THE SCHOOL DISTRICT OF PHILADELPHIA OFFICE OF …assets.pearsonschool.com/...SDP_Rubric_HSMath.pdf · Office of Curriculum, Instruction and Assessment, Christopher Shaffer, Deputy

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Office of Curriculum, Instruction and Assessment, Christopher Shaffer, Deputy Chief

THE SCHOOL DISTRICT OF PHILADELPHIA OFFICE OF CURRICULUM, INSTRUCTION, AND ASSESSMENT MATH TEXTBOOK RUBRIC

Network: Date:

Name: Product: Pearson Algebra 1, Geometry, Algebra 2 Common Core ©2015

Vendor: (Please check off the Vendor from the list below) Content Area: Mathematics

Great Minds Targeted Area: Grades 9-12

Houghton Mifflin IT/ETG Review:

McGraw Hill Publisher: Pearson

X Pearson

3 = Extensive Meets all of the criteria

2 = Sufficient Meets most of the criteria

1 = Weak Meets some of the criteria

0 = Non-Existing Does not meet any of the criteria

Categories

I. Materials align to PA Common Core Standards for Mathematics

Content Standards alignment to PA Common Core Standards has Common Core State Standards (CCSS) correlation

Standards for Mathematical Practice are routinely reinforced with suggestions and resources provided for implementation ○ Make sense of problem and persevere in solving them; Reason abstractly and quantitatively; Construct viable arguments and critique the reasoning of

others; Model with mathematics; Use appropriate tools strategically; Attend to precision; Look for and make use of structure; Look for and express regularity in repeated reasoning.)

Standards for Mathematical Practice are connected to Reading, Writing, Speaking and Listening Standards

Rating 3 2 1 0

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Evidence:

Content Standards alignment to PA Common Core Standards has Common Core State Standards (CCSS) correlation Pearson Algebra 1, Geometry, Algebra 2 Common Core is aligned to the Pennsylvania Common Core Standards. Correlation documents are available upon request.

Standards for Mathematical Practice are routinely reinforced with suggestions and resources provided for implementation Pearson Algebra 1, Geometry, Algebra 2 Common Core was written specifically for the CCSS. The program fully addresses the Common Core Content Standards and incorporates the Standards for Mathematical Practice throughout every lesson. This program was built for the traditional pathway of the CCSS and provides the rigor, flexibility, and data-driven tools teachers need to teach the standards with confidence. Chapter-infused Common Core performance tasks are an integral part of instruction. They are not add-ons to the program. Instead, they foster mathematical connections by bringing together the content standards with the Standards for Mathematical Practice. The chapter-level performance tasks feature the following:

Chapter-Opening Performance Task. The chapter opener introduces the real-world, problem solving task.

Apply What You’ve Learned. Students revisit the chapter-opening task and continue to connect the content standards to the practice standards at least twice per chapter.

Pull It All Together. Students pull together all their new mathematical learning to complete the chapter's performance task.

On Your Own. Students complete an additional performance task to reinforce their learning.

Connecting Content and Practice. The performance tasks incorporated into each chapter help students make explicit connections between the Standards for Mathematical Content and the Standards for Mathematical Practice throughout instruction.

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Each chapter in the program features a mathematical modeling lesson that gives students an opportunity to model with mathematics. Mathematical Modeling in 3 Acts tasks are made up of three parts, called acts:

Act 1: The Hook. Students watch a video that prompts them to ask questions. Rather than being given all information up front, students actively define the word problem they are going to solve. Act 1 provides an entry point for every student, no matter their level of mathematical proficiency.

Act 2: Modeling with Math. Students model with mathematics. They apply the mathematical concepts learned in the chapter and select the appropriate tools to solve the problem they defined in Act One. This is closer to the work of STEM professionals—it is both more challenging and more fun than typical word problems.

Act 3: The Solution. Students watch a video where the answer to the problem is revealed. In Act 3, students root for their conjectures and analyze their results. This act of analyzing and justifying solutions embodies the spirit of the Standards for Mathematical Practice.

Students can also extend their learning with a Sequel problem. The Sequel is a re-imagined word problem related to the original problem, which requires students to model with mathematics. For a detailed overview of how the program supports each Standard for Mathematical Practice, see pages 7–21 of the Common Core Overview and Implementation Guide (these pages are included in the appendix).

Standards for Mathematical Practice are connected to Reading, Writing, Speaking and Listening Standards The program provides ample opportunities for students to engage in mathematical discourse that supports the reading, writing, speaking, and listening standards, including the following examples:

In the first two acts of Mathematical Modeling in 3 Acts, students focus on speaking and listening as they work to define a problem and figure out the best way to model with math to solve the problem. Writing is incorporated throughout all three acts of the mathematical modeling tasks, as students are required to write about their conjectures and analyze their conjectures.

Performance tasks incorporated throughout the chapters require students to explain their reasoning in writing.

The Solve It! that opens every lesson requires students to explain their reasoning verbally or in writing. Solve It! always asks students to justify their solutions and reasoning.

Writing exercises require students to write about mathematics and provide clear, concise explanations of terms, concepts, or processes.

Reasoning exercises require students to formulate arguments to support their solutions.

Error Analysis exercises require students to critique the solution presented for a problem.

