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Comprehensive Balanced Mathematics Model Middle School 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 Create four towers (single cube wide) of differing heights using 1-inch cubes, beginning with a single cube. Determine the surface area of each tower.

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Reasoning and Proof Mathematics should make sense to students Example Describe the pattern relating the surface areas to the towers as they become taller. Build one more tower to test your pattern.

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Communication An important step in communicating mathematical thinking to others is organizing and clarifying one’s ideas. Example Express the pattern (relationship) in a mathematical sentence (equation).

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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 How would the pattern change if the towers are double wide rather than single? Draw 4 double-width towers on dot paper to test your prediction.

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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 Create a table of values and graph representing the relationship of the height of the single-wide towers and their corresponding surface areas. You may use computer software or a graphing calculator.

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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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