correlated to the Instructional Materials Adoption: … to the Instructional Materials Adoption: ......

correlated to the

Instructional Materials Adoption: 21st Century Learning Evaluation CriteriaGeneric, General, and Specific Evaluation Criteria, 2010-2015Seventh Grade Mathematics

1

PUBLISHER: Saxon (an imprint of HMH Supplemental Publishers Inc.) SUBJECT: Mathematics SPECIFIC GRADE: Grade 7 COURSE: TITLE: Saxon Math Course 2 COPYRIGHT DATE: 2007 SE ISBN: 978-1-591-41835-1 TE ISBN: 978-1-600-32073-6

GENERIC EVALUATION CRITERIA 2010-2015

Seventh Grade Mathematics

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

CRITERIA

NOTES

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).

At Saxon, we strive to provide a fair and unbiased presentation of people and issues at all times. Examples in our textbooks, media products, and promotional materials reflect the diversity of today’s classroom and of our society. We take great care to use examples of people from different backgrounds in a variety of roles in an effort to provide students with positive models. Toward these ends, we established overall targets based roughly on the latest federal census figures. During the publication process, our editors and designers use these targets to select examples that match our instructional goals while also emphasizing diversity. See examples in Teacher’s Manual: -Instruction: pages 72 #4-6 and #11, 75-78, 85 Ex. 4, 110, 130 Ex. 5, 158 Ex. 1,

2

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

CRITERIA

NOTES

275 Ex. 3-4, 297, and 332 #a-e -Problem-Solving: pages 120-121, 157, 169, 194, 255, 280, 309, and 342 -Written Practice: pages 52 and 133 Early Finishers, 172 #2-3 and #5, 185 #3-4 and #7, 191 #1-2, 213 #2-3, 225 #1-2, 282 #1-2, 314 #3, 327 #4, and 372 #4-5 -Assessments: pages 142A (Power Up Test 3 and Cumulative Test 3A/3B #4), 215A (Power Up Test 5 and Cumulative Test 5A/5B #3-4), 254A (Cumulative Test 6A/6B #2-3), and 392A (Power Up Test 10 and Cumulative Test 10A/10B #4)

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).

Equity in the Saxon Mathematics K-8 Series is shown through written dialogue rather than visual display. Graphics and illustrations are strictly mathematical and support instruction. The lessons in our mathematics program are very generic without any cultural bias. Below are various examples used throughout Course 2. See examples in Teacher’s Manual: -Instruction: pages 72 #4-6 and #11, 75-78, 85 Ex. 4, 110, 130 Ex. 5, 158 Ex. 1, 275 Ex. 3-4, 297, and 332 #a-e -Problem-Solving: pages 120-121, 157, 169, 194, 255, 280, 309, and 342 -Written Practice: pages 52 and 133 Early Finishers, 172 #2-3 and #5, 185 #3-4 and #7, 191 #1-2, 213 #2-3, 225 #1-2, 282 #1-2, 314 #3, 327 #4, and 372 #4-5 -Assessments: pages 142A (Power Up Test 3 and Cumulative Test 3A/3B #4), 215A (Power Up Test 5 and Cumulative Test 5A/5B #3-4), 254A (Cumulative Test 6A/6B #2-3), and 392A (Power Up Test 10 and Cumulative Test 10A/10B #4)

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INSTRUCTIONAL MATERIALS ADOPTION: 21st CENTURY LEARNING EVALUATION CRITERIA

GENERAL EVALUATION CRITERIA 2010-2015


(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

Saxon provides: -Daily problem solving with discussion -Distributed/cumulative practice & assessment to gradually build on skills already taught -Real-world activities and cross-curricular problems build math connections -Higher-order thinking skills highlighted in margins (“Thinking Skill”) and in Written Practice to deepen math understanding -Investigations and manipulatives for

• 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



A=Adequate

M=Minimal

N=Nonexistent

I A M N

4

exploration and engagement with math content -Additional real-world investigations online at www.saxonmath.com/wv -Additional online activities to reinforce & practice math content -Early Finishers problems for enrichment with real-world applications -Math Language & Reading Math support in margins to build knowledge of math terms & formulas -Glossary at back of text with lesson reference numbers to reinforce math terms & formulas



A=Adequate

M=Minimal

N=Nonexistent

I A M N

5

B. 21st Century Tools

Saxon provides: -Introductory problem solving lesson -Daily problem-solving activities with four-step process -Graphing Calculator activities (examples on pg. 31, 310, and 624, or see www.saxonmath.com/wv) -Investigations and Performance Tasks/Activities allow students to develop math communication skills (Inv. 5 on pgs. 359-362, Inv. 8 on pgs. 558-561, Performance Task 7 on pg. 292C in Teacher’s Manual) -Additional real-world investigations with internet research, word processing, and/or drawing software (see www.saxonmath.com/wv)

• 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)

6

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




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

Saxon provides: -Student eBook -Instructional Presentations for projection of content onto SMART board or screen -Test & Practice Generator to allow for computer-based practice and test-taking -Additional investigations online provide for internet research and drawing software use

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

access) materials.

