Welcome
Welcome to the student & parent section of the CPM Geometry web page. You may download resource pages for assignments here. The skill builders offer you explanations of course topics and examples along with extra practice problems and their answers. The links to Hotmath.com provide homework help.
The CPM curriculum, designated one of five "Exemplary Mathematics Programs" by the U.S. Department of Education in October, 1999, is taught by more than 3,000 teachers in more than 900 schools across the country. It was originally a grant-funded curriculum and assessment development project located in Sacramento County, California. When the first edition of Algebra 1 was released in 1992, there were about 200 teachers using CPM materials, mostly in seven urban sites in California. By the 1995-96 school year there were more than 2,000 teachers using CPM materials, mostly in California, with about 100 teachers located in Washington State, Wisconsin, Illinois, Pennsylvania, and Washington, D.C. Today CPM is used in more than 35 states.
• Covers the expected content in any geometry course.
• Reviews 85% of Algebra 1 topics explicitly and uses algebra in geometric applications (e.g., supplementary angle problems contain numerical and algebraic expressions as angle measures).
• Focuses logical explanations throughout the text. Provides two and a half chapters specifically focused on proof. Allows as rigorous or relaxed an approach to proof as appropriate for the students.
• The first half of the book introduces the fundamentals of lines, angles, and plane figures (about 70% of the content). The first half of the book:
-- Starts with familiar, concrete topics in an enjoyable format designed for early student success. Topics include the Pythagorean Theorem, area of triangles and quadrilaterals, and linear equations.
-- Introduces proof through logic games and puzzles.
-- Uses the problem solving strategies of organizing data, making tables and lists, and looking for patterns to introduce the concepts for lines and angles.
-- Explores three dimensional visualization, studying prisms and pyramids for the first of two times in the course.
-- Studies transformations and then triangle congruence.
-- The sixth chapter serves as a review of the first half of the course. It introduces several styles of proof and applies them to prove most of the
conjectures developed inductively in chapters 0-5.
• The second half of the course concentrates on bigger ideas. Except for circles, each chapter focuses on one or two topics. The second half of the course:
-- Starts with right triangle trigonometry so that students may solve more interesting, complex problems in subsequent chapters.
-- Emphasizes similarity for two dimensional and three dimensional figures.
-- Explores polygons, spending the latter portion of the chapter on proof, including characteristics of quadrilaterals.
-- Introduces the fundamentals of circles, including arcs and angles, followed by the second study of prisms and pyramids, along with cylinders and cones.
-- The last two chapters apply ideas from the course. The first chapter (11) uses area models to study geometric probability. The last chapter offers applications and big problems that use many of the main ideas from the course.
• Constructions are offered in an appendix that can provide an interlude unit of two or three days between the first and second parts of the book.
The National Math Debate: How CPM Tips the Scales
Mathematics education has been in the headlines for several years. Much of the coverage of math curriculum debates has been reduced to an either/or shouting match between proponents of basic skills and those who emphasize understanding concepts. Advocates of basics emphasize learning rules and procedures. Those who stress understanding are characterized as more interested in the process of mathematics than its content. These descriptions are distorted simplifications of both positions. Even if true, neither approach, by itself, would prepare American mathematics students to be successful in a global economy that requires mathematical literacy.
We know that mathematics has, to a large extent, served as an academic filter. Math is usually presented as material that students either "get" or they don't. A 1995 national survey of the mathematics taken by high school students shows that while 95% will take Algebra 1, only 60% enroll in Algebra 2 and a mere 33% survive to take pre-calculus. We simply must do better with all of our students to provide them with a complete mathematics curriculum.
A complete curriculum includes mastering basic skills and procedures, understanding mathematical principles, and acquiring problem solving strategies. The CPM program presents mathematical ideas in contexts that help students make sense of otherwise abstract principles. Students are taught how to gather and organize information about problems, break problems into smaller parts, and look for patterns that lead to solutions. Each course is built around several core ideas that are used to develop related topics, skills and procedures. Students master skills and come to understand ideas over several days and weeks. Much of their classroom time is spent doing guided investigations– much like a math lab–that develop ideas in concrete, visual ways. They also apply their learning to realistic problems that require more than merely mimicking examples of rules.
The Third International Mathematics and Science Study (TIMMS) ranked the mathematics performance of American students near the bottom of the countries in the study. Most revealing from the report were the results of a video study of classrooms in Japan, Germany, and the United States. In Japan's structured lessons, students and teachers engage in activities that lead to understanding the content of the lessons. In German and American classrooms, students sit passively while teachers tell them what they are supposed to know. Furthermore, they rush through textbooks that have 60, 70, even 80 topics, getting at best superficial exposure to them.
The CPM curriculum, emphasizing core ideas, active student participation in lessons, and consistent practice of ideas over time predates the recommendations drawn from the TIMSS study by five years. CPM has offered approaches to learning mathematics that parallel practices in successful countries since 1989. CPM courses contain the mathematical content required of each course. The teacher-authors present the material in ways that actively involve students in developing and understanding ideas. Students improve their study skills and build life-long strategies for solving problems that are applicable in most academic disciplines, the workplace, and daily life.
How: CPM Educational Program Answers Your Questions
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What does The CPM Program Strive to Accomplish?The CPM Program strives to:
- Help more students learn more mathematics more effectively;
- Regenerate student interest and performance in college preparatory mathematics;
- Enable students to take more college preparatory mathematics classes; and
- Provide students with a mathematics education that will make them competitive and successful in the global marketplace.
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What Makes The CPM Curriculum Effective?
- The CPM curriculum is effective because of its unique emphasis of both basic skills and problem solving strategies. Where other mathematics programs emphasize only the mechanics of mathematics, the CPM materials develop the basics while encouraging students to understand ideas, see relationships between them, and apply mathematical principles to complex problems.
- CPM courses prepare students for the global marketplace they will face after graduation, either in institutions of higher learning or in the job market.
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Because It Works
- A study of 13,000 students that compared traditional and CPM students' responses to typical end-of-the-year course word problems showed that, on average, CPM students scored 33% higher than non-CPM students.
- California SAT9 math results for 1998-2002 show that CPM high schools score on average 6-10% higher than the state averages for grades 9-11, in every year.
- CPM students score as well as non-CPM students (and sometimes dramatically better) on tests designed to measure skills and procedures.
- Golden State Examination (GSE in California) results for algebra and geometry showed significant increases in the number of students earning recognition after the CPM materials were adopted, during the 1990's.
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Because The Global Marketplace is Changing
- Corporate and industry executives across the country have been concerned for years that the majority of their employees do not have the same mathematical skills as their foreign competitor's employees.
- Most of the jobs for the new millennium will be mathematics, science, and technology related.
- Corporate recruiters agree that graduates entering the workforce need skills that mathematics curricula have missed in the past. They need to be able to:
- Solve problems in a team environment;
- Analyze problems that have no obvious solution; and,
- Propose multiple solutions to new problems and test their validity.
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Because It Shows Students How Mathematics Works and How to Use It
- The CPM curriculum offers students quality instruction by teachers who use several methods to teach the course materials.
- The CPM curriculum provides students with the basic skills and opportunities to develop concepts and devise solutions in a team environment.
- The CPM curriculum challenges students with rich, involved problems that require them to use basic skills in complex problems.
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Because It is Accepted By Every Major College and University
- CPM high school courses contain substantially the same topics as Algebra 1, Geometry, Algebra 2, and Mathematical Analysis. They are accepted by every college and university in the country.
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