities to analyze and solve

grade-appropriate real-world problems with • whole numbers, • decimals, • fractions, • percents, percent increase and decrease, • integers, and

including, but not limited to, rates, tips, discounts, sales tax and interest and verify solutions using estimation techniques.

B. Algebra

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SE: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (19), Investigation 2: Linear Models and Equations (27–32); Growing, Growing, Growing Investigation 2: Examining Growth Patterns (29); Frogs, Fleas, and Painted Cubes Investigation 2: Quadratic Expressions (35); Say It With Symbols Investigation 2: Combining Expressions (24–25, 33), Investigation 3: Solving Equations (37–39), Investigation 5: Reasoning With Symbols (81); Shapes of Algebra Investigation 2: Linear Equations and Inequalities (26–27), Investigation 5: Linear Inequalities (70–75) TG: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (36), Investigation 2: Linear Models and Equations (43–54); Growing, Growing, Growing Investigation 2: Examining Growth Patterns (59); Frogs, Fleas, and Painted Cubes Investigation 2: Quadratic Expressions (84–85); Say It With Symbols Investigation 2: Combining Expressions (49–52, 59), Investigation 3: Solving Equations (65–72), Investigation 5: Reasoning With Symbols (130); Shapes of Algebra Investigation 2: Linear Equations and Inequalities (43–50), Investigation 5: Linear Inequalities (101–112)

1. provide opportunities to use a variety of strategies to solve

one and two-step linear equations and inequalities with rational solutions; to defend the selection of the strategy; to graph the solutions and justify the reasonableness of the solution.

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SE: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (16), Investigation 3: Inverse Variation (47–52, 58); Growing, Growing, Growing Investigation 3: Growth Factors and Growth Rates (43); Kaleidoscopes, Hubcaps, and Mirrors Investigation 4: Applying Congruence and Symmetry (74); West Virginia Additional Lessons Grade 8 Topic 1: Proportional Reasoning (1-2) TG: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (36), Investigation 3: Inverse Variation (62–74, 79); Growing, Growing, Growing Investigation 3: Growth Factors and Growth Rates (77); Kaleidoscopes, Hubcaps, and Mirrors Investigation 4: Applying Congruence and Symmetry (110); West Virginia Additional Lessons Grade 8 Topic 1: Proportional Reasoning (1-2)

2. provide examples and opportunities to identify

proportional relationships in real-world situations, then to find and select an appropriate method to determine the solution; to justify the reasonableness of the solution.

SE: Say It With Symbols Investigation 1: Equivalent Expressions (9–11), Investigation 3: Solving Equations (46) TG: Say It With Symbols Investigation 1: Equivalent Expressions (33–36), Investigation 3: Solving Equations (88)

3. provide examples and opportunities to add and subtract

polynomials limited to two variables and positive exponents.

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SE: Shapes of Algebra Investigation 2: Linear Equations and Inequalities (24–25, 35), Investigation 3: Equations With Two or More Variables (40–41), Investigation 4: Solving Systems of Linear Equations Symbolically (52–58), Investigation 5: Linear Inequalities (80) TG: Shapes of Algebra Investigation 2: Linear Equations and Inequalities (43–46, 54), Investigation 3: Equations With Two or More Variables (65–68), Investigation 4: Solving Systems of Linear Equations Symbolically (76–94), Investigation 5: Linear Inequalities (121)

4. provide examples and opportunities to use systems of

linear equations to analyze situations and solve problems.

SE: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (6–7,10–11), Investigation 2: Linear Models and Equations (27–29, 32), Investigation 3: Inverse Variation (47–48); Looking for Pythagoras Investigation 3: The Pythagorean Theorem (32); Growing, Growing, Growing Investigation 1: Exponential Growth (5–6, 8–10), Investigation 4: Exponential Decay (49–51), Investigation 5: Patterns with Exponents (66); Frogs, Fleas, and Painted Cubes Investigation 2: Quadratic Expressions (19–20), Investigation 3: Quadratic Patterns of Change (40–41, 49), Investigation 4: What Is a Quadratic Function? (60–63)

5. provide examples and opportunities to apply inductive and deductive

reasoning to write a rule from data in an input/output table, to analyze the table and the rule to determine if a functional relationship exists.