Saxon provides: -Additional practice and resources available at www.saxonmath.com/wv

2. provide a website which provides links to relevant sites as well as

lesson plans, student activities and parent resources.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

7

Saxon provides: -Instructional presentations for modeling of lesson content, examples, and practice -Online activities to reinforce math concepts and allow for problem solving

3. Integrate technology seamlessly when appropriate to model

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

B. Scientifically-Based Research Strategies

Consistent and incremental instruction & practice provided throughout the Saxon Math program allow for long-term mastery of skills. See Teacher’s Manual: 1) TOC/Contents By Strand (pg. T25-T41) 2) Content Trace in Section Overviews (examples on pg. 6D, 221D, 432D and 631D) 3) “Looking Forward” box at end of each lesson (examples on pg. 59, 127, 263, and 549)

1. Consistently require students to link prior knowledge to new

information to construct their own viable understandings of mathematical ideas.

There are daily multi-step problem solving opportunities, alternate methods (see Teacher’s Manual pg. 6B and 75B), non-routine problems in Power Up, Practice, and Investigations (see pg. 107#h, 141 #27, and 359-362)

2. Consistently provide opportunities for students to solve complex

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



A=Adequate

M=Minimal

N=Nonexistent

I A M N

8

Saxon provides numerous opportunities for students to communicate mathematically. See Teacher’s Manual: 1) Problem-solving discussions (examples on pg. 45B and 235B) 2) Section Overviews (examples on pg. 75B and 363B) 3) Math Conversations in margin during Written Practice (examples on pg. 105-106 and 339-341) 4) Performance Tasks/Activites and Investigations (examples on pg. 142C, 216-220, and 328B)

3. Consistently provide opportunities for students to communicate their

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

Saxon consistently asks students to justify, analyze, verify, draw conclusions, or explain their mathematical thinking during daily instruction and practice (for examples, see pg. 59 #17, 112 #9, 207 #30, 233 #29, and 326 #f)

4. Routinely require students to develop and defend mathematical

conjectures, arguments, reasoning and proof.

Saxon provides full investigations every 10 lessons (see examples on pg. 143-148, 427-431 and 558-561) in addition to activities embedded in lessons (see examples on pg. 243, 433 and 546) and online (see www.saxonmath.com/wv)

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

that enable them to make connections among mathematical ideas.

Saxon provides numerous opportunities to develop a variety of mathematical representations through: 1) Problems using pictures or diagrams (see examples on pg.

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.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

9

45, 121-123, 234 #30, and 329) 2) Representation (see examples in Teacher’s Manual pg. 149B and 296B) 3) Lesson Activities/Investigations (see examples on pg. 72-74 and 265-266) 4) Glossary with lesson reference numbers (pg. 847-880) Saxon provides a number of resources to support differentiated instruction: 1) Margin support with boxes for Math Background, English Learners, Inclusion, Manipulative Use, and Alternate Approaches (see examples in Teacher’s Manual on pg. 29, 67, 96, 176, and 363F) 2) Margin support for instruction during Power Up, New Concepts, and Written Practice, including instruction checkpoints, error alerts, conversations, and extensions (see examples in Teacher’s Manual pg. 128-133 and 280-284) 3) “Reteaching Masters” book with additional support for every lesson 4) “Adaptations” – complete parallel program for students with special needs, included adapted practice and assessments

7. Present varied teaching models with emphasis on differentiated

instruction in content, process, and product.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

10

C. Critical Thinking

Daily problem solving discussions are emphasized throughout the program (see examples in Teacher’s Manual on pg. 60B, 120B, and 490B), with opportunities for math conversations (see examples in Teacher’s Manual on pg. 98-99 and 299-301) and numerous higher order thinking questions highlighted in the Written Practice (see examples on pg. 44 #29, 125 #2, and 322 #30)

1. emphasize questioning models to promote higher order thinking skills

based on depth of knowledge.

