CPM Algebra Overview

Algebra ConnectionsCalifornia Edition

A Presentation to Teachers for the

California Mathematics Adoption

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.


Research Base


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


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 LessonThe Structure of the Teacher

MaterialsWe will examine a lesson developing the content for Standard 9.0:


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


Lesson 6.2.3


Lesson Objective:

Students will develop the Elimination Method for solving systems of equations.

Lesson 6.2.3


Suggested Lesson Activity:

Description of lesson and strategies for implementation, such as questions for students

Lesson 6.2.3


Closure:

Every lesson contains closure strategies for teachers.

Introduction:

• Motivates learning

• Gets students active

• Challenging

Lesson 6.2.3


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


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


Practice:

Embedded in classwork

Context:

Focus on solving word problems.

Lesson 6.2.3


Explicit Notes:

Following most lessons is a “Math Notes” box containing:

• Formal definitions

• Solved examples

• Multiple strategies

• Explanation of special cases

Effective Learning Strategy


Students develop and practice topics in study teams:

• Research-based

• Structured problems with clear objectives

• Active engagement with the lesson

• Mathematical discourse

Homework


Review & Preview Icon designates where homework starts.

Homework includes:

• Spaced practice with previous work

• Practice with current work

• Extensions and enrichment

Hotmath Help


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


Assessment Handbook• Individual tests• Team tests• Participation quizzes• Student presentations• Portfolios

Chapter Assessment Plans

Tests and Problem Bank

Student and class observations

Universal Access


Solved Examples:

Additional resource containing solved examples of content with complete explanations.

Teacher Intervention


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


Reading Level

Flesh-Kincaid:

Using the Flesh-Kincaid scale of readability, the student Algebra Connections scores are:


7.4 64.0

Grade Level Reading Ease

Conclusion


Ways of Thinking

• Justifying

• Generalizing

• Applying and Extending

• Making Connections

• Reversing Thinking


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


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.


Symbolic manipulation is developed through use of concrete tools

€

2x − x +1− (2 − 3)

Further Guidance


For big activities and key challenging problems, Further Guidance is available for students who need additional assistance.

Education

CPM Algebra Overview