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II. Materials: (Please apply a score to each section A-E):

A. Foundational Skills

Coherence: New content is based on previous understandings and provides opportunities to connect knowledge and skills across standard clusters, domains and learning progressions

Rating 3 2 1 0

Evidence:

Coherence: New content is based on previous understandings and provides opportunities to connect knowledge and skills across standard clusters, domains and learning progressions Aligned to the Traditional Pathway of the Common Core State Standards for Mathematics (CCSSM), our program is organized around the Big Ideas of mathematics. Chapters in the program correlate to the CCSSM conceptual categories, domains, and content clusters. A focused and coherent mathematics curriculum provides in-depth instruction on a limited number of important categories of mathematics content. The program extends focus and coherence beyond just providing in-depth instruction on a limited number of important categories of mathematics content. It extends focus and coherence by making explicit the Big Ideas in mathematics that students need to know and by showing how those ideas are related. A Big Idea in mathematics—called a Key Idea in the CCSSM—is a statement of an idea that is central to learning mathematics. It links numerous smaller ideas—called Essential Understandings—into a coherent whole. The program connects all CCSSM content standards to Big Ideas.

Conceptual Category Big Idea

Number & Quantity Properties

Equivalence

Proportionality

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Algebra Properties

Variable

Equivalence

Proportionality

Solving Equations and Inequalities

Functions Variable

Function

Equivalence

Modeling Modeling

Function

Geometry Visualization

Transformations

Measurement

Reasoning & Proof

Similarity

Coordinate Geometry

Statistics and Probability Data Collection & Analysis

Data Representation

Probability

Connecting Big Ideas. Big Ideas in Pearson Algebra 1, Geometry, Algebra 2 Common Core align with the conceptual categories of the CCSSM.

Several Big Ideas run across conceptual categories, connecting ideas across content topics, and this is one reason they are “big.” To illustrate this, the following figure shows the Big Idea called Equivalence and gives examples of content topics in different conceptual categories.

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II. Materials: (Please apply a score to each section A-E):

A. Foundational Skills

Conceptual Categories Big Idea

Number & Quantity

Explain why the rectangular and polar forms of a given complex number represent the same number. (N.CN.4).

Algebra

Choose and produce an equivalent form of an expression. (A.SSE.3).

Functions

Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. (F.IF.8).

Equivalence

A single quantity may be represented by many different expressions.

The facts about a quantity may be expressed by many different equations (or inequalities).

Crossing Conceptual Categories. The Big Idea called Equivalence connects content topics in different conceptual categories.

The program includes lesson quizzes that teachers can use to remediate or enrich as needed. Teachers receive a Prescription for Remediation that helps them make appropriate decisions about review assignments. Resources for remediation, on-level, and enrichment are provided to verify teachers help all students master the CCSSM.

B. Text Complexity

Focus: Lessons and units are grade appropriate with evidence of varying depths of knowledge required

Lesson objectives and expectations are clearly detailed

Examples are clear and concise with detailed steps and visuals that build from concrete to representational to abstract development of concepts

Real-world applications require students to draw from prior knowledge as well as new knowledge

Connections to college and career readiness are integrated throughout materials

Rigor: Requires students to engage with and demonstrate challenging mathematics with appropriate balance among problem solving in application, conceptual understanding, and procedural skills and fluency ○ Application: Provides ongoing opportunities for students to independently apply mathematical concepts in real-world situations, solve challenging problems,

and choose and apply appropriate strategies to new situations

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B. Text Complexity ○ Conceptual Understanding: Develops students’ depth of understanding through tasks, brief problems, questions, multiple representations and opportunities

for them to write and speak about their understanding ○ Procedural Skill and Fluency: Provides guidelines for performing quick and accurate procedural skills, fluency and mathematical procedures

Rating 3 2 1 0

Evidence:

Focus: Lessons and units are grade appropriate with evidence of varying depths of knowledge required The program features lessons and units at a variety of Depth of Knowledge (DOK) levels. The Common Core Overview and Implementation Guide provides an overview of the DOK levels available throughout the program. See pages 52–55 of the Common Core Overview and Implementation Guide (these pages are also included in the appendix). Questioning strategies in the Teacher’s Edition support teachers in checking for understanding. For examples of the probing questions available for various DOK levels in a lesson, see pages 546–549 of the Algebra 1 Teacher’s Edition. The two-volume Teacher’s Edition includes notations of the major clusters and standard alignments in all lessons and activities (see the Algebra 1 Teacher’s Edition, pages 545A–545B and 546 for examples). The Teacher’s Edition also features research-based instructional strategies for differentiating instruction for English Language Learners (ELLs), below-level, on-level, and advanced students (see the Algebra 1 Teacher’s Edition, page 552A for an example).

Lesson objectives and expectations are clearly detailed Lesson objectives and expectations are clearly detailed in the Teacher’s Edition, which includes math background for every chapter and lesson. (See the Algebra 1 Teacher’s Edition, pages 544–545B for chapter examples and page 546 for a lesson example.) The two-volume Teacher’s Edition includes notations of the major clusters and standard alignments in all lessons and activities. The Teacher’s Edition also features research-based instructional strategies for differentiating instruction for English Language Learners (ELLs), below-level, on-level, and advanced students (see the Algebra 1 Teacher’s Edition, pages 545A-545B and page 546 for examples).

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Examples are clear and concise with detailed steps and visuals that build from concrete to representational to abstract development of concepts Clear steps and visuals are well integrated into the program. The instructional model encompasses a variety of instructional strategies, including visual and interactive. The Student Edition provides concrete instructional strategies, and the digital components of the program include both abstract and authentic pictorial instructional strategies. The lesson examples build from concrete to abstract development of concepts and conclude real-world applications with rich visuals. For an example of this building of concepts, see the Algebra 1 Student Edition, pages 562–563 and 568–570.