Saxon provides many opportunities for discussion and reasoning through problem solving discussions (see examples in Teacher’s Manual on pg. 93B and 323B), Math Conversations (see examples in Teacher’s Manual on pg. 232-233 and 344-346), Performance Tasks & Activities (see examples in Teacher’s Manual on pg. 215C and 392B), and Written Practice problems (see examples on pg. 51 #18, 192 #10, and 351 #28)

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.

Saxon provides instruction, activities, and practice that contain numerous real-world applications as listed in each Section Overview of the Teacher’s Manual (see examples on pg. 75B, 221B, and 562B)

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

throughout the instruction, and promotes and develops critical thinking.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

11

D. Life Skills

Saxon provides extensive practice with numerous connections to life skills, including: working with money (pg. 33 Early-Finishers, 79 #2, 204 #2, 225 #1 and 567 #13), sales tax (pg. 307# 22, 422-423, and 622 #15), salaries (pg. 224 #6 and 577 #4), sales (pg. 349 #3 and 602 #15) research (investigations online: www.saxonmath.com/wv), weather (pg. 51 #11, 230-231, and 572 #10), time (pg. 84-84 and 232 #2), health & science (pg. 192 # 10 and 199 Early Finishers), liquid measurements (pg. 156 #28 and 340 #7), other measurements (pg. 112 #10, 253 #11, and 377 #8), traveling/gas mileage (pg. 113 Early Finishers, 409 #1, and 547 #2), averages (pg. 251 #1 and 566 #3 ), scale drawing (pg. 677-682)

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).

Saxon provides: -Opportunities for students to interact with others through lesson activities and investigations -Projects to be worked on in groups and presented to the class (www.saxonmath.com/wv) -Development of literacy skills through carefully scaffolded word problems -Independent practice and homework to build student work

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

communications, problem solving and self-directional skills).



A=Adequate

M=Minimal

N=Nonexistent

I A M N

12

habits

E. Classroom Management Saxon provides: -Daily whole-group warm-up (consisting of fact practice, mental math exercises, and a problem-solving discussion), new concept instruction, and guided practice -Instructional presentations to allow for student interaction with new content and problems -Written practice for independent skill development & reinforcement -Opportunities for small group remediation during Written Practice to address specific concerns using problems or Reteaching Masters -Lesson activities & investigations for collaborative learning

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

learning.

Including in the program are: -Initial problem-solving lesson to introduce 4-step process and problem-solving strategies -Daily problem solving discussions -Investigations, Activities, and Performance Tasks/Activities to allow for exploration of math concepts

2. Consistently require students to explore mathematical ideas,

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

Saxon provides: -Margin support in Teacher’s Manual for differentiation: English Learners, Inclusion, manipulatives, math background, error alerts, math conversations, online activities, and extensions

3. provide suggestions for differentiated instruction (e.g., practice

activities, learning stations, assessment, lesson plans).



A=Adequate

M=Minimal

N=Nonexistent

I A M N

13

-Reteaching Masters for reinforcement of prior lessons -Complete parallel program (“Adaptations”) with modified practice sheets and assessments



A=Adequate

M=Minimal

N=Nonexistent

I A M N

14

F. Instructional Materials Saxon’s core instructional pedagogy is incremental and gradual instruction, giving students time and ample opportunities to practice and master math skills. Teacher’s Manual provides the guide for math instruction with additional options for teaching, practice, and engagement with math skills provided in margin, Reteaching Masters, Test & Practice Generator, Online Activities, and Performance Tasks/Activities.

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.

Saxon provides: -Daily problem-solving activities during which students decide upon a strategy to solve both routine and non-routine problems -Investigations every 10 lessons to allow students to spend a full class period exploring a mathematical concept in depth -Performance tasks/activities to allow students to respond to prompts and be scored using a rubric

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

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

Teacher’s Manuals include: -Easy-to-follow presentation of lesson content -Questioning strategies, modeling

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

of mathematical discourse to further mathematical understanding.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

15

suggestions, and Teacher Tips in margin of Teacher’s Manual -Daily guide to problem-solving activity and discussion

Saxon provides a 2-volume Teacher’s Manual with Section Overviews every 10 lessons and Lesson Overviews for every lesson, investigation, and test. These pages include all the resources needed for instruction and assessment, including: -Lesson planner table with lists of materials and resources -Lesson highlights (including process & communication skills) and technology resources -Content highlights (big picture) -Content trace, including when and where skills are practiced and assessed in the future -Lesson preparation, including math vocabulary and NCTM standards -Guide to Power-Up discussion

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

to access and use.

