High School - Gateway 3

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the underlying design of the materials distinguish between lesson problems and student exercises for each lesson. Students are learning new mathematics in each lesson and then applying what they have learned in order to build knowledge. The spaced and spiraling nature of the series helps build mastery. Each chapter, section, and lesson has a variety of problems and exercises, and has intentional purpose in developing learning and thinking.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in this series are designed well and take into account effective lesson structure and pacing. The materials encourage fluency through their spaced homework, helping students retain and apply new learning throughout the series. Rote procedural exercises are present, but not in mass quantities. The exercises are given in intentional sequences.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that students are asked to produce a variety of products during each lesson in each chapter to demonstrate their learning. The series continuously asks students to produce models, practice fluency, create arguments, justify their answers, attend to mathematical practices and make real-world connections. This is done through homework, closure reflections, portfolios, team tasks, explanations, models, arguments (with stop light problems using error analysis), learning logs, cumulative assessments, checkpoint problems and journal entries.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in this series are designed well and take into account effective lesson structure and pacing. Each chapter in each textbook contains teacher notes in the chapter introduction that provides clarity on the lesson design and intent and a suggested assessment plan. For example Algebra 2, chapter 4 says "This chapter begins with a focus on two ways to solve equations and systems of equations: algebraically and graphically. You will build on your understanding of solving and solutions from previous courses to gain a broader and stronger understanding of the meaning of solutions. In Section 4.2, you will expand your understanding of solving and solutions to include inequalities. You will solve problems designed to illustrate how inequalities might be used for more complicated applications."

The series makes use of a wide range of virtual manipulatives. The materials have their own collection of virtual manipulatives including algebra tiles, base ten blocks, probability tools, data representation tools, transformation tools, similarity toolkit, numbers lines and graphing tools. The materials also make regular use of premade Desmos.com graphs and other applets. There are general manipulatives and tools that the materials recommend always having available. A few examples of these include, but are not limited to colored pencils, graph paper, markers, masking tape, meter sticks, rulers, scissors, and tape. Then, there are specific manipulatives and tools that will be needed for specific lessons. A few examples of these include, but are not limited to rope, foil pans, bouncy balls, candles, calculator-based rangers, digital scales and yo-yo's.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. In many sections of the student materials, the leading paragraph of the lesson begins by listing three to four questions, then asks students to use these questions to guide the work in the lesson. In addition, the teacher resources provide teachers with guiding questions for the teacher to use when circulating the room. For example, in the teacher notes for section 3.1.1 in Algebra 1 the teacher is given the following: "As you circulate, ask questions that require students to justify their patterns or that encourage students to look for patterns, such as, “What is the exponent of the result? How is that related to the original problem?” and “How can you convince me that your shortcut works?" There are additional questions later in the teacher resources that are listed as useful questions for other parts of the lesson.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Each lesson has a full printed write-up to explain the content and instructional goals as well as a video with the same purpose. Each lesson also describes how to use the supporting technology as well as how to run the lesson if technology is not available. There is a TI-83 student and teacher guide included. For example, the eBook teacher notes for the opening of Chapter 7 in Geometry includes overview paragraphs, guiding questions, a chapter outline, a teacher guide video, Smart Board file, discussion on the Standards for Mathematical Practices, a "Where's it Going?" paragraph, and a suggested assessment plan.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials contain adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject. Lesson videos and lesson teacher notes (both printed and in the eBook) provide teachers with a full preparation for each lesson, including historical notes, video models, mathematical background and adult-level explanations to guide the teacher. The series provides a newsletter with lesson ideas and up-to-date strategies and best practices to guide teachers in planning and in advanced learning of the mathematics. Past editions of the newsletter are archived in the teacher support of the teacher materials.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in the series provide strategies for teachers to identify and address common student errors and misconceptions. The stoplight problems provide opportunities for students to find errors and critique reasoning. The teacher notes also provide tips for teachers to address common errors. The closure sections provide opportunities for discussion of common errors and misconceptions, along with the cooperative learning tasks.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials in the series provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills. The teacher materials provide rubrics along with information on giving feedback on portfolios, team tests, presentations and participation quizzes. Students also have feedback available through the eBook homework help and the animated explanations.

Every lesson has a Review & Preview section. In this section, there are homework helps that are hyperlinked to selected hints, answers and e-tools to help provide feedback to students on skills and concepts. This part of each lesson reviews problems from past learning objectives, chapters and courses within the series. One example is in section 4.1.3 of Geometry where students work 6 problems from previous chapters in Geometry.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide strategies to help teachers sequence or scaffold lessons so the content is accessible to all learners. A "universal access" guide with directions on scaffolding for ELL and special needs students is provided. One strategy included is to focus on checkpoint or essential problems for struggling learners so that they have access to the same level of rigor but with fewer problems.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide teachers with strategies meeting the needs of a range of learners. There are eBook materials in the teacher resources that include a list of strategies for a wide range of learners. Specifically, the Universal Access Guidebook and Literacy Guidebook explain how to assist students who are making normal progress, or need additional help, or are underprepared for the course, or who have special needs such as English language learners, advanced learners or struggling readers.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations. There are many investigations and modeling problems that allow for multiple solutions and strategies. Many problems encourage multiple representations (graph, verbal, analytical, numerical). Most of the beginning lessons within a chapter offer scaffolding that allows multiple entry points into the opening problem, which allows for students with a range of learning abilities to have access to the problem.

• For example, Algebra 1, lesson 5.1.1, opens the chapter on sequences with an investigation of two friends who dream of raising rabbits. The question gives a scenario and asks how many rabbits would there be after one year. There are four questions that ask students to identify patterns and make predictions, thinking in teams about the strategies they would use. Problem 5-2 is designed for further guidance for students who need more direct strategies to use. These strategies include drawing a diagram, creating a table and looking at specific patterns. Eventually, students will work their way to recursive equations, explicit equations and graphing of these equations and the functions these equations represent.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics. The series clearly identifies checkpoint problems and core problems with guidance on how to modify the pacing for special populations so all students have access to on grade level resources. "Math Note" sections throughout the lesson provide definitions and examples with regard to vocabulary. Additionally, every lesson is provided in Spanish, and through the eBook translator, can be translated into most languages.

The instructional materials reviewed for the High School CPM Traditional series meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth. A pacing guide shows pacing for students who are at grade level as well as those who are advanced. For advanced students most lessons include enrichment and additional problems within the lesson. The teacher materials explicitly state that advanced students also benefit from the richness of the problems in the text and will often be able to develop considerable depth in their work. Examples of enrichment and additional problems include, but are not limited to:

• In Geometry lesson 6.2.3, the teacher materials note that problem 6-72 is an extension. Problem 6-68 is the core problem, while 6-69 and 6-70 are optional problems needed for further guidance.
• In Algebra 1 lesson 4.2.2, the teacher materials note the core problems as 4-42 and 4-47. Problems 4-43 through 4-45 are noted as further guidance or enrichment problems.