Real-world applications require students to draw from prior knowledge as well as new knowledge Pearson Algebra 1, Geometry, Algebra 2 Common Core lessons help educators teach through problem solving while simultaneously developing students’ understanding of key mathematical concepts. Students develop procedural fluency and solve real-world problems that require the application of mathematics and the formulation of models. The Solve It! that opens every lesson is a real-world problem that expects students to use prior knowledge to solve a problem that connects to what they will learn in the upcoming lesson. The lesson-opening Solve It! connects to prior learning and sets the stage for future learning. See page 400 of the Algebra 1 Student Edition for an example of a lesson-opening Solve It! Activity. In addition, Mathematical Modeling in 3 Acts lessons requires students to draw from prior knowledge as well as new knowledge to engage in the complete modeling cycle.

Connections to college and career readiness are integrated throughout materials The program is designed to prepare students for college and career. Students spend the majority of their time in each course on the widely applicable prerequisites for college and career, as seen in the following figure. Content from CCSSM Widely Applicable as Prerequisites for a Range of College Majors, Postsecondary Programs, and Careers

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B. Text Complexity

High School Clusters and

StandardPearson High School Mathematics Common Core ©2015

Number and Quantity

N-RNA & N-RN.B Algebra 1: CB 1-6, 7-2, 7-3, 7-4, 7-5 Algebra 2: CB 6-1, 6-4

N-Q.A Algebra 1: 2-5, 2-6, CB 2-6, 2-7, 4-4, 5-7, 12-2, 12-4, 3-3, 4-5, 5-2, 5-5, 6-4, 9-3, 12-3 Geometry: 1-8 Algebra 2: 1-3, 1-4, 2-1, 3-2, 2-10, 6-4, 9-5, 9-6

Algebra

A-SSE.A & A-SSE.B Algebra 1: 1-1, 1-2, 1-7, 3-7, 4-5, 4-7, 5-3, 5-4, 5-5, 7-7, 7-8, 8-5, 8-6, 8-7, 8-8, 9-4, 9-5 Algebra 2: 1-6, 4-4, 4-5, 5-1, 5-3, 6-1, 6-2, 6-3, 6-4, 7-1, 7-2, 7-3, 7-5, 8-4, CB 9-5, 9-5

A-APR.A, A-APR.B, A-APR.C, A-APR.D

Algebra 1: 8-1, 8-2, 8-3, 8-4, 9-3, CB, 9-3, 11-2, 11-3, 11-4 Algebra 2: 4-5, 5-2, 5-4, CB 5-5, 5-6, CB 5-7, 5-7, 8-5, 8-6

-CED.A Algebra 1: 1-8, 1-9, 2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8, 3-2, 3-3, 3-4, 3-6, 3-7, 3-8, 4-5, 5-2, 5-3, 5-4, 5-5, 6-4, 6-5, 7-6, 9-1, 9-2, 9-3, CB 9-4, 9-4, 9-5, 9-6, 9-8, 10-5, 11-5, 11-6, 11-7, CB 11-7 Algebra 2: 1-4, 1-5, 1-6, 2-2, 2-3, 2-4, 2-5, 2-8, 3-1, 3-2, 3-3, 3-4, CB 3-4, 4-1, 4-2, CB 4-5, 4-5, 4-9, 6-5, 7-1, 7-2, CB 7-6, 8-1, CB 8-1, 8-2, 8-3, 8-6

A-REI.A, A-REI.B, A-REI.C A-REI.D

Algebra 1: 1-9, 2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8, 3-2, 3-3, 3-4, 3-5, 3-6, 4-2, 4-3, 4-4, CB 4-4, CB 6-1, 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, CB 6-6, 7-6, 9-3, 9-4, 9-5, 9-6, 9-8, 10-4, 10-5 Algebra 2: 1-4, 1-6, 3-1, 3-2, 3-3, 3-6, 4-5, 4-6, 4-7, 4-8, 4-9, 5-3, 6-5, 7-5, CB 7-6, 8-6,

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B. Text Complexity

Functions

F-IF.A, F-IF.B, F-IF.C Algebra 1: 4-2, 4-3, 4-4, 4-6, 4-7, 4-8, 5-1, 5-3, 5-4, 5-5, 5-8, CB 5-8, 7-6, 7-7, 9-1, CB 9-2, 9-2, 9-4, 9-5, 9-7, 10-5, 11-6, 11-7 Algebra 2: 2-2, CB 2-4, 2-4, 2-5, 2-7, 2-8, 4-1, 4-2, CB 4-3, 4-3, 5-1, 5-2, 5-8, 5-9, 6-8, 7-1, 7-2, 7-3, CB 7-5, CB 8-2, 9-2, 9-3, 13-4, 13-5, 13-6, 13-7, 13-8,

F-BF.A.1 Algebra 1: 4-7, 5-3, 5-4, 5-5, 7-8, 9-7 Algebra 2: 6-6, 7-2, 8-3, 9-1, 9-2, CB 9-2, 9-3

F-LE.A.1 Algebra 1: 5-1, 7-7, 9-7

Geometry

G-CO.A.1 Geometry: 1-2, 1-3, 1-4, 1-6, 3-1, 10-6

G-CO.C.9 & G-CO.C.10

Geometry: 2-6, 3-2, 3-5, 4-5, 5-1, 5-2, 5-4

G-SRT.B Geometry: 4-2, 4-3, 4-4, 4-5, 4-6, 4-7, 5-1, 5-2, 5-4, 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 7-2, 7-3, 7-4, 7-5, 8-1

G-SRT.C Algebra 1: 10-1, 10-6 Geometry: 8-1, 8-2, CB 8-3, 8-3, 8-4, CB 8-4 Algebra 2: 14-3

G-CO.A Geometry: 1-2, 1-3, 1-4, 1-6, 3-1, CB 9-1, 9-1, CB 9-2, 9-2, 9-3, CB 9-3, 9-4, 9-6, 10-6 Algebra 2: 12-5

G-CO.B Geometry: 9-1, 9-2, 9-3, 9-4, 9-5

G-SRT.A Geometry: CB 9-6, 9-7

Statistics and Probability

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B. Text Complexity

S-ID.A.2 Algebra 1: 12-3, 12-4, CB 12-3 Algebra 2: 11-10

S-ID.C.7 Algebra 1: 5-7

S-IC.A.1 Algebra 2: 11-8

The front matter of the Teacher’s Edition provides correlations to the Common Core and a pacing guide (see the Algebra 1 Teacher’s Edition, pages T4–T17).