Saxon provides: -A variety of visual models for math concepts, including diagrams, charts, pictures, and concrete manipulatives -Alternate methods for solving problems -Instructional presentations to allow for interaction with concepts -Margin support in Teacher’s Manual for varying instruction

5. Include various instructional models to address varied learning styles

of students.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

16

Saxon provides: -Support in margins of Teacher’s Manual for English Learners & Inclusion students, plus Math Background and Teacher Tips -Written Practice designed as a math workshop to address any gaps in students’ knowledge -Reteaching Masters to further address struggling learners -Test & Practice Generator to design additional targeted practice -Extensions in margins of Teacher’s Manual and Early Finishers problems at end of certain Written Practice sections -Complete parallel program (Saxon Math Adaptations) with more intensive support for struggling learners, including modified lessons & assessments -Daily fact practice and mental math problems to build basic computation skills

6. Provide extensive and varied opportunities to differentiate individual

needs for skill-building.

Saxon provides: -Reteaching Masters with support for struggling learners -Test & Practice Generator for designing tests and practice sheets for struggling and advanced learners, to be given traditionally (pen & pencil) or on the computer -Enrichment problems in student book (Early Finishers) and Teacher’s Manual (Extend the Problem) -Instructional Posters to serve as

7. Provide supplemental materials for intervention and enrichment.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

17

reference points for struggling learners -Student glossary in back of student book (with Spanish terms) Saxon provides a 2-volume Teacher’s Manual with Section Overviews and Lesson Overviews that highlight content and process standards, including connections to NCTM Standards

8. Provide teachers with support to properly integrate the process

standards using the available resources.

Teacher’s Manuals contain Section/Lesson Overviews with detailed preparation for upcoming lesson(s). Each lesson includes margin support for instruction, including Math Background boxes to build content knowledge.

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

teacher.

Saxon provides cumulative Written Practice and assessment, ensuring that older content is integrated with new content to build mastery and allow students to see connections between skills. Power Up includes practice of basic skills and problem-solving discussions to gradually build comfort with problem-solving strategies and processes.

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



A=Adequate

M=Minimal

N=Nonexistent

I A M N

18

G. Assessment Included in the program are: -Grade-specific test preparation booklets for West Virginia -Test & Practice Generator to allow teacher to develop targeted assessments/practice sheets reformatted to fit common test styles (options include: NAEP, ACT, AP Exam, PSAT, SAT, and TOEFL)

1. provide assessment formats commensurate with WV assessment

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

Saxon provides: -Performance tasks/activities that are scored on a rubric -Higher order thinking questions embedded in Written Practice to allow students to explore different ways to solve the problem, show their work, and explain their process -Tracking of student progress using the eGradebook or Test & Practice Generator to assist with evaluation

2. provide opportunities for assessment based on performance-based

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

Benchmark and progress monitoring consist of: -Power Up and Cumulative assessments every 5 lessons -Benchmark assessments every 20 lessons (approximately every 6 weeks) -Student progress tracking tools (eGradebook and Test & Practice Generator) -Class and individual test analysis

3. provide benchmark and ongoing progress monitoring.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

19

forms -Student Progress Chart to track mastery of basic facts Saxon provides performance tasks and activities scored on a rubric in addition to frequent cumulative tests. Additionally, Saxon Math Adaptations is a complete parallel program which includes modified tests for students with special needs.

4. provide rubric-based differentiated assessment.

Monitoring student progress is accomplished with resources for reteaching and reassessment: the Monitoring Student Progress eGradebook and the Test & Practice Generator, the latter of which allows students to take computer-based tests with the results immediately documented in the provided tracking system

5. provide an electronic system for managing assessment data to

facilitate the implementation of tiered instruction

Saxon provides guided lesson practice and corrected written practice problems to allow students to monitor their learning. The Instructional Masters Book provides three types of Lesson Recording Forms (one for the Power Up & Lesson Practice, one with boxes and gridlines to provide extra support, and one with just boxes) to allow students to organize their work and focus on specific problems of higher difficulty (e.g. word problems, starred problems). Saxon also provides a Student Progress Chart to track mastery of basic

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

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



A=Adequate

M=Minimal

N=Nonexistent

I A M N

20

fact practice in the Power Up. Saxon provides: -Placement and baseline tests to determine student levels at beginning of the school year -Formative assessment through Power-Up, Lesson Practice, Written Practice, & Investigations -Summative assessments (Power-Up and Cumulative Tests every 5 lessons, Benchmark Tests every 20 lessons, End of Course Exam)

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

for diagnostic, formative, and summative purposes.

