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Monday, October 8, 2012 Presenter : Elaine Watson, Ed.D .

Montville Township Public Schools Middle and High School Introduction to Common Core State Standards for Mathematics. Monday, October 8, 2012 Presenter : Elaine Watson, Ed.D. Introductions. Share What feeds your soul personally? What is your professional role?

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Monday, October 8, 2012 Presenter : Elaine Watson, Ed.D .

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  1. Montville Township Public SchoolsMiddle and High SchoolIntroduction toCommon Core State Standards for Mathematics Monday, October 8, 2012 Presenter: Elaine Watson, Ed.D.

  2. Introductions Share What feeds your soul personally? What is your professional role? What feeds your soul professionally?

  3. Formative Assessment How familiar are you with the CCSSM?

  4. Goals for this Workshop You will leave with a deeper understanding of: The Content Standards & Practice Standards The types of tasks that build students’ ability to “practice” the Practice Standards How to navigate rich online CCSSM resources How to practice formative instruction to reach the different learners in your class

  5. What are the standards, anyway? The standards are the end product of what students need to understand and be able to do with the content.  They do not attempt to tell teachers how to teach the content.  Teaching is an art. There is no one method that fits all teachers or all students.

  6. CCSSM Equally Focuses on… Standards for Mathematical Content Standards for Mathematical Practice Same for All Grade Levels Specific to Grade Level

  7. CCSSM Video The Mathematical Standards: How They Were Developed and Who Was Involved

  8. Modeling is both a K - 12 Practice Standard and a 9 – 12 Content Standard.

  9. Modeling Cycle Problem Formulate Validate Report Compute Interpret

  10. Modeling Cycle Problem Identify variables in the situation Select those that represent essential features

  11. Modeling Cycle Formulate Select or create a geometrical, tabular, algebraic, or statistical representation that describes the relationships between the variables

  12. Modeling Cycle Compute Analyze and perform operations on these relationships to draw conclusions

  13. Modeling Cycle Interpret Interpret the result of the mathematics in terms of the original situation

  14. Modeling Cycle Validate Validate the conclusions by comparing them with the situation…

  15. Modeling Cycle Validate Re - Formulate Report on conclusions and reasoning behind them

  16. Modeling Cycle Problem Formulate Validate Report Compute Interpret

  17. Modeling Cycle The word “modeling” in this context is used as a verb that describes the process of transforming a real situation into an abstract mathematical model.

  18. CCSSM VideoHigh School Math Courses

  19. Students can: start with a model and interpret what it means in real world terms OR start with a real world problem and create a mathematical model in order to solve it.

  20. Possible or Not? Here is an example of a task where students look at mathematical models (graphs of functions) and determine whether they make sense in a real world situation.

  21. Possible or Not?

  22. Questions: Mr. Hedman is going to show you several graphs. For each graph, please answer the following: A. Is this graph possible or not possible? B. If it is impossible, is there a way to modify it to make it possible? C. All graphs can tell a story, create a story for each graph.

  23. One A. Possible or not? B. How would you modify it? C. Create a story.

  24. Two A. Possible or not? B. How would you modify it? C. Create a story.

  25. Three A. Possible or not? B. How would you modify it? C. Create a story.

  26. Four A. Possible or not? B. How would you modify it? C. Create a story.

  27. Five A. Possible or not? B. How would you modify it? C. Create a story.

  28. Six A. Possible or not? B. How would you modify it? C. Create a story.

  29. Seven A. Possible or not? B. How would you modify it? C. Create a story.

  30. Eight A. Possible or not? B. How would you modify it? C. Create a story.

  31. Nine A. Possible or not? B. How would you modify it? C. Create a story.

  32. Ten A. Possible or not? B. How would you modify it? C. Create a story.

  33. All 10 Graphs What do all of the possible graphs have in common?

  34. And now... For some brief notes on functions!!!! Lesson borrowed and modified from Shodor. Musical Notes borrowed from Abstract Art Pictures Collection.

  35. Pyramid of Pennies Here is an example of a task where students look at a real world problem, create a question, and create a mathematical model that will solve the problem.

  36. Dan Meyer’s 3-Act Process Act I Show an image or short video of a real world situation in which a question can be generated that can be solved by creating a mathematical model.

  37. Dan Meyer’s 3-Act Math Task Pyramid of Pennies

  38. Dan Meyer’s 3-Act Process Act I (continued) 1. How many pennies are there? 2. Guess as close as you can. 3. Give an answer you know is too high. 4. Give an answer you know is too low.

  39. Dan Meyer’s 3-Act Process Act 2 Students determine the information they need to solve the problem. The teacher gives only the information students ask for.

  40. Dan Meyer’s 3-Act Process What information do you need to solve this problem?

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