Rigor: Requires students to engage with and demonstrate challenging mathematics with appropriate balance among problem solving in application, conceptual understanding, and procedural skills and fluency The proven effective five-step lesson design balances the three elements of rigor. The program balances conceptual understanding, procedural fluency, and the application of mathematics to solve problems and formulate models:

Each lesson begins with Interactive Learning, the Solve It!, which immediately engages students in their daily learning according to the Standards for Mathematical Practice. (See the Algebra 1 Student Edition page 364 for a Solve It! example.)

The second step of the lesson, Guided Instruction, uses visual learning principles and a Thinking/Reasoning strand (seen in the Know/Need/Plan and Think/Plan/Write boxes) to introduce the Essential Understanding of the lesson by teaching through and for problem-solving. Interactive Learning and Guided Instruction are designed to address the essential elements in the Common Core conceptual category of mathematical modeling. (See the Algebra 1 Student Edition pages 364–366 for a Guided Instruction example.)

In the third step of the lesson, the Lesson Check, Do you know HOW? exercises measure students’ procedural fluency, while Do you UNDERSTAND? problems measure students’ conceptual understanding. (See the Algebra 1 Student Edition page 367 for a Lesson Check example.)

In the fourth step of the lesson, Practice problems are designed to develop students’ fluency in the Content Standards and proficiency with the Mathematical Practices. Real-world STEM problems as well as problems designed to elicit the use of one or more of the Standards for Mathematical Practice are clearly labeled in the Practice step of the lesson. (See the Algebra 1 Student Edition pages 367–369 for examples of Practice problems.)

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B. Text Complexity

The final phase of the lesson, Assess and Remediate, features a Lesson Quiz to measure students’ understanding of lesson concepts. By using the balanced and proven effective approach of the Pearson five-step lesson design, teachers can teach the CCSS with confidence. (See the Algebra 1 Teacher’s Edition, Volume 2, pages 588A–588B for an example of the point-of-use differentiated instruction support found at the end of every lesson.)

Application: Provides ongoing opportunities for students to independently apply mathematical concepts in real-world situations, solve challenging problems, and choose and apply appropriate strategies to new situations The program provides opportunities for applications, including application problems and performance tasks interwoven throughout chapters. In addition, Mathematical Modeling in 3 Acts provides one mathematical modeling lesson per chapter, and students engage in real-world mathematical modeling through each chapter’s mathematical modeling task. See the Algebra 1 Student Edition page 365 for instructional application examples. For other real-world application examples found in practice exercises, see problems with blue headers in the Algebra 1 Student Edition on pages 367–369. View Mathematical Modeling in 3 Acts tasks at point-of-use in the chapter Table of Contents on Pearson Realize using your PearsonRealize.com demo account username and password.

Conceptual Understanding: Develops students’ depth of understanding through tasks, brief problems, questions, multiple representations and opportunities for them to write and speak about their understanding Pearson Algebra 1, Geometry, Algebra 2 Common Core has a strong focus on critical reasoning, argumentation, and critique of arguments. Students are often asked to explain their solutions and the thinking that led them to these solutions. The Solve It! activities always ask students to justify their solutions and their reasoning (see the Algebra 1 Student Edition page 364 for an example of a Solve It!). Exercises throughout the program ask students to construct arguments to defend their solutions and to respond to the solutions and arguments of others:

Think-Plan boxes often focus on helping students analyze situations, justify conclusions, and reason inductively and deductively (see the Algebra 1 Student Edition page 380).

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B. Text Complexity

In the Reasoning exercises, students are expected to formulate arguments to support their solutions (see the Algebra 1 Student Edition pages 381 and 383).

Compare and Contrast exercises provide opportunities to argue the similarities or differences of concepts or solution (see the Algebra 1 Student Edition page 383).

Error Analysis exercises require students to critique the solution presented for a problem (see the Algebra 1 Student Edition page 398).

Procedural Skill and Fluency: Provides guidelines for performing quick and accurate procedural skills, fluency and mathematical procedures The program provides ample opportunities for students to develop procedural fluency. Guided Instruction sections always include skill examples to develop students’ procedural fluency. The lesson-level formative assessment, the Lesson Check, includes Do You Know How? exercises specifically designed to assess students’ procedural fluency with the lesson content. (See the Algebra 1 Student Edition page 402.)

C. Quality Questioning

Develops students’ depth of knowledge through the presentation of complex problems and questions

Misconceptions are identified and accompanied by strategies to address them

Engages students in productive struggle through relevant, thought-provoking questions, problems and tasks that stimulate interest and elicit mathematical thinking

Rating 3 2 1 0

Evidence:

Develops students’ depth of knowledge through the presentation of complex problems and questions The Teacher’s Edition includes probing questions for the presentation of complex problems and questions. See the Algebra 1, Teacher’s Edition pages 454–455 for an example of the probing questions provided for an application question.

Misconceptions are identified and accompanied by strategies to address them The Teacher’s Edition identifies common errors that students make during Got It? exercises so teachers can correct student misconceptions when students are most likely to make errors. See the Error Prevention on page of the Teacher’s Edition. This will always be found along with

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C. Quality Questioning

the Got It? problem in the Guided Instruction step of the lesson. See the Algebra 1 Teacher’s Edition page 461 to view the Error Prevention tip provided in the Teacher’s Edition for every lesson. In addition, Error Analysis exercises throughout the program require students to look for flaws in an argument as they critique the reasoning of others, so students become aware of common errors by identifying them (see the Algebra 1 Student Edition, page 404, question 30).