Saxon provides a variety of assessments, including: basic facts, computation, word problems, multiple choice, short answer, and open-ended questions (Performance Tasks)

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

choice, short answer, and free response.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

21

H. Process Standards

Saxon provides: -A daily problem solving activity and discussion designed to introduce students strategies and move them toward becoming independent problem solvers -Section Overviews in Teacher’s Manual for every 10 lessons with embedded problem-solving strategies identified (see examples on pg. 114B, 273B, and 592B)

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.

Saxon’s Section Overviews note specific opportunities for students to discuss, explain, and formulate mathematical thinking to be shared in class or on paper (see examples on pg. 114B, 273B, and 592B). Support is also provided for the teacher in the margins of the Teacher’s Manual through Math Conversations, including numerous opportunities for extension (see examples on pg. 191-193 and 397-399).

2. Communication: Routinely challenge students to communicate their

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

Saxon provides: -Performance tasks/activities and investigations (in book and online) to allow for exploration of math concepts (see examples in TE on pg. 181B and 328B) -Written Practice problems provide numerous opportunities for students to develop and

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.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

22

explain math reasoning (see examples on pg 92 #27, 225 #5, and 377 #4) Saxon’s Section Overviews note specific opportunities to make connections between math strands as well as the real world (see examples in Teacher’s Manual pg. 114B, 273B, and 592B)

4. Connections with Mathematics: Consistently establish connections,

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

The Section Overviews note specific opportunities for students to create different representations of math skills using manipulatives, models, diagrams, pictures, words, symbols, or other representations (see examples in Teacher’s Manual pg. 114B, 273B, and 592B and on pg. 91 #10, 115-117, 160 #5, 223 #14, 299 #5, and 359-362)

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.

23

SPECIFIC EVALUATION CRITERIA Seventh Grade Mathematics

Seventh grade objectives place emphasis on preparing students to take Algebra I in the eighth grade year. With less emphasis

on paper/pencil computation, calculators are emphasized in all facets of the mathematics daily work as well as test situations. Review of all basic mathematics skills occurs in a relevant context. Problem solving is embedded in the curriculum, a variety of new concepts are utilized, and cooperative learning promotes communication skills. 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.

24

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.

25

(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

A. Number and Operations

Instruction: (New Concept) 26-31, 55-57, 67-69, 100-101, 175-176, 201, 210, 213, 235-238, 242-244, 303-305, 355, 413-416, 420-423, 540-541, 592-594, 693-696 Instruction: (Investigation) 73-74, 293-295 Maintenance: (Written Practice) 33, 38-39, 58-59, 70-71, 86, 99, 106, 111, 155, 161, 174, 226, 239-240, 271, 278, 315, 333, 417-418, 424-425, 445, 457, 511, 517, 527, , 542, 547, 556, 566, 572, 577, 584, 589, 591, 595, 601, 615-616, 622-623, 634, 640, 646, 658, 675, 684, 698, 708, 722, 742

1. provide examples and exercises to compare, order, and differentiate

among integers, decimals, fractions, and irrational numbers using multiple representations (e.g., symbols, manipulatives, graphing on a number line).



A=Adequate

M=Minimal

N=Nonexistent

I A M N

26

A. Number and Operations (Cont.)

Instruction: (New Concept) 134-139, 686-689, 693-696, 717-720, 760-761 Maintenance: (Written Practice) 140-142, 691, 698, 722, 742, 762-764

2. provide opportunities to model the relationship between perfect

squares and square roots using physical representations; to estimate square root and evaluate using technology.