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TG: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (16–20, 25–30); Investigation 2: Linear Models and Equations (43–46, 51–54), Investigation 3: Inverse Variation (62–66); Looking for Pythagoras Investigation 3: The Pythagorean Theorem (52–56);Growing, Growing, Growing Investigation 1: Exponential Growth (16–20, 29–38), Investigation 4: Exponential Decay (85–88), Investigation 5: Patterns with Exponents (114–115); Frogs, Fleas, and Painted Cubes Investigation 2: Quadratic Expressions (20–24), Investigation 3: Quadratic Patterns of Change (89–94, 110), Investigation 4: What Is a Quadratic Function? (129–135) SE: Thinking with Mathematical Models Investigation 2: Linear Models and Equations (24–25), Investigation 3: Inverse Variation (47–51); Shapes of Algebra Investigation 3: Equations With Two or More Variables (37–38) TG: Thinking with Mathematical Models Investigation 2: Linear Models and Equations (38–42), Investigation 3: Inverse Variation (62–70); Shapes of Algebra Investigation 3: Equations With Two or More Variables (56–60)

6. provide opportunities to graph linear equations and

inequalities within the Cartesian coordinate plane by generating a table of values (with and without technology).

32

SE: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (10–11), Growing, Growing, Growing Investigation 1: Exponential Growth (5–7), Investigation 4: Exponential Decay (48–49), Investigation 5: Patterns with Exponents (59–6168–69); Frogs, Fleas, and Painted Cubes Investigation 1: Introduction to Quadratic Relationships (6), Investigation 3: Quadratic Patterns of Change (40–43, 49); Say It With Symbols Investigation 4: Looking Back at Functions (57–59), Investigation 5: Reasoning With Symbols (75, 82–83) TG: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (25–30), Growing, Growing, Growing Investigation 1: Exponential Growth (20–30), Investigation 4: Exponential Decay (81–84), Investigation 5: Patterns with Exponents (99–102, 114–115); Frogs, Fleas, and Painted Cubes Investigation 1: Introduction to Quadratic Relationships (20–24), Investigation 3: Quadratic Patterns of Change (89–105, 110); Say It With Symbols Investigation 4: Looking Back at Functions (97–106), Investigation 5: Reasoning With Symbols (123–126, 131)

7. provide examples and opportunities to formulate and

apply a rule to generate an arithmetic, geometric and algebraic pattern.

33

SE: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (18), Investigation 2: Linear Models and Equations (27–29, 41), Investigation 3: Inverse Variation (49–51); Looking for Pythagoras Investigation 1: Coordinate Grids (14); Frogs, Fleas, and Painted Cubes Investigation 1: Introduction to Quadratic Relationships (16); Shapes of Algebra Investigation 1: Equations for Circles and Polygons (8–9, 16, 18), Investigation 2: Linear Equations and Inequalities (32), Investigation 3: Equations With Two or More Variables (39–40), Investigation 5: Linear Inequalities (74–75) TG: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (35), Investigation 2: Linear Models and Equations (43–46, 59), Investigation 3: Inverse Variation (67–70); Looking for Pythagoras Investigation 1: Coordinate Grids (32); Frogs, Fleas, and Painted Cubes Investigation 1: Introduction to Quadratic Relationships (44); Shapes of Algebra Investigation 1: Equations for Circles and Polygons (23–26, 33), Investigation 2: Linear Equations and Inequalities (53), Investigation 3: Equations With Two or More Variables (61–64), Investigation 5: Linear Inequalities (101–108)

8. provide examples and opportunities to determine the

slope of a line using a variety of methods including • graphing • change in y over change in x • equation

