1. Comprehensive Balanced Mathematics Model Elementary 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 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?

5. 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.

6. 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.

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 List how many ways you might use money. Discuss why it is important to know how much money you have.

8. 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.

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