Instruction: (New Concept) 7-10, 14-17, 21-23, 26-31, 40-42, 54-55, 60-63, 68-69, 76-78, 83-85, 88-90, 93-94, 100-104, 107-111, 128-131, 152-154, 163-166, 169-172, 175-179, 182-185, 188-190, 195-197, 209-213, 247-251, 267-269, 280-282, 287, 290, 296-299, 304-305, 309-313, 317-320, 323-326, 329-332, 336-339, 342-343, 347-349, 352-355, 370-371, 375-376, 380-382, 386-389, 413-416, 420-423, 447-449, 453-455, 466-468, 480-482, 490-492, 502-503, 513-514, 518-519, 524-526, 529-531, 534-536, 562-565, 575-577, 586-589, 604-606, 631-632, 636-638, 642-645, 648-650, 653-655, 660-663, 677-682, 717-720, 778-779, 804-806, 825-828

3. provide opportunities to demonstrate fluency and justify solutions in

performing operations with rational numbers including negative numbers for

adding subtracting multiplying dividing,

using simple computation and problem-solving situations (should be at beginning of sentence)



A=Adequate

M=Minimal

N=Nonexistent

I A M N

27


Instruction: (Investigation) 72A-74, 496A-501, 558A-561 Maintenance: (Written Practice) 11-12, 18-19, 24-25, 32-33, 43-44, 58-59, 64-65, 70-71, 79-81, 85-87, 90-92, 98-99, 104-106, 111-113, 131-133, 140-142, 154-156, 160-162, 166-168, 172-174, 179-181, 185-187, 191-193, 197-199, 213-215, 251-254, 261-263, 270-272, 282-284, 290-292, 299-301, 305-308, 313-316, 320-322, 326-328, 333-335, 339-341, 344-346, 349-351, 356-358, 372-374, 377-379, 382-385, 390-392, 417-419, 423-426, 437-439, 450-452, 456-458, 468-471, 482-484, 493-495, 504-506, 515-517, 520-522, 526-528, 531-533, 537-539, 565-568, 577-579, 589-591, 607-609, 632-635, 639-641, 645-647, 650-652, 656-659, 683-685, 720-723, 780-783

3. provide opportunities to demonstrate fluency and justify solutions

in performing operations with rational numbers including negative numbers for

adding subtracting multiplying dividing,

using simple computation and problem-solving situations (should be at beginning of sentence) (cont.)

Instruction: (New Concept) 14-17, 60-63, 100, 353, 296-299, 447-449, 582-583, 586-588, 661-663, 712-713, 805-806, 825-828 Maintenance: (Written Practice) 18-19, 65, 299, 451, 591, 667, 716, 743, 831

4. provide examples and exercises to justify the use of the commutative,

associative, distributive, identity and inverse properties to simplify numeric expressions.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

28


Instruction: (New Concept) 422-423, 636-638, 765-769 Maintenance: (Written Practice) 424, 445, 462-463, 506, 528, 538, 578, 622, 639-640, 646, 650-651, 657, 664, 673, 675, 683, 690, 696-677, 707, 721, 736, 742, 751, 755, 762, 763, 770-771, 780, 782-783, 788, 796, 806-807, 813, 821, 828, 834, 836, 841, 842

5. provide examples and exercises to analyze and solve grade-

appropriate real-world problems with whole numbers, integers, decimals, fractions and percents including problems involving

discounts, interest, taxes, tips, percent increase or decrease, and

to justify solutions including using estimation and reasonableness.

Instruction: (New Concept) 336-339, 400-402, 599-600, 717-720, 779 Maintenance: (Written Practice) 339-341, 390, 418, 425, 579, 603, 723, 744, 782-783

6. provide opportunities to use inductive reasoning to find and justify the

laws of exponents with numeric bases.

Instruction: (New Concept) 364, 403, 778-779 Maintenance: (Written Practice) 372, 390, 417, 456, 468, 521, 539

7. provide examples and exercises to solve and interpret problems from

real life contexts using numbers in scientific notation (positive and negative exponents) with and without technology.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

29


B. Algebra

Instruction: (New Concept) 29-31, 393-397 Maintenance: (Written Practice) 33 39, 51, 59, 65, 71, 80, 87, 113, 132, 140, 161, 187, 206, 227, 284, 321, 399, 410, 585

1. provide opportunities to use inductive reasoning to find missing

elements in a variety of arithmetic and geometric patterns including algebraic sequences and series.

Instruction: (New Concept) 369-371, 586-588 Maintenance: (Written Practice) 373-374, 378-379, 385, 392, 399, 405, 411-412, 439, 445-446, 484, 488, 506, 511, 517, 521, 528, 556, 568, 574, 574, 585, 595, , 609, 616, 641, 685, 691, 698, 709, 736

2. provide examples and exercises to evaluate algebraic expressions

with whole numbers, integers, absolute value and exponents using the order of operations.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

30

B. Algebra (Cont.)

Instruction: (New Concept) 110-111, 393-394 Instruction: (Investigation) 624-630 Maintenance: (Written Practice) 125, 239, 283, 424

3. provide opportunities to solve problems by creating an input/output

function table(including, but not limited to, spreadsheets) to predict future values, given a real-world situation involving rational numbers.

