Educator Effectiveness Academy Summer 2012

1. Welcome Mathematics Educators Educator Effectiveness Academy Summer 2012 Day 2

2. 4 Corners Icebreaker How many miles did you drive to get here today? • 5 miles or less • Between 5 and 15 miles • 15 to 25 miles • Over 25 miles

3. 4 Corners Icebreaker How many years of teaching experience do you have? • 1-5 years • 6-10 years • 11-15 years • Over 15 years

4. 4 Corners Icebreaker Which of these describes your favorite vacation? • Action and adventure • Laying on a beach and reading a book • Sightseeing • Visiting family and friends

5. OUTCOMES The participants will: • analyze an MSDE lesson plan to determine how UDL and the Standards for Mathematical Practice are addressed. • develop an understanding of the terms “Practice Forward Task” and “Integrative Task.” • watch a demonstration of the Curriculum Management System. • clarify their understanding of the EEA Project requirements.

6. Warm Up Outcome The participants will make a list of the pieces of information that should be included in a lesson plan.

7. Warm Up • Rally Table • What information would you include in a lesson plan?

8. MSDE Lesson Plan 3 Categories • Background Information • Learning Experience • Supporting Information

9. MSDE Lesson Plan Components • Background Information • Content/Course • Unit • Essential Questions/Enduring Understandings Addressed in • the Lesson • Standards Addressed in This Lesson • Lesson Topic • Relevance/Connections • Student Outcomes • Prior Knowledge Needed to Support This Learning • (Vertical Alignment) • Method for determining student readiness for the lesson

10. MSDE Lesson Plan Components Learning Experience

11. MSDE Lesson Plan Components • Supporting Information • Interventions/Enrichments • Students with Disabilities/Struggling • Learners • English Language Learners • Gifted and Talented • Materials • Technology • Resources

12. Outcome The participants will analyze an MSDE lesson plan to determine how UDL and the Standards for Mathematical Practice are addressed.

13. Lesson Plan Analysis • Focus Questions • In what ways do the activities in this lesson plan support the proficiencies described in the Standards for Mathematical Practice? • How do the activities address the needs of all learners? • How do the activities support the development of the content standards that the lesson plan targets?

14. Lesson Plan Analysis • Summary • In what ways do the activities in this lesson plan support the proficiencies described in the Standards for Mathematical Practice?

15. Lesson Plan Analysis • Summary • 2. How do the activities address the needs of all learners?

16. Lesson Plan Analysis • Summary • 3. How do the activities support the development of the content standards that the lesson plan targets?

17. Analysis – FINAL NOTE!!! • FINAL NOTE!!! • Any pre-made lesson plan should be adapted to meet the needs of the students in yourclassroom.

18. Jump for Joy… Take A Break!!!!!

19. Outcome The participants will become familiar : • Practice Forward Task • Integrative Task

20. PARCC Assessment • Two considerations in the design of the PARCC assessments. • Some items will: • Measure multiple standards • Connect content and practices

21. Let’s Do a Little Math

22. Let’s Do a Little Math School officials want to build a new football field that will be 120 yards by 53 yards. However, the owner of a local nursery has donated enough grass seed to plant 81,000 square feet of grass. Since they have more than enough grass seed for the football field, school officials would like to plant a uniformly wide border around the field. What are the dimensions of a rectangular area with a uniformly wide border which has an area of 81,000 square feet ?

23. x Total area = 81,000 square feet= 9,000 square yards Solution 53 yards 120 yards x x The dimensions of the rectangular area

24. “Let’s Do a Little Math”Evaluating the Problem • Evaluate the problem for the mathematical content that the problem assesses by answering the following questions. • To complete this problem successfully : • Which mathematical concepts must a • student understand? • Which mathematical skills must a • student be able to use?

25. “Let’s Do a Little Math”Evaluating the Problem • Which behaviors described • in the Standards for Mathematical • Practice would come into play as • a student solves this problem?

