The homework problems give students the opportunity to apply previously-learned concepts to new contexts. By solving the same types of problems in different ways, students deepen their understanding. CPM offers open access homework support at homework. Read less about the lesson structure. Chapters are divided into sections that are organized around core topics. Within each section, lessons include activities, challenging problems, investigations and practice problems.
Read more about the course structure. These notes are placed in a purposeful fashion, often falling one or more lessons after the initial introduction of a concept. This approach allows students time to explore and build conceptual understanding of an idea before they are presented with a formal definition or an algorithm or a summary of a mathematical concept.
Learning Log reflections appear periodically at the end of lessons to allow students to synthesize what they know and identify areas that need additional explanation. Toolkits are provided as working documents in which students write Learning Logs, interact with Math Notes and create other personal reference tools.
Each chapter offers review problems in the chapter closure: typical problems that students can expect on an assessment, answers, and support for where to get help with the problem. Chapter closure also includes lists of Math Notes and Learning Logs, key vocabulary in the chapter, and an opportunity to create structured graphic organizers.
Checkpoints offer examples with detailed explanations, in addition to practice problems with answers. In addition to practice problems with answers, the Parent Guide with Extra Practice provides examples with detailed explanations and guidance for parents and tutors. Each chapter comes with an assessment plan to guide teachers into choosing appropriate assessment problems.
CPM provides a secure online test generator and sample tests. The Assessment Guidebook contains guidance for a wide variety of assessment strategies.
By using each of these representations, students develop experience with multiple entry points into a problem and have the chance to apply their knowledge of one representation to build understanding of others. Students focus on identifying the connections and interrelationships among these representations to find new ways of looking at problems. Lessons are structured for students to actively collaborate by working in study teams. The text provides structured roles for each student to support their active participation in learning mathematics.
During class time, students work in these teams on challenging problems that introduce new material. These activities are designed to provide teachers with the freedom to decide how structured or open they want the lesson to be for their students. The homework problems also allow students to apply concepts and skills in new contexts and to deepen their understanding by solving the same type of problem in different ways.
This course contains several content threads that extend through multiple chapters and help to highlight connections between ideas. Chapter 1 begins by introducing the graphing calculator, building procedures for successful participation in study teams, and anticipating two major themes of the course: investigating functions and relations and modeling data. Chapter 2 continues this development with a focus on generalizing arithmetic and geometric sequences.
Chapter 3 focuses on representing the family of exponential functions with graphs, tables, equations and applied situations. Read more about the course outline. Chapter 4 focuses on modeling non-linear data and developing general equations for a variety of functions and relations. Students learn to transform graphs of several parent functions including parabolas, hyperbolas, square roots, exponentials, cubics, and absolute values. Students review their strategies for solving equations and looking at those solutions in multiple representations in Chapter 5.
They extend these strategies to use them with inequalities and systems of inequalities. Chapters 6 and 7 introduce students to inverses of the functions they have previously investigated, including exponentials, logarithms, and matrices.
These seven chapters, and usually Chapter 9, which explores polynomial functions along with real and complex roots, comprise the core of most Algebra 2 courses. In order to prevent grader bias based on whether a student was in the CPM or traditional mathematics group, all tests were coded with six-digit identifiers known only to those who compiled the results of the study.
To calibrate their scoring and create reliability, the graders spent preliminary time discussing what was expected in responses to each question, and what would constitute a response to assign each of the five possible scores.
In addition, every test was scored by at least two graders. Approximately algebra and geometry students participated in an assessment where each student had 20 minutes to solve two written-response items. The results favored CPM students for both genders and all ethnic groups. Approximately algebra and geometry students participated in an assessment where each student had 20 minutes to solve two written-response items, one of which was taken directly from another examination.
The results favored CPM students for both genders and all ethnic groups and were significant at the. Approximately 13, algebra, geometry and algebra 2 students participated in an assessment where each student had 30 minutes to solve three written-response items with grading done at three sites. For the third year in a row, CPM students scored significantly higher in algebra and algebra 2 and slightly higher in geometry.
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