CPM Algebra Overview

Algebra Connections California Edition A Presentation to Teachers for the California Mathematics Adoption College Preparatory Mathematics Rigorous • Aligned • Balanced • Accessible

Background of CPM
Supported by research in methodology and studies of student results, available at
www.cpm.org
CPM has developed curriculum for 18 years
Written with the help of California classroom teachers based on their experience of what effectively develops both procedural skills and conceptual understanding.
Rigorous • Aligned • Balanced • Accessible

Research Base Rigorous • Aligned • Balanced • Accessible
Research Support:
Social interaction increases the ability of students to learn ideas
The integration of knowledge is best supported by engaging in a wide array of problems around a single idea.
Long-term retention and transfer of knowledge are best-supported by spaced learning.

Research Summary Rigorous • Aligned • Balanced • Accessible
Examples of California data:
Students in California CPM schools scored 6 - 10 percentage points above the state average for grades 9-11 on the SAT-9 test for 1998 - 2002.
8th Grade CST scores for 2002-2007 in CPM schools are 59% above the state average.
Students in both low-performing and high performing schools score higher than matched groups of comparison schools.
Reports are posted at www.cpm.org.

Program Components
The Algebra Connections Program for this review includes:
CA Edition Student text
Teacher binder with assessment
Extra Practice workbook
Parent Guide
Homework help (hotmath.com)

Examining a Lesson The Structure of the Teacher Materials We will examine a lesson developing the content for Standard 9.0: Rigorous • Aligned • Balanced • Accessible 9.0: Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables to sketch the solution sets.

Lesson 6.2.3 Rigorous • Aligned • Balanced • Accessible

Lesson 6.2.3 Rigorous • Aligned • Balanced • Accessible Lesson Objective: Students will develop the Elimination Method for solving systems of equations.

Lesson 6.2.3 Rigorous • Aligned • Balanced • Accessible Suggested Lesson Activity: Description of lesson and strategies for implementation, such as questions for students

Lesson 6.2.3 Rigorous • Aligned • Balanced • Accessible Closure: Every lesson contains closure strategies for teachers.
Introduction:
Motivates learning
Gets students active
Challenging

Lesson 6.2.3 Rigorous • Aligned • Balanced • Accessible Conceptual Development: When appropriate, manipulatives (such as algebra tiles) are used to help students move from concrete to abstract understanding.
Structured lesson
Problem-based learning

Lesson 6.2.3 Rigorous • Aligned • Balanced • Accessible Socratic Method: Questions that students answer to develop a new concept
Requires students to be actively thinking
Outlines a process for solving the problem

Lesson 6.2.3 Rigorous • Aligned • Balanced • Accessible Practice: Embedded in classwork Context: Focus on solving word problems.

Lesson 6.2.3 Rigorous • Aligned • Balanced • Accessible Explicit Notes: Following most lessons is a “Math Notes” box containing:
Formal definitions
Solved examples
Multiple strategies
Explanation of special cases

Effective Learning Strategy Rigorous • Aligned • Balanced • Accessible Students develop and practice topics in study teams:
Research-based
Structured problems with clear objectives
Active engagement with the lesson
Mathematical discourse

Homework Rigorous • Aligned • Balanced • Accessible Review & Preview Icon designates where homework starts. Homework includes:
Spaced practice with previous work
Practice with current work
Extensions and enrichment

Hotmath Help Rigorous • Aligned • Balanced • Accessible Help with Homework: Students have access to free tutorial help with hints and solutions to all homework questions.

Teacher & Student Interaction Forms of Teacher Interaction:
Targeted lectures
Clarifying instructions
Checking for understanding
Testing student results
Questioning student processes
Providing closure

Multiple Assessment Resources Rigorous • Aligned • Balanced • Accessible
Assessment Handbook
Individual tests
Team tests
Participation quizzes
Student presentations
Portfolios
Chapter Assessment Plans
Tests and Problem Bank
Student and class observations

Universal Access Rigorous • Aligned • Balanced • Accessible Solved Examples: Additional resource containing solved examples of content with complete explanations.

Teacher Intervention Rigorous • Aligned • Balanced • Accessible Extra Practice: Offers multiple practice problems (with answers) for use in class or at home. Answers: Answers are provided so that students can get instant feedback on developing skill.

Parental Support Parent Guide To help parents help their children Rigorous • Aligned • Balanced • Accessible

Reading Level Flesh-Kincaid: Using the Flesh-Kincaid scale of readability, the student Algebra Connections scores are: Rigorous • Aligned • Balanced • Accessible Grade Level Reading Ease 7.4 64.0

Conclusion Rigorous • Aligned • Balanced • Accessible

Ways of Thinking
Justifying
Generalizing
Applying and Extending
Making Connections
Reversing Thinking
Rigorous • Aligned • Balanced • Accessible Algebra Connections focuses attention on five “ways of thinking” mathematically:

Chapter Closure
Reflective activities
Key vocabulary
Graphic organizers
Practice problems with answers for self-assessment
Ways of Thinking
Rigorous • Aligned • Balanced • Accessible Each chapter offers extensive closure opportunities, including:

Use of Algebra Tiles
“ Legend” reminds students and teachers which tiles are positive and negative
“ Minus” region negates the tiles in that region, helping students represent the opposite of a negative.
Rigorous • Aligned • Balanced • Accessible Symbolic manipulation is developed through use of concrete tools

Further Guidance Rigorous • Aligned • Balanced • Accessible For big activities and key challenging problems, Further Guidance is available for students who need additional assistance.

CPM Algebra Overview

by Dennis Ashendorf on May 22, 2010

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