Algebra ConnectionsCalifornia Edition
A Presentation to Teachers for the California Mathematics
Adoption
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Background of CPM 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. Supported by research in
methodology and studies of student results, available at
www.cpm.orgRigorous Aligned Balanced
Research BaseResearch 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
bestsupported by spaced learning.Rigorous Aligned Balanced
Research SummaryExamples 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.Rigorous Aligned Balanced
Program ComponentsThe Algebra Connections Program for this
review includes: CA Edition Student text Teacher binder with
assessment Extra Practice workbook Parent Guide Homework help
(hotmath.com)
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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.
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Lesson 6.2.3
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Lesson 6.2.3Lesson Objective:Students will develop the
Elimination Method for solving systems of equations.
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Lesson 6.2.3Suggested Lesson Activity:Description of lesson and
strategies for implementation, such as questions for students
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Lesson 6.2.3Closure:Every lesson contains closure strategies for
teachers.
Introduction: Motivates learning Gets students active
ChallengingRigorous Aligned Balanced
Lesson 6.2.3Conceptual Development:When appropriate,
manipulatives (such as algebra tiles) are used to help students
move from concrete to abstract understanding. Structured lesson
Problem-based learningRigorous Aligned Balanced
Lesson 6.2.3Socratic Method:Questions that students answer to
develop a new concept Requires students to be actively thinking
Outlines a process for solving the problemRigorous Aligned
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Lesson 6.2.3Context:Focus on solving word problems.
Practice:Embedded in classwork
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Lesson 6.2.3Explicit Notes:Following most lessons is a Math
Notes box containing: Formal definitions Solved examples Multiple
strategies Explanation of special casesRigorous Aligned
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Effective Learning StrategyStudents develop and practice topics
in study teams: Research-based Structured problems with clear
objectives Active engagement with the lesson Mathematical
discourseRigorous Aligned Balanced
HomeworkReview & Preview Icon designates where homework
starts. Homework includes: Spaced practice with previous work
Practice with current work Extensions and enrichmentRigorous
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Hotmath HelpHelp with Homework:Students have access to free
tutorial help with hints and solutions to all homework
questions.
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Teacher & Student InteractionForms of Teacher Interaction:
Targeted lectures Clarifying instructions Checking for
understanding Testing student results Questioning student processes
Providing closureRigorous Aligned Balanced
Multiple Assessment Resources Assessment Handbook Individual
tests Team tests Participation quizzes Student presentations
Portfolios Chapter Assessment Plans Tests and Problem Bank Student
and class observationsRigorous Aligned Balanced
Universal AccessSolved Examples:Additional resource containing
solved examples of content with complete explanations.
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Teacher InterventionExtra 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.Rigorous Aligned Balanced
Parental SupportParent GuideTo help parents help their
children
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Reading LevelFlesh-Kincaid:Using the FleshKincaid scale of
readability, the student Algebra Connections scores are:
7.4Grade Level
64.0Reading Ease
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Conclusion
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Ways of ThinkingAlgebra Connections focuses attention on five
ways of thinking mathematically: Justifying Generalizing Applying
and Extending Making Connections Reversing ThinkingRigorous Aligned
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Chapter ClosureEach chapter offers extensive closure
opportunities, including: Reflective activities Key vocabulary
Graphic organizers Practice problems with answers for
self-assessment Ways of ThinkingRigorous Aligned Balanced
Use of Algebra TilesSymbolic manipulation is developed through
use of concrete tools 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.
2x - x + 1- (2 - 3)
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Further GuidanceFor big activities and key challenging problems,
Further Guidance is available for students who need additional
assistance.
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