Engages students in productive struggle through relevant, thought-provoking questions, problems and tasks that stimulate interest and elicit mathematical thinking The program has several elements that serve to engage students in productive struggle. Mathematical Modeling in 3 Acts lessons embody the spirit of the Standards for Mathematical Practice and require students to engage in productive struggle that helps them persevere with mathematics. (See Mathematical Modeling in 3 Acts lessons in Pearson Realize at the chapter Table of Contents.) In addition, the real-world Solve It! that opens every lesson provides a chance for students to engage in productive struggle with mathematics while connecting to prior learning and setting the stage for future learning. (See the Algebra 1 Student Edition page 400 for an example of a Solve It!)

D. Writing

Provides opportunities to write about mathematical understanding and applications

Allows for written defense of mathematical concepts drawn by students

Rating 3 2 1 0

Evidence:

Provides opportunities to write about mathematical understanding and applications The program provides ample opportunities for writing throughout lessons and activities, including the following:

The Solve It! that opens every lesson requires students to explain their reasoning verbally or in writing. Solve It! always asks students to justify their solutions and reasoning (see the Algebra 1 Student Edition page 400).

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D. Writing

Writing exercises require students to write about mathematics and provide clear, concise explanations of terms, concepts, or processes (see the Algebra 1 Student Edition page 402, number 6, and page 404, number 29).

Reasoning exercises require students to formulate arguments to support their solutions (see the Algebra 1 Student Edition page 402, number 5).

Error Analysis exercises require students to critique the solution presented for a problem (see the Algebra 1 Student Edition page 404, number 30).

The performance tasks that are carried throughout the chapter require students to explain their reasoning (see the Algebra 1 Student Edition, pages 363, 377, 405, and 407).

Allows for written defense of mathematical concepts drawn by students The program requires students to justify their solutions in writing, including the following:

Reasoning exercises require students to formulate arguments to support their solutions (see the Algebra 1 Student Edition page 402, number 5).

Error Analysis exercises require students to critique the solution presented for a problem (see the Algebra 1 Student Edition page 404, number 30).

The performance tasks that are carried throughout the chapter require students to explain their reasoning (see the Algebra 1 Student Edition, pages 363, 377, 405, and 407).

E. Speaking and Listening

Provides opportunities for students to discuss mathematical thought processes

Allows for the presentation of mathematical concepts and conclusions

Strategies for communicating the language of mathematics are routinely presented and discussed

Rating 3 2 1 0

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Evidence:

Provides opportunities for students to discuss mathematical thought processes The program provides ample opportunities for students to discuss mathematical thought processes, including the following:

In the first two acts of Mathematical Modeling in 3 Acts, students focus on speaking and listening as they work to define a problem and figure out the best way to model with math to solve the problem. Writing is incorporated throughout all three acts of the mathematical modeling tasks, as students are required to write about their conjectures and analyze their conjectures. (View Mathematical Modeling in 3 Acts lessons from PearsonRealize.com in the chapter Table of Contents)

The Solve It! that opens every lesson requires students to explain their reasoning verbally or in writing. Solve It! always asks students to justify their solutions and reasoning (see the Algebra 1 Student Edition page 400).

Allows for the presentation of mathematical concepts and conclusions The program allows for the presentation of mathematical concepts and conclusions:

Dynamic Activities allow students to explore mathematical concepts with virtual manipulatives.

Five digital math tools (number line, graphing utility, algebra tiles, 2D Geometric Constructor, and 3D Geometric Constructor) help student to see mathematical concepts through these powerful digital tools.

The interactive digital lessons on Pearson Realize provide animated problems that teachers can project on a whiteboard to present mathematical concepts and conclusions.

To access Dynamic Activities and the math tools, go to the tools menu in the PearsonRealize.com demo account with your demo account username and password. Select Dynamic Activities and math tools from the dropdown tools menu.

Strategies for communicating the language of mathematics are routinely presented and discussed The program is structured to teach for and through problem solving:

Key math terms are highlighted in the printed Student Edition and then collected in the Visual Glossary found as an appendix in each course.

In addition, the Digital Glossary found on the digital courseware gives students ready access to pronunciation and Spanish translations as well as definitions with supporting visuals.

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E. Speaking and Listening

Lessons also include Take Note boxes that summarize key concepts and terms (see the Algebra 1 Student Edition page 418 for a Take Note example).

The Student Companion provides additional vocabulary support for each lesson in addition to meaningful practice and a lesson check.

III. Differentiation of instruction offers opportunities for all to participate:

Text features accommodate students who may have difficulty reading

Vocabulary is presented to address multiple learning modalities

Suggestions for planning, preparation and delivery of instruction for students from diverse backgrounds are provided in teaching resources

Allows for scaffolding (such as supports for use of manipulatives and graphic organizers)

Resources and suggestions for students receiving specialized services (including mentally gifted are grade appropriate.

Resources and suggestions for ELL students are grade appropriate

Rating 3 2 1 0

Evidence:

Text features accommodate students who may have difficulty reading Materials are designed to be accessible to students who may have difficulty reading:

Information and directions are clearly written and explained, using multiple forms of discourse—verbal, numeric, and visual—required to communicate evidence about questions of any complexity.

The call-out Think/Plan and Think/Write boxes help students focus on the key elements of problem solving in a visually friendly way that effectively chunks text (see the Algebra 1 Student Edition pages 426–427 and 434).

The visual design of the program is clean, and visuals connect to the math, helping students who may have trouble reading make sense of math visually.