26. Practice Forward Task A task that is intentionally designed to elicit one or more Standards for Mathematical Practice in connection to specified content standards. PARCC Definition

27. Frayer Model for Practice Forward Task

28. Definition (in your own words) A type of math task that will appear on the PARCC assessments that will provide evidence as to how well a student can use the math practices. Practice Forward Task

29. Facts/Characteristics • Will be tied to content • Would be difficult to complete • without engaging in the • practices • Can assess more than one • practice at a time Practice Forward Task

30. Practice Forward Task • Example • A physics professor says “Of course it is easy to see that • when .” • Give a possible explanation in terms of the structure of the expression on the left why the professor might say that.

31. Practice Forward Task School officials want to build a new football field that will be 120 yards by 53 yards. However, the owner of a local nursery has donated enough grass seed to plant 81,000 square feet of grass. Since they have more than enough grass seed for the football field, school officials would like to plant a uniformly wide border around the field. What are the dimensions of a rectangular area with a uniformly wide border which has an area of 81,000 square feet ? What characteristics does this problem display that would allow it to be classified as a “Practice Forward Task?”

32. Practice Forward Task Non Example

33. Frayer Model for • Will be tied to content • Would be difficult to complete • without engaging in the • practices • Can assess more than one • practice at a time A type of math task that will appear on the PARCC assessments that will provide evidence as to how well a student can use the math practices. Practice Forward Task • A physics professor says “Of course it is easy to see that • when v=c .” • Give a possible explanation in terms of the structure of the expression on the left why the professor might say that.

34. Integrative Task A task that may best be coded to a cluster heading, domain or grade or course rather than a specific standard. PARCC Definition

35. Integrative Task School officials want to build a new football field that will be 120 yards by 53 yards. However, the owner of a local nursery has donated enough grass seed to plant 81,000 square feet of grass. Since they have more than enough grass seed for the football field, school officials would like to plant a uniformly wide border around the field. What are the dimensions of a rectangular area with a uniformly wide border which has an area of 81,000 square feet ? What characteristics does this problem display that would allow it to be classified as an “Integrative Task?”

36. Integrative Task • Conceptual Category: Number • Domain : Quantities • Standards • N.Q.1 Use units as a way to understand problems and to • guide the solution of multi-step problems; choose • and interpret units consistently in formulas; choose • and interpret the scale and the origin in graphs and • data displays. ★ • N.Q.2 Define appropriate quantities for the purpose • of descriptive modeling. ★ • N.Q.3 Choose a level of accuracy appropriate to limitations • on measurement when reporting quantities. ★

37. Integrative Task • Conceptual Category: Algebra • Domain : Creating Equations • Standards • A.CED.1 Create equations and inequalities in one variable • and use them to solve problems. Include equations • arising from linear and quadratic functions, and • simple rational and exponential functions. • A.CED.3 Represent constraints by equations or inequalities, • and by systems of equations and/or inequalities, and • interpret solutions as viable or non-viable options in a • modeling context.

38. Integrative Task Conceptual Category: Algebra Domain :Reasoning with Equations and Inequalities Standards A.REI.4 Solve quadratic equations in one variable. A.REI.4b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

39. Create a Frayer Model for Integrative Task

40. Integrative Task Share and justify your example.

41. Integrative Task Post one example from your group (include list of Mathematical Skills addressed as justification.) Integrative Task

42. Gallery Walk

43. “Turn and Talk” Summary • Big Question • How will you modify your instruction to build student capacity for successful completion of Integrative and Practice Forward Tasks?

44. Check for Understanding

45. Check for Understanding Group members should stand one behind another

46. Hot Seat Question #1 Which set of standards describe the varieties of expertise that mathematics educators at all levels should seek to develop in their students?

47. Hot Seat • Question #2 • The standards: • Model with Mathematics • Use Appropriate Tools Strategically • Attend to Precision • are from of which set of Standards?

48. Hot Seat Question #3 Which type of task is intentionally designed to elicit one or more Standards for Mathematical Practice in connection to specified content standards?

49. Hot Seat • Question #4 • The three principles of Universal Design for Learning call for instruction that provides • Multiple Means of: • Principle I: ____?___________ • Principle II: ____?___________ • Principle III: _____?__________

50. Hot Seat Question #5 Which type of task is best coded to a cluster heading, domain or grade or course rather than a specific standard?