34

SE: Thinking with Mathematical Models Investigation 2: Linear Models and Equations (30–31), Investigation 3: Inverse Variation (49–51); Growing, Growing, Growing Investigation 2: Examining Growth Patterns (20–21), Investigation 3: Growth Factors and Growth Rates (34), Investigation 4: Exponential Decay (51–52); Frogs, Fleas, and Painted Cubes Investigation 4: What Is a Quadratic Function? (56); Say It With Symbols Investigation 1: Equivalent Expressions (5–6), Investigation 2: Combining Expressions (23–25, 33), Shapes of Algebra Investigation 3: Equations With Two or More Variables (37–38) TG: Thinking with Mathematical Models Investigation 2: Linear Models and Equations (47–54), Investigation 3: Inverse Variation (62–70); Growing, Growing, Growing Investigation 2: Examining Growth Patterns (45–48), Investigation 3: Growth Factors and Growth Rates (62–66), Investigation 4: Exponential Decay (89–92); Frogs, Fleas, and Painted Cubes Investigation 4: What Is a Quadratic Function? (85-88); Say It With Symbols Investigation 1: Equivalent Expressions (20–24), Investigation 2: Combining Expressions (45–52, 59), Shapes of Algebra Investigation 3: Equations With Two or More

9. provide examples and opportunities to represent and

solve real-world grade-appropriate problems using multiple strategies and justify solutions.

35

Variables (56–60) SE: Growing, Growing, Growing (74–75) TG: Growing, Growing, Growing (119–120)

10. provide opportunities to identify a real life problem

involving change over time; make a hypothesis as to the outcome; develop, justify, and implement a method to collect, organize, and analyze data; generalize the results to make a conclusion; compare the hypothesis and the results of the investigation; present the project using words, graphs, drawings, models, or tables.

C. Geometry

SE: Kaleidoscopes, Hubcaps, and Mirrors Investigation 4: Applying Congruence and Symmetry (75, 76); Shapes of Algebra Investigation 1: Equations for Circles and Polygons (8–9); West Virginia Additional Lessons Grade 8 Topic 4: Transversals and Angle Pairs (9-10) TG: Kaleidoscopes, Hubcaps, and Mirrors Investigation 4: Applying Congruence and Symmetry (110); Shapes of Algebra Investigation 1: Equations for Circles and Polygons (23–26); West Virginia Additional Lessons Grade 8 Topic 4: Transversals and Angle Pairs (7-8)

1. provide opportunities to justify the relationships among

corresponding, alternate interior, alternate exterior and vertical angles when parallel lines are cut by a transversal using models, pencil/paper, graphing calculator, and technology.

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SE: West Virginia Additional Lessons Grade 8 Topic 8: Euler’s Formula (19-20) TG: West Virginia Additional Lessons Grade 8 Topic 8: Euler’s Formula (15-16)

2. provide opportunities to classify polyhedrons according to

the number and shape of faces; use inductive reasoning to determine the relationship between vertices, faces and edges (edges + 2 = faces + vertices).

SE: West Virginia Additional Lessons Grade 8 Topic 3: Perpendicular and Angle Bisectors (7-8) TG: West Virginia Additional Lessons Grade 8 Topic 3: Perpendicular and Angle Bisectors (5-6)

3. provide examples and opportunities to identify, apply, and

construct perpendicular and angle bisectors with and without technology ) given a real-world situation.

SE: Thinking with Mathematical Models Investigation 3: Inverse Variation (59); Kaleidoscopes, Hubcaps, and Mirrors Investigation 1: Three Types of Symmetry (8–14), Investigation 2: Symmetry Transformations (27–35, 43, 46), Investigation 4: Applying Congruence and Symmetry (68–69); Investigation 5:Transforming Coordinates (79–87) TG: Thinking with Mathematical Models Investigation 3: Inverse Variation (79); Kaleidoscopes, Hubcaps, and Mirrors Investigation 1: Three Types of Symmetry (23–34), Investigation 2: Symmetry Transformations (45–66, 73), Investigation 4: Applying Congruence and Symmetry (103–108); Investigation 5:Transforming Coordinates (113–130)

4. provide opportunities to create geometric patterns

including tiling, art design, tessellations and scaling using transformations (rotations, reflections, translations) and predict results of combining, subdividing, and changing shapes of plane figures and solids.