In addition, the Student Companion work text can be a great notetaking support for students who struggle with reading.

Vocabulary is presented to address multiple learning modalities Pearson Algebra 1, Geometry, Algebra 2 Common Core provides Additional Vocabulary Support worksheets for every lesson to help students develop mathematical vocabulary. These worksheets provide scaffolding for ELLs and other struggling students.

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Additionally, the program also provides teaching strategies for ELLs in every lesson in the Teacher’s Edition (see the Algebra 1 Teacher’s Edition Volume 2 page 466A for an example of the ELL teaching support provided). These teaching strategies can be used to help students better read mathematics. The digital resources of the program offer vocabulary visually and in audio in both English and Spanish, helping address multiple learning modalities.

Suggestions for planning, preparation and delivery of instruction for students from diverse backgrounds are provided in teaching resources Students learn in different ways and at different paces. Unique, built-in resources differentiate instruction to support all levels of learners in becoming successful problem solvers. Pearson Algebra 1, Geometry, Algebra 2 Common Core provides teachers the tools they need to meet the diverse needs of 21st century classroom—from extra practice and performance tasks to activities, games, and puzzles. Differentiating instruction helps all students develop conceptual understanding, fosters mathematical reasoning, and refines problem-solving strategies. The wealth and flexibility of resources enables easy adaptation for teachers to the changing needs of the classroom. The overall lesson plan design and program support materials provide classroom support in a series of whole group, small group, and personalized individual instructional opportunities. The Teacher’s Edition features a two-page spread after every lesson, titled Differentiated Remediation. This section contains differentiated resources for every lesson. Lesson Resources in the Teacher’s Edition provide a Lesson Quiz to be used as a tool to differentiate remediation. Additional resources to meet student needs are listed at point-of-use. (See the Algebra 1 Teacher’s Edition, Volume 2, pages 466A–466B for an example of a Differentiated Remediation spread found at the end of every lesson.) Furthermore, Pearson has systematically developed our educational products by implementing criteria and standards that reflect multiethnic, multiracial, and multicultural perspectives. Our educational materials accurately portray diverse groups within our society as well as diversity within groups. Our programs use language that is appropriate to and respectful of our cultural diversity. We involve members of diverse ethnic and cultural groups in the concept development of our products as well as in the writing, editing, illustrating, and designing.

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Allows for scaffolding (such as supports for use of manipulatives and graphic organizers) Pearson Algebra 1, Geometry, Algebra 2 Common Core allows for scaffolding:

The Student Companion work text offers scaffolded support to help students take notes and master vocabulary.

Every lesson includes Think About a Plan, which provides support for students to think through the problem solving process and develop the problem skills and processes used by effective problem solvers.

The program includes Dynamic Activities and five digital math tools that are manipulatives that can be used to present and explore high school mathematics concepts.

Resources and suggestions for students receiving specialized services (including mentally gifted are grade appropriate; Resources and suggestions for ELL students are grade appropriate Pearson Algebra 1, Geometry, Algebra 2 Common Core features an audio/visual English and Spanish glossary. Homework Video Tutors are available in both English and Spanish. The program also includes an online multilingual handbook with glossary and definitions in each of the following 10 languages: English, Cambodian, Cantonese, Haitian, Korean, Spanish, Vietnamese, Hmong, Filipino, and Mandarin. To view these resources on PearsonRealize.com, use your the demo account username and password. In print, Student Companions and practice and problem solving workbooks (both Teacher’s Guide and Student Workbook) are available in both English and Spanish.

Strategic Intervention Within the Teacher’s Edition, a two-page spread after every lesson titled Differentiated Remediation contains differentiated resources for every lesson. Lesson resources in the Teacher’s Edition provide a lesson quiz to be used as a tool to differentiate remediation. Additional resources to meet student needs are listed at point-of-use. (See the Algebra 1 Teacher’s Edition, Volume 2, pages 466A–466B for an example of a Differentiated Remediation spread found at the end of every lesson.) After students take a lesson quiz, the teacher is provided a prescription for remediation and has options for intervention, on-level, and extension activities for every lesson. Students who are approaching grade level can benefit from re-teaching worksheets, hands-on activities, digital manipulatives (Dynamic Activities and the five digital math tools), online animated problems with audio explanations, homework video tutors in

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English and Spanish, Virtual Nerd™ tutorial videos, ELL support in the form of worksheets and activities, and alternate teaching strategies noted throughout the Teacher’s Edition. Students who are on grade level will use practice and standardized test prep worksheets for every lesson. Additional resources throughout the program, such as Solve It! activities and Concept Bytes, support on-level students. For students who are above grade level, we provide enrichment worksheets and activities, games, and puzzles for every lesson. Additional resources, such as Find the Errors and Chapter Projects, extend learning for advanced students.

Intensive Intervention Teachers have the option of assigning tests and quizzes online. Each online assessment is auto-scored, and the appropriate intervention is automatically assigned to each student based on performance. Compiled achievement data appears in different reports, making it easier for teachers to analyze whole class/individual student performance and track mastery of the standards.

IV. Technology for Instructional Supports:

Online access to textbook

Online teaching resources for interactive whiteboard

Online student supports for remediation, practices and enrichment

Grade appropriate supports for the implementation of handheld technology

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Evidence:

Online access to textbook Both the Teacher’s Edition and Student Edition are available as an eText on iPad®, Android™ devices connected to the Google Play store, and Windows 8 devices, as well as available via PearsonRealize.com. To view the eText on PearsonRealize.com, use your demo account username and password and select eText from the dropdown menu. Using the latest in digital instructional technology, Pearson Realize provides a pedagogical interface to support mathematics classrooms. The digital courseware can be used as a standalone digital course or integrated with print materials to provide a blended classroom environment.

