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Comprehensive Balanced Mathematics Model Elementary Okaloosa County School District Dr. Lynda Penry

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Elements of the Comprehensive Mathematical Model Components of Mathematics Math Model Examples Principles of Mathematics Descriptors Best Practices Self-Reflection Survey Resources

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Components Problem Solving Reasoning and Proof Communication Connections Representation

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Problem Solving Unless students can solve problems, the facts, concepts and procedures they know are of little use. Example I have four pennies, four dimes, and four nickels in my pocket. If I take three coins out of my pocket, how much money could I have taken?

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Reasoning and Proof Mathematics should make sense to students Example (Using the same money problem) I took 30¢ out of my pocket. Which coins did I take out of my pocket? Provide evidence of your answer and share in some type of group setting.

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Communication An important step in communicating mathematical thinking to others is organizing and clarifying one’s ideas. Example If I take three coins out of my pocket, could I have 24¢? Explain with words or pictures how you solved the problem.

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Connections Students build new understandings on previous knowledge Students build new understandings between mathematics and other subject areas Students build new understandings between mathematics and every-day life. Example List how many ways you might use money. Discuss why it is important to know how much money you have.

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Representation Students can develop and deepen their understanding of mathematical concepts and relationships as they create, compare, and use various representations. Example Make a graph of the class solutions and ask students to analyze the data.

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Questions to Foster Mathematical Understanding “Does anyone have the same answer but a different way to explain it?” “Can you convince us that that makes sense?” “Can you model that to prove your thinking?” “Does that always work?” “How does this relate to …?” “Can you give us an example of …?”

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Principles of Mathematics The Equity Principle The Curriculum Principle The Teaching Principle The Learning Principle The Assessment Principle The Technology Principle

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Self-Reflection Survey Individual reflection Based on Best Practices of the Principles of Mathematics

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Resources Web sites used in OCSD classes Principles and Standards for School Mathematics - NCTM

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