Instruction: (New Concept) 281 375-376, 380-382, 562-565, 637-639, 677-679, 682 Maintenance: (Written Practice) 468, 477, 486, 504, 515, 520, 531, 547, 578, 583, 584, 589, 590, 595, 596, 633, 639, 641, 646, , 691, 696, 697, 707, 714, 721, 736, 742, 751, 756, 762, 780, 807, 821, 834

4. provide opportunities to analyze proportional relationships in real-

world situations, to select an appropriate method to determine the solution and to justify reasoning for choice of method to solve.

Instruction: (New Concept) 540-541 Instruction: (Investigation) 496-500 Maintenance: (Written Practice) 506, 511, 517, 522, 528, 533, 539, 543, 549, 557, 573, 585, 567, 609, 617

5. provide opportunities to solve one-step linear equations and

inequalities using a variety of strategies containing rational numbers with integer solutions; to graph solutions, and to justify the selection of the strategy and the reasonableness of the solution.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

31

B. Algebra (Cont.)

Instruction: (New Concept) 394-395 Instruction: (Investigation) 625-630 Maintenance: (Written Practice) 634, 781

6. provide opportunities to plot lines within the Cartesian coordinate

plane from a table of values to solve mathematical real-world problems.

Instruction: (New Concept) 745-750 Maintenance: (Written Practice) 753, 756, 764, 771, 781, 797, 807, 815, 823, 830, 835, 842

7. provide examples and activities to determine the slope of a line from

its graphical representation.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

32

B. Algebra (Cont.)

Instruction: (New Concept) 502-504 507-509, 562-565, 636-638, 677-682, 706-707, 755, 765-769 Instruction: (Investigation) 501 Maintenance: (Written Practice) 424, 445, 462-463, 468, 477, 486, 504, 506, 515, 520, 528, 531, 538, 547, 578, 583, 584, 589, 590, 595, 596, 622, 633, 639, 640, 641, 646, 650-651, 657, 664, 673, 675, 677, 683, 685, 690, 691, 696, 697, 707, 714, 721, 736, 742, 751, 755, 756, 762-763, 771-772, 780, 782-783, 788, 796, 806-807, 813, 828, 834, 836, 841, 842

8. provide opportunities to represent algebraically and solve real-world

application problems and justify solutions.

Instruction: (New Concept) 281, 375-376, 380-382, 562-565, 637-639, 677-679 682 Maintenance: (Written Practice) 468, 477, 486, 504, 515, 520, 531, 547, 578, 583, 584, 589, 590, 595, 596, 633, 639,641, 646, 691, 696, 697, 707, 714, 721, 736, 742, 751, 756, 762, 780, 807, 821, 834

9. provide opportunities to identify a real life problem involving

proportionality; 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 conclusion; present the project using words, graphs, drawings, models, or tables.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

33

C. Geometry

Instruction: (New Concept) 123, 288-289 Instruction: (Investigation) 699, 701-702 Maintenance: (Written Practice) 126, 156, 174, 199, 206, 291, 301, 358, 367, 458, 470, 567, 634, 665, 691, 757, 782, 808

1. provide opportunities to identify and construct

• angle-pairs (adjacent, complementary, supplementary, vertical) • congruent segments and angles • perpendicular bisectors of segments • angle-bisectors

Instruction: (New Concept) 406-409 Instruction: (Investigation) 429-431 Maintenance: (Written Practice) 411, 446, 452, 516

2. provide opportunities to apply line symmetry to classify plane figures.

Instruction: (New Concept) 550-555 Maintenance: (Written Practice) 557, 565, 573, 579, 584, 591, 601, 609, 622, 657, 666, 674, 683, 770, 780, 813, 821

3. provide opportunities to apply rotations, reflections, translations to

plane figures and determine the coordinates of its transformation and to compare and contrast the new figure with the original.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

34

C. Geometry (Cont.)

Instruction: (New Concept) 122-124, 281, 375-376, 380-382, 562-565, 637-639, 668-673, 677-682, 765-769, 682 Instruction: (Investigation) 773-777 Maintenance: (Written Practice) 468, 477, 486, 504, 515, 520, 531, 547, 578, 583, 584, 589, 590, 595, 596, 633, 639,641, 646, 676, 691, 692, 696, 697, 707, 709, 714, 721, 736, 738, 742, 751, 756, 757, 762, 771, 780, 782, 789, 807, 808, 815, 821, 823, 830, 834, 836, 843

4. provide examples and exercises to pose and solve ratio and

proportion problems including scale drawings and similar polygons.