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The online learning environment includes the Student and Teacher’s Editions, instruction and presentation tools, student-generated videos, Virtual Nerd tutorial videos for each lesson, classroom management tools and editable resources, and online assessment with remediation.

Online teaching resources for interactive whiteboard Pearson provides a wealth of support tools that can be used with interactive whiteboards:

The Interactive Digital Path features online math tools, including a graphing utility, number line, algebra tiles, a 2D geometric constructor, and a 3D geometric constructor. It can be displayed on an interactive whiteboard. Teachers can use these online manipulatives to model problem solving.

Resources found on the Answers and Solutions CD-ROM can also be displayed on an interactive whiteboard.

eTexts include a whiteboard view, where teachers can display the eTexts and use highlighting tools on the text.

Online student supports for remediation, practices and enrichment Within the Interactive Digital Path, a Virtual Nerd tutorial video is provided for every lesson. These videos feature three viewing windows, and the Dynamic Whiteboard™ allows students to drill down easily to review prerequisite content. Students also have access to homework video tutors in English and Spanish. Use the PearsonRealize.com demo account username and password to view Virtual Nerd tutorials in the practice step of the digital lesson. In addition, MathXL within Pearson Realize provides interactive online practice. Students have access to interactive learning aids that help support their learning. The Help Me Solve This learning aid breaks down a problem into steps and provides students with feedback at each step of the problem, which is great for kinesthetic learners who learn by doing. The View an Example learning aid generates a similar example with different numbers, which is great for visual learners. Teachers can enrich instruction with interactive lesson content and video that makes real-world connections and models thinking and reasoning using interactive math tools designed for the high school student. Students can complete lessons independently and receive immediate feedback using the online content to support in-class instruction. All teaching resources are available in one easy-to-access location in print and online (access these resources from the tools dropdown on PearsonRealize.com or at point-of-use in the PearsonRealize.com lesson).

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Grade appropriate supports for the implementation of handheld technology The Dynamic Whiteboard feature in the Virtual Nerd tutorial videos anticipates students’ questions, so they can easily drill down to related prerequisite content. The award-winning online design, combined with tutorial videos, delivers personalized content and actively engages students. Students can also download the Virtual Nerd Mobile Math app from the Apple® iTunes® app store or Google Play™ store. On the Virtual Nerd Mobile Math app, students can search by topic, Common Core standard, or by their course—and they can save their favorite videos and create a playlist to review content. The app also includes middle grades content and ACT/SAT prep videos.

Virtual Nerd Videos. Students and parents can access lesson videos on handheld devices anytime to reinforce new concepts.

V. Assessment:

Designed to elicit observable evidence where students can independently demonstrate the targeted standard(s)

Assesses student proficiency using methods that are accessible and unbiased

Includes aligned rubrics, answer keys and scoring guidelines that provide guidance for interpreting student performance

Uses curriculum-embedded assessments such as pre-, formative, summative and self-assessment measures

Requires understanding of appropriate terminology and symbolic representation in order to read, write to explain, and interpret the language of mathematics

Activities allow for remediation, practice, and enrichment

Culminating activities/projects require students to research outside of immediate text and rely on prior and new knowledge

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V. Assessment:

Rating 3 2 1 0

Evidence:

Designed to elicit observable evidence where students can independently demonstrate the targeted standard(s) Pearson Algebra 1, Geometry, Algebra 2 Common Core includes formative instruction practices and formative assessments to help students develop critical mathematical reasoning skills. These include the following:

Following each example problem in the Guided Instruction step of the lesson, the Got It? problem provides an instant assessment of student understanding and serves as an initial formative assessment.

Within the Lesson Check, Do you know HOW? and Do you UNDERSTAND? assess how well students can apply the lesson skills. (Do you Know HOW? measures procedural fluency. Do you UNDERSTAND? assesses conceptual understanding.)

Our program assesses for both conceptual understanding and fluency within lesson-level formative assessments. Within the Teacher’s Edition, the teacher is provided with support at point-of-use on how to remediate throughout the lesson. Each lesson includes a lesson quiz that helps teachers to assess students’ understanding of the lesson content. Teachers can then provide the appropriate remediation, on-level, or enrichment support needed to differentiate instruction effectively. Resources for remediation, on-level, and enrichment are provided in the Teacher’s Edition wrap at point-of-use. Pearson Algebra 1, Geometry, Algebra 2 Common Core also includes formative and summative assessments, ExamView software, and a grading rubrics specifically devised to assess the Standards for Mathematical Practice. (See pages 56–57 of the Common Core Overview and Implementation Guide to view the Standards for Mathematical Practice Observational Protocol Rubric.)

Assesses student proficiency using methods that are accessible and unbiased Student proficiency is assessed using methods that are accessible and unbiased. Assessments are available in print or online and are designed to be unbiased.

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Includes aligned rubrics, answer keys and scoring guidelines that provide guidance for interpreting student performance The program offers comprehensive reports, blank answer sheets, and answer keys. It also includes a Standards for Mathematical Practice Observational Protocol rubric to assess student proficiency with the Standards for Mathematical Practice (see pages 56–57 of the Common Core Overview and Implementation Guide for the observational protocol rubric). Scoring guidelines are provided at point-of-use in the Teacher’s Edition for the performance tasks found throughout the chapter (see the Algebra 1 Teacher’s Edition, Volume 2, pages 417, 438, 459, 466, and 473 for guidance on grading the chapter performance tasks).

