Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom?

1. Principal's Workshop: How Does the Common Core Change What We Look For in the Math Classroom? Panama City, Florida January 22 & 23, 2013 Presenter: Elaine Watson, Ed.D.

2. How Does the Common Core Change What We Look For in the Math Classroom? Video from Inside Mathematics: Principal explaining changes she sees in math classrooms

3. Hunt Institute Video: The Importance of Mathematical Practice http://vimeo.com/album/1702025/video/29568008

4. 1. Make Sense of Problems and Persevere in Solving “It’s not that I’m so smart, it’s just that I stay with problems longer.” Albert Einstein

5. 1. Make Sense of Problems and Persevere in Solving 5th Grade Perseverance

6. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: Explainto self the meaningof a problem and look for entrypointsto a solution Analyzegivens, constraints, relationships and goals Make conjectures about the form and meaning of the solution

7. 1. Make Sense of Problems and Persevere in Solving • Plan a solution pathway rather than simply jump into a solution attempt • Consider analogous problems • Try special cases and simpler forms of original problem Mathematically proficient students:

8. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: Monitorandevaluatetheir progress and change course if necessary… “Does this approach make sense?”

9. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: Perseverein Solving by: Transformingalgebraic expressions Changingthe viewing window on a graphing calculator Movingbetween the multiple representations of: Equations, verbal descriptions, tables, graphs, diagrams

10. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: Check their answers “Does this answer make sense?” Does it include correct labels? Are the magnitudesof the numbers in the solution in thegeneral ballpark tomake sensein the real world?

11. 1. Make Sense of Problems and Persevere in Solving Mathematically proficient students: Check their answers Verify solution using adifferent method Compareapproach with others: How does their approach compare with mine? Similarities Differences

12. 2. Reason Abstractly and Quantitatively Mathematically proficient students: Make sense of quantities and their relationships in a problem situation Bring two complementary abilities to bear on problems involving quantitative relationships: The ability to… decontextualize to abstract a given situation, represent it symbolically, manipulate the symbols as if they have a life of their own contextualize to pause as needed during the symbolic manipulation in order to look back at the referent values in the problem

13. 2. Reason Abstractly and Quantitatively Mathematically proficient students: Reason Quantitatively, which entails habits of: Creating acoherent representation of the problem at hand considering the unitsinvolved Attending to the meaning of quantities, not just how to compute them Knowing andflexibly using different properties of operations and objects

14. Watch the video and note where you see evidence of Middle School Classifying Equations 1. Make Sense of Problems and Persevere in Solving 2. Reason Abstractly and Quantitatively

15. 3.Construct viable arguments and critique the reasoning of others Mathematically proficient students: Understand and use… stated assumptions, definitions, and previously established results… when constructing arguments

16. 3.Construct viable arguments and critique the reasoning of others In order for students to be practicing this standard, they need to be talking to each other, so teachers need to plan lessons that include a lot of large group and small group discussions. A classroom culture must be cultivated in which it is as safe to disagree as it is to agree.

17. 3.Construct viable arguments and critique the reasoning of others Here are some sentence structures from the first video: I agree that ______________ because __________ I disagree because __________________________ How can we be sure? What do you think? Are you convinced? Do we all agree?

18. 3.Construct viable arguments and critique the reasoning of others What SMPs do you observe the students practicing? Here's the Problem from the video:Write several different types of equations for 2.4. Draw some different types of pictures to represent 2.4. Is 2.4 the same thing as the quotient 2 remainder 4? Why or why not?http://youtu.be/EA3YkawKEWc

19. 4. Model with Mathematics Modeling is both a K - 12 Practice Standard and a 9 – 12 Content Standard.

20. 4. Model with Mathematics Mathematically proficient students: Use powerful tools for modeling: Diagrams or graphs Spreadsheets Algebraic Equations

21. 4. Model with Mathematics Mathematically proficient students: Models we devise depend upon a number of factors: Howprecisedo we need to be? What aspects do we most need to undertand, control, or optimize? Whatresourcesof time and tools do we have?

22. 4. Model with Mathematics Mathematically proficient students: Models we devise are also constrained by: Limitations of our mathematical, statistical, and technical skills Limitations of our ability to recognize significant variablesand relationships among them

23. 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.

24. Modeling Cycle Problem Formulate Validate Report Compute Interpret

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

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

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

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

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

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

31. Modeling Cycle Problem Formulate Validate Report Compute Interpret

32. 6. Attend to precision Mathematically proficient students: Try to communicate precisely to others: Use clear definitions State the meaning of symbols they use Use the equal sign consistently and appropriately Specify units of measure Label axes

33. 6. Attend to precision Mathematically proficient students: Try to communicate precisely to others Calculate accurately and efficiently Express numerical answers with a degree of precision appropriate for the problem context Give carefully formulated explanations to each other Can examine claims and make explicit use of definitions

34. 6. Attend to precision Students Practicing and Discussing Precision

35. Use the Standards for Mathematical Practice Lesson Alignment Template.What SMPs do you see? http://ummedia04.rs.itd.umich.edu/~dams/umgeneral/seannumbers-ofala-xy_subtitled_59110_QuickTimeLarge.mov

36. 7. Look for and make use of structure Mathematically proficient students: Look closely to discern a pattern or structure In x2 + 9x + 14, can see the14as2 x 7 and the9as2 + 7 Can see complicated algebraic expressions as being composed of several objects: 5 – 3 (x – y)2 is seen as 5 minus a positive number times a square, so its value can’t be more than 5 for any real numbers x and y

37. 8. Look for and express regularity in repeated reasoning. Mathematically proficient students: Notice if calculations are repeated Look for both general methods and for shortcuts Maintain oversight of the process while attending to the details.

38. What Practice Standards do you see? Sean: Is 6 Even and Odd?

39. Do All 8 Practice Standards Need to be Used in Every Lesson? There are some rich problems that elicit all 8 of the Practice Standards. However, these types of problems can’t be done on a daily basis. Instructional time still needs to be balanced between building the students’ technical skills and No…but the teacher should plan so that over the span of a few days, the students are given learning opportunities to of the practicing standards

40. A Balanced Approach math facts how to approach and a novel situation procedures mathematically

41. Math Facts and Procedures Memorizing Math Facts and Naked Number Exercises are Important! Practice Standards that apply: #2 Reason Quantitatively #6 Attend to Precision #7 Look for and Use Structure #8 Use Repeated Reasoning

42. Does Every Worthwhile Problem Have to Model a Real World Situation?

43. What SMPs Do You Observe Maya Practicing? What errors do you notice? What would you do to have Maya notice the errors? Maya Representing 52

44. Let’s Practice Some Modeling 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.

45. 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.

46. Possible or Not?

47. 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.

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

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

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