37

SE: Thinking with Mathematical Models Investigation 2: Linear Models and Equations (41, 43), Investigation 3: Inverse Variation (59); Growing, Growing, Growing Investigation 2: Examining Growth Patterns (30), Investigation 5: Patterns with Exponents (66); Frogs, Fleas, and Painted Cubes Investigation 2: Quadratic Expressions (36); Kaleidoscopes, Hubcaps, and Mirrors Investigation 2: Symmetry Transformations (43); West Virginia Additional Lessons Grade 8 Topic 2: Scale Models (3-5) TG: Thinking with Mathematical Models Investigation 2: Linear Models and Equations (59), Investigation 3: Inverse Variation (79); Growing, Growing, Growing Investigation 2: Examining Growth Patterns (58), Investigation 5: Patterns with Exponents (114–115); Frogs, Fleas, and Painted Cubes Investigation 2: Quadratic Expressions (85); Kaleidoscopes, Hubcaps, and Mirrors Investigation 2: Symmetry Transformations (72)

5. provide examples and opportunities to create scale

models of similar figures using ratio, proportion with pencil/paper and technology and determine scale factor.

38

SE: Looking for Pythagoras Investigation 1: Coordinate Grids (14); Investigation 3: The Pythagorean Theorem (40–42), Investigation 4: Using the Pythagorean Theorem (60–61); Frogs, Fleas, and Painted Cubes Investigation 4: What Is a Quadratic Function? (72–3); Kaleidoscopes, Hubcaps, and Mirrors Investigation 1: Three Types of Symmetry (21–23), Investigation 2: Symmetry Transformations (44); West Virginia Additional Lessons Grade 8 Topic 5: Exploring Cross Sections (11-14), Topic 7: Testing Conjectures (17-18) TG: Looking for Pythagoras Investigation 1: Coordinate Grids (32); Investigation 3: The Pythagorean Theorem (79), Investigation 4: Using the Pythagorean Theorem (95); Frogs, Fleas, and Painted Cubes Investigation 4: What Is a Quadratic Function? (153); Kaleidoscopes, Hubcaps, and Mirrors Investigation 1: Three Types of Symmetry (40), Investigation 2: Symmetry Transformations (72); West Virginia Additional Lessons Grade 8 Topic 5: Exploring Cross Sections (9-10), Topic 7: Testing Conjectures (13-14)

6. provide examples and opportunities to make and test a

conjecture concerning • regular polygons, • the cross section of a solid such as a cylinder,

cone, and pyramid, • the intersection of two or more geometric figures in

the plane (e.g., intersection of a circle and a line), and justify the results.

39

D. Measurement

SE: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (20, 22), Investigation 3: Inverse Variation (59); Looking for Pythagoras Investigation 3: The Pythagorean Theorem (40–42), Investigation 4: Using the Pythagorean Theorem (63); Kaleidoscopes, Hubcaps, and Mirrors Investigation 1: Three Types of Symmetry (21–23); West Virginia Additional Lessons Grade 8 Topic 6: Investigating Volume (15-16) TG: Thinking with Mathematical Models Investigation 1: Exploring Data Patterns (36), Investigation 3: Inverse Variation (79); Looking for Pythagoras Investigation 3: The Pythagorean Theorem (70), Investigation 4: Using the Pythagorean Theorem (96); Kaleidoscopes, Hubcaps, and Mirrors Investigation 1: Three Types of Symmetry (40); West Virginia Additional Lessons Grade 8 Topic 6: Investigating Volume (11-12)

1. provide examples and opportunities to select and apply an

appropriate method to solve; justify the method and the reasonableness of the solution of problems involving volume of

• prisms • cylinders • cones • pyramids • spheres

given real-world problem solving situations.

