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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 Balanced
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 Balanced
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 Aligned Balanced
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 Balanced
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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