Instruction: (New Concept) 679-682 Instruction: (Investigation) 773-777 Maintenance: (Written Practice) 697, 709, 721, 729, 738, 757

5. provide opportunities to solve problems and explain the relationships

among scale factor and area and volume including • square of a scale factor • cube of a scale factor



A=Adequate

M=Minimal

N=Nonexistent

I A M N

35

C. Geometry (Cont.)

Instruction: (New Concept) 655-656 Instruction: (Investigation) 773-777 Maintenance: (Written Practice) 544, 758, 814

6. Provide examples and exercises to solve mathematical real-world

problems using compound geometric figures.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

36

D. Measurement

Instruction: (New Concept) 109, 111, 130-131, 231, 332, 655-656, 732-735, 755 Instruction: (Investigation) 626, 773-777 Maintenance: (Written Practice) 51, 142, 160, 162, 166, 168, 333, 340, 411, 437, 463, 493, 510, 533, 544, 547, 556, 583, 589, 600, 667, 756, 758, 763, 772, 781, 782, 807, 814, 821, 830, 842

1. provide opportunities to select and apply an appropriate method to solve (including, but not limited to, formulas) justify the method and the reasonableness of the solution, given a real-world problem solving situation involving

• perimeter • circumference • area • surface area of prisms (rectangular and triangular) • volume of prisms and cylinders • distance and temperature (Celsius, Fahrenheit )

Instruction: (New Concept) 686-689, 784-787 Maintenance: (Written Practice) 691, 698, 709, 723, 730, 757, 764, 771, 782, 789, 797, 802, 807, 816, 828, 835, 842

2. provide examples and exercises to use the Pythagorean Theorem to

find the length of any side of a right triangle and apply to problem solving situations.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

37

D. Measurement (Cont.)

Instruction: (New Concept) 107-111, 228-231, 352-355, 604-606, 799-801 Maintenance: (Written Practice) 112, 118, 133, 141, 193, 356, 358, 367, 377, 383, 446, 470, 478, 510, 532, 556, 584, 607, 633, 635, 639, 646, 650, 707, 743, 807, 814, 821, 829, 843

3. provide examples and exercises to convert units of measurement, linear, area and volume, within customary and metric systems.

E. Data Analysis and Probability

Instruction: (New Concept) 95-98, 104, 255-259, 311, 648-650 Instruction: (Investigation) 558-561 Maintenance: (Written Practice) 272, 306, 356, 426, 451, 516, 566, 577, 585, 590, 595, 607, 640, 646, 659, 665, 676, 683, 696, 709, 714, 737, 742, 756, 781, 806, 813, 821, 841

1. provide opportunities to determine theoretical probability of an event,

make and test predictions through experimentation.



A=Adequate

M=Minimal

N=Nonexistent

I A M N

38

E. Data Analysis and Probability

Instruction: (New Concept) 257-260 Instruction: (Investigation) 293A-295, 359A-362, 624A-630 Maintenance: (Written Practice) 262, 272, 278, 306, 333, 346, 351, 367, 397, 426, 495, 556, 622, 640, 697

2. provide opportunities to determine combinations and permutations

by constructing sample spaces (e.g., listing, tree diagrams, frequency distribution tables).

Instruction: (New Concept) 273-277 Instruction: (Investigation) 293-295, 359-362 Maintenance: (Written Practice) 277, 282, 306, 339, 345, 366, 377, 417, 468, 506, 537, 585, 656, 790

3. provide opportunities to collect, organize, graphically represent, and

interpret data displays including frequency distributions, line-plots, scatter plots, box and whiskers, and multiple-line graphs.

Instruction: (New Concept) 196-197 Instruction: (Investigation) 293-295, 359-362 Maintenance: (Written Practice) 197, 244, 290, 300, 301, 314, 384, 438, 439, 464, 483, 539, 549, 566, 595, 674, 690, 753, 788

4. provide opportunities to analyze and solve application problems involving measures of central tendency (mean, median, mode) and dispersion (range) from data, graphs, tables, and experiments using appropriate technology to compare two sets of data.

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