40

SE: Looking for Pythagoras Investigation 2: Squaring Off (20–21), Investigation 3: The Pythagorean Theorem (35, 40, 42), Investigation 4: Using the Pythagorean Theorem (46–52, 60); Kaleidoscopes, Hubcaps, and Mirrors Investigation 4: Applying Congruence and Symmetry (68–69) TG: Looking for Pythagoras Investigation 2: Squaring Off (39–42), Investigation 3: The Pythagorean Theorem (61–64, 79), Investigation 4: Using the Pythagorean Theorem (74–90, 94); Kaleidoscopes, Hubcaps, and Mirrors Investigation 4: Applying Congruence and Symmetry (103–108)

2. provide examples and opportunities to solve problems

involving missing measurements in plane and solid geometric figures using formulas and drawings including irregular figures, models or definitions.

SE: Looking for Pythagoras Investigation 4: Using the Pythagorean Theorem (49, 57, 62) TG: Looking for Pythagoras Investigation 4: Using the Pythagorean Theorem (79–82, 94)

3. provide examples and opportunities to solve right triangle

problems where the existence of triangles is not obvious using the Pythagorean Theorem and indirect measurement in real-world problem solving situations.

41

E. Data Analysis and Probability

SE: West Virginia Additional Lessons Grade 8 Topic 9: Permutations and Combinations (21-24) TG: West Virginia Additional Lessons Grade 8 Topic 9: Permutations and Combinations (17-18)

1. provide examples and opportunities to determine and

explain whether a real-world situation involves permutations or combinations, then use appropriate technology to solve the problem.

SE: Shapes of Algebra Investigation 2: Linear Equations and Inequalities (33); Samples and Populations Investigation 2: Choosing a Sample From a Population (42–43); West Virginia Additional Lessons Grade 8 Topic 10: Theoretical Probability (25-26), Topic 11: Experimental Probability (27-28) TG: Shapes of Algebra Investigation 2: Linear Equations and Inequalities (53); Samples and Populations Investigation 2: Choosing a Sample From a Population (73); West Virginia Additional Lessons Grade 8 Topic 10: Theoretical Probability (19-20), Topic 11: Experimental Probability (21-22)

2. provide examples and opportunities to compare the

experimental and theoretical probability of a given situation (including compound probability of a dependent and independent event).

42

SE: Shapes of Algebra Investigation 1: Equations for Circles and Polygons (18); Samples and Populations Investigation 1: Comparing Data Sets (5–16), Investigation 2: Choosing a Sample From a Population (31–33, 40), Investigation 3: Solving Real-World Problems (47–53), Investigation 4: Relating Two Variables (62–68, 74–75, 78) TG: Shapes of Algebra Investigation 1: Equations for Circles and Polygons (33); Samples and Populations Investigation 1: Comparing Data Sets (20–46), Investigation 2: Choosing a Sample From a Population (63–66, 73), Investigation 3: Solving Real-World Problems (77–89); Investigation 4: Relating Two Variables (96–106, 108, 109)

3. provide examples and opportunities to create and

extrapolate information from multiple-bar graphs, box and whisker plots, and other data displays using appropriate technology.

SE: Samples and Populations Investigation 2: Choosing a Sample From a Population (27–35, 44), Investigation 3: Solving Real-World Problems (47–53), Investigation 4: Relating Two Variables (62–68) TG: Samples and Populations Investigation 2: Choosing a Sample From a Population (54–70, 74), Investigation 3: Solving Real-World Problems (47–53), Investigation 4: Relating Two Variables (62–68)

4. provide examples and opportunities to analyze problem

situations, games of chance, and consumer applications using random and non-random samplings to determine probability, make predictions, and identify sources of bias.

43

SE: Thinking with Mathematical Models Investigation 3: Inverse Variation (57); Samples and Populations Investigation 2: Choosing a Sample From a Population (31–35) TG: Thinking with Mathematical Models Investigation 3: Inverse Variation (78); Samples and Populations Investigation 2: Choosing a Sample From a Population (63–70)

5. provide examples and opportunities to draw inferences,

make conjectures and construct convincing arguments involving different effects that changes in data values have on measures of central tendency misuses of statistical or numeric information, based on data analysis of same and different sets of data.

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