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

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

3. Components  Problem Solving  Reasoning and Proof  Communication  Connections  Representation

4. 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.

5. 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.

6. 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).

7. 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.

8. 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.

9. 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 …?”

10. Principles of Mathematics  The Equity Principle  The Curriculum Principle  The Teaching Principle  The Learning Principle  The Assessment Principle  The Technology Principle

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

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