NCDPI Curriculum and Instruction Mathematics

1. “Teaching for Understanding” “To B or Not to b?” NCDPI Curriculum and Instruction Mathematics

2. Posted on January 28, 2013 by Bill McCallum Once every few months or so I receive a message about the following standard: 6.G.2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V=lwh and V=bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Guess what people think the problem is before reading on? http://commoncoretools.me/2013/01/28/to-b-or-not-to-b/

3. Norms • Listen as an Ally • Value Differences • Maintain Professionalism • Participate Actively http://thebenevolentcouchpotato.wordpress.com/2011/11/30/norm-peterson-bought-the-house-next-door/

4. Who’s in the Room?

5. “Teaching for Understanding” Phil Daro Math SCASS February 12, 2013

6. Dr. Phil Daro “In Person” (Almost)

7. Problem: Mile wide –inch deep curriculum Cause: Too little time per concept Cure: More time per topic “LESS TOPICS”

8. Why do students have to do math problems? • To get answers because Homeland Security needs them, pronto. • I had to, why shouldn’t they? • So they will listen in class. d. To learn mathematics.

9. To Learn Mathematics • Answers are part of the process, they are not the product. • The product is the student’s mathematical knowledge and know-how. • The ‘correctness’ of answers is also part of the process. Yes, an important part.

10. What is learning? • Integrating new knowledge with prior knowledge; explicit work with prior knowledge • Prior knowledge varies across students in a class (like fingerprints); this variety is key to the solution, it is not the problem. • Thinking in a way you haven’t thought before and understanding what and how others are thinking.

11. “Answer Getting vs. Learning Mathematics” United States: • “How can I teach my kids to get the answer to this problem?” Japan: • “How can I use this problem to teach the mathematics of this unit?”

12. “The Butterfly Method”

14. Discussion • How might these ideas challenge teachers in your district or school? • How can we move from “answer getting” to “learning mathematics”? • What evidence do you have that teachers might not know the difference?

15. “The Butterfly Method”

16. Commercial Break!! Blogstop.com

17. “Faster Isn’t Smarter”byCathy Seeley“Hard Arithmetic is not Deep Mathematics”p. 83

18. “Hard Arithmetic is not Deep Mathematics” • What issues or challenges does this message raise for you? • In what ways do you agree or disagree? • What barriers might keep students from reaching these standards, and how can you tackle these barriers?

20. Let’s Do Some Math!

21. Area and Perimeter • What rectangles can be made with a perimeter of 30 units? Which rectangle gives you the greatest area? How do you know? • What do you notice about the relationship between area and length of the sides?

22. Instructions • Discuss the following at your table • What thinking and learning occurred as you completed the task? • Would this task be considered “Deep Mathematics”? Why or why not?

23. Compared to…. 5 10 What is the area of this rectangle? What is the perimeter of this rectangle?

24. Traveling With Graphs Bing.com

27. Compared to…. What is the area of a rectangle with a length of 2in. and a height of 8in.? What is the area of a triangle whose base is 3 units and it’s height is 8 units? If Carl rode a bicycle for 3 hours and traveled 40 miles, what was his average speed?

28. Traveling With Graphs • What concepts are addressed in this situation? • What strategies could be used to develop conceptual understanding? • At what level could this task be used as a lesson task? How is this task foundational for future concepts?

29. “Who’s doing the talking, and who’s doing the math?” Cathy Seeley, former president, NCTM

30. How do we move from a culture of “answer getting” to one of “learning mathematics”?

31. “Modeling in Mathematics” by CCSSO and Math SCASS (Council of Chief State School Officers) (The State Collaborative of Assessment and Student Standards)

32. What is modeling? A word with different meanings 1. “Modeling a Task” - An instructional strategy where the teacher shows step by step actions of how to set up and solve the task Use step by step actions to “model” how to solve this task Mathematical Task: 2 + ___ = 8

33. What is modeling? A word with different meanings 2. “Model with Manipulatives” - Start with the math then use manipulatives to demonstrate and understand how to solve the problem. math Toothpicks as a model

34. What is modeling? A word with different meanings 3. “Model with Mathematics” - Start with the task and choose an appropriate mathematical model to solve the task Choose a grade appropriate mathematical model to solve the task: e.g. writing the number sentence 4 – 2 = 2 Four birds sat on a wire, 2 flew away. How many birds remain on the wire?

35. What is modeling? A word with different meanings 4. “A Model with Mathematics”

36. What is modeling? A word with different meanings • “Modeling a Task” • “Modeling with Manipulatives” • “Model with Mathematics” • “A Model with Mathematics”

37. What is modeling? A word with different meanings • “Modeling a Task” • “Modeling with Manipulatives” • “Model with Mathematics” • “A Model with Mathematics”

38. What makes something a modeling task? • Are there criteria for “modeling tasks”? • What are the skills involved?

39. Let’s Do Some Math!

41. How well posed is well enough? • Should a student still have questions after they read the task? • Should students have to find their own information outside of what is given in the problem? • Should assumptions be stated, or reasoned differently by each individual student?

42. Problems to Ponder Think about…… How each problem is posed. How much information is provided and when it’s provided? How much information is needed and how will they find it? • Painting A Barn • The Ice Cream Van • Birthday Cakes • Graduation • Sugary Soft Drinks

43. Painting A Barn Alexis needs to paint the four exterior walls of a large rectangular barn. The length of the barn is 80 feet, the width is 50 feet, and the height is 30 feet. The paint cost $28 per gallon, and each gallon covers 420 square feet. How much will it cost Alexis to paint the barn? Explain your work.

44. Ice Cream Van You are considering dividing ice cream van during the summer vacation. Your friend who “knows everything” tells you that “its easy money.” You make a few inquiries and find that the van costs $600 per week to rent. Each ice cream cone costs 50 cent to make and sell for $1.50.

45. Birthday Cakes Would all the birthday cakes eaten by all the people in Arizona in one year fit inside the University of Phoenix football stadium? Cody Patterson Original

46. Graduation The SLV High School graduation started at 1:00 pm. After some speeches, the principal started reading off the names of the students, alphabetically by last name. When he finishes, the graduation will end.

47. Sugary Soft Drinks How many packets of sugar are in a 20 ounce bottle of soda? http://threeacts.mrmeyer.com/sugarpackets/

48. Lunch

49. Collecting and Selecting Information“Modeling Information Descriptors” Determine what information is needed and find the information yourself Brainstorm what you need and then are given it All and only relevant information is given Told what you need, you go and find it Given information, but you decide what is useful

50. Collecting and Selecting Information“Modeling Information Descriptors” Use the contents of the envelope on your table to: • Match each task with it’s aligned “Collecting and Selecting Information” description.