Uses curriculum-embedded assessments such as pre-, formative, summative and self-assessment measures Pearson Algebra 1, Geometry, Algebra 2 Common Core is data-driven and designed to prepare students for rigorous next-generation assessments. Each chapter within the Student Edition features a chapter-long performance task, similar to those students will encounter on next-generation assessments. Students are introduced to the performance task at the start of the chapter, they revisit the performance task at least twice per chapter, and they complete the task in a Pull It All Together task at the end of the chapter. A rubric is provided to assess student work. Teachers can use the ancillary Common Core Standards Practice and Review Teacher’s Guide, a comprehensive resource that contains formative and summative assessments, including the following:

Formative Assessments

○ Screening Test

○ Benchmark Tests

○ Weekly Common Core Standards Practice

Summative Assessments

○ Quarter Test (versions G and K)

○ Mid-Course Test (versions G and K)

○ Final Test (versions G and K)

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V. Assessment:

Standardized Support

○ Common Core Practice End-of-Course Comprehensive Assessment

○ Common Core Practice Performance-Based Assessments

○ SAT and ACT Practice Test

Requires understanding of appropriate terminology and symbolic representation in order to read, write to explain, and interpret the language of mathematics The program requires understanding of appropriate terminology and symbolic representation to read, write to explain, and interpret the language of mathematics. The writing exercises, open-ended exercises, and Think About a Plan exercises all serve to ensure students demonstrate the requisite understanding of appropriate terminology and symbolic representation. (See the Algebra 1 Student Edition page 451 questions 51 and 52, and page 458 question 50 for examples of these type of exercises.)

Activities allow for remediation, practice, and enrichment The curriculum includes diagnostic teaching, differentiated instruction throughout the lesson highlighted in the Teacher’s Edition wrap, and leveled exercise sets for on-level students. For beyond-grade level students, every lesson includes the following:

Higher-order thinking questions throughout the lesson exercises

Differentiated homework options noted in the Teacher’s Edition

Extension resources The online assessment system provides instant analysis of student performance. The system prescribes automatic remediation and reports on student and class progress. The remediation provided is in multiple formats: video, tutorial, activity, worksheet, games, and audio. After students take a lesson quiz, the teacher is provided a prescription for remediation and has options for intervention, on-level, and extension activities for every lesson. Students who are approaching grade level can benefit from the following curriculum resources:

Re-teaching worksheets

Hands-on activities

Digital manipulatives (Dynamic Activities and digital math tools)

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V. Assessment:

Online animated problems with audio explanations

Homework video tutors in English and Spanish

Virtual Nerd tutorial videos

ELL support in the form of worksheets and activities

Alternate teaching strategies noted throughout the Teacher’s Edition

Online practice is powered by MathXL within Pearson Realize and includes online practice with point-of-use learning aids including View an Example and Help Me Solve This. The View an Example learning aid shows a similar example with different numbers, and the learning aid Help Me Solve This breaks down a problem in steps and provides feedback at every step of the problem while walking students through how to solve the problem in a step-by-step way.

Culminating activities/projects require students to research outside of immediate text and rely on prior and new knowledge Pearson digital courseware includes an online next-generation practice assessment and two performance tasks that feature multi-step, real mathematical tasks designed to mirror the tasks students will encounter on next generation assessments. Innovative test items, like drag-and-drop and free response, are featured in the online next generation practice assessment. In addition, online auto-graded chapter tests include two next-generation items. Mathematical Modeling in 3 Acts requires students to model with mathematics in Act 2, which is real-world mathematical modeling where students must identify the data needed to solve the problem and how to obtain that data. To solve the tasks in Mathematical Modeling in 3 Acts and their accompanying Sequel problems, students must rely on prior knowledge and new knowledge while researching outside the text. Chapter projects (available to download from PearsonRealize.com in the Teacher Resource Download Center) also require students to research outside of immediate text and rely on prior knowledge and new knowledge.

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VI. Parent Connections:

Suggestions for improving study habits

Online parent homework help center

Activities for ongoing practice (such as: interactive notebooks, study cards, flashcards, vocabulary reinforcement, games)

Rating 3 2 1 0

Evidence:

Suggestions for improving study habits Pearson Algebra 1, Geometry, Algebra 2 Common Core offers several methods to improve study habits. The Virtual Nerd Mobile Math app is free for mobile iOS and mobile Android devices connected to the Google Play store. Students can search the app by lesson, topic, or standard to view tutorial videos. In addition, the program features a parent letter that educators can use to communicate with parents (found in the Common Core Overview and Implementation Guide on page 58). The online digital courseware, PearsonRealize.com, offers homework video tutors in English and Spanish, as well as Virtual Nerd tutorial videos. Students can drill down within the Virtual Nerd tutorial videos to review a prerequisite concept. In addition, MathXL within Pearson Realize provides learning aids that help students learn to develop self-efficacious study habits. The Help Me Solve This learning aid walks students through how to solve a problem step-by-step, while the View an Example learning aids lets students view a similar worked-out example.

Online parent homework help center Parents can access the free Virtual Nerd Mobile Math app (available for Apple and Android mobile devices) to review algebra and geometry content and help their students more effectively.

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VI. Parent Connections:

Activities for ongoing practice (such as: interactive notebooks, study cards, flashcards, vocabulary reinforcement, games) The online digital courseware, PearsonRealize.com, offers homework video tutors in English and Spanish, as well as Virtual Nerd tutorial videos. Students can drill down within the Virtual Nerd tutorial videos to review a prerequisite concept. In addition, MathXL within PearsonRealize.com provides learning aids that help students practice. The Help Me Solve This learning aid walks students how to solve a problem step-by-step, while the View an Example learning aids lets students view a similar worked-out example.

Documents

THE SCHOOL DISTRICT OF PHILADELPHIA OFFICE OF …assets.pearsonschool.com/...SDP_Rubric_HSMath.pdf · Office of Curriculum, Instruction and Assessment, Christopher Shaffer, Deputy