North Carolina Mathematics Curriculum Standards

1. Day 1 of 6 Spring 2008 North Carolina Mathematics Curriculum Standards LEA Leadership Team Professional Development

2. This file has been modified from a 2008 MSP project. Goals for Day 1 • To establish a baseline for our work and its evaluation • To provide an overview of the PD plan • To model the importance of mathematical processes: problem solving, connections, representations, communication, reasoning • To support your role as a member of an LEA Leadership Team

3. I can count to 20…before you can! • Play with one partner • You may say 1 or 2 numbers at a turn • You must begin at one - no skipping or repeating numbers • Person who gets to 20 is the winner

4. ? ? What… ? • Mathematics is involved in the task? • Strategies did you use? • Grades would find this challenging? • Reason would a teacher have to use the game? • Thinking is required if rules are changed?

5. K-8 Mathematics Curriculum Standards Every student in North Carolina deserves to be taught mathematics by a well-qualified teacher using high-quality materials and instructional strategies that support student learning

6. Principles and Standards for School Mathematics “Being able to reason is essential to understanding mathematics. By developing ideas, exploring phenomena, justifying results, and using mathematical conjectures …students should see and expect that mathematics makes sense.” From Principles and Standards of School Mathematics (NCTM, 2000, p. 56)

7. Processes: Ways to Learn • Problem solving • Reasoning and Proof • Representations • Connections • Communication Concepts, skills, algorithms, applications are internalized through these processes

8. Ways to Demonstrate Learning • At every level students reveal their thinking and understanding through these processes • When teachers recognize the logic behind students’ answers, they are able to identify misconceptions and incomplete knowledge • Fluency in using processes is a must for 21st Century success

9. Problem-Solving Examples Students need to experience multiple types of problems • Routine drill and practice • Routine practice in contexts • More complex problems that involve multiple strategies or possible solutions • Non-routine problems for which there is no obvious solution path

10. Routine Drill and Practice • Subtract 356 - 132 • Multiply 7 x 8 • Estimate 27¢ + 32¢ • 2/3 yard = ? inches

11. Routine Drill and Practice in Context • Thelonius Fiddles’ Company is going to sell special Mother’s Day boxes of candy for $8.50 each. Sales tax is 6% and shipping is $2.00. What would be the cost of one box? • If he sells 10 boxes, including tax and shipping, for $125, would this be a bargain? Why or why not?

12. Complex Problems • Should have multiple strategies or possible solutions • Should include the expectation that students will explain their work or reflect on their answers • For example, Fiddles Fudge Factory

13. Non-Routine Problems • Non-routine problems usually have no obvious solution path • Discussion of how the problem is solved becomes particularly important to help students solidify mathematical understandings • Sharing helps other students learn new strategies

14. Non-Routine Non-Routine Problems • Thelonius gives candy samples to different businesses. To the first business he gives half of his samples plus one sample • To the second, third, and fourth businesses he again gives half of his samples plus one • To the last and fifth business, he gives away half plus one and has no samples left. How many samples did he start with?

15. You’ve Just Been Hired! • Design Specialist for Fiddles Fudge Factory • Major sales initiative coming • New packaging needed • Thelonious is adamant; costs must be kept minimal

16. Complex Routine Fiddles Fudge Factory Thelonious Fiddles owns a candy company that specializes in making delicious fudge. For the upcoming season, Thelonious wants his designers (you) to create new packaging for a Mother’s Day box containing 60 one-inch cubes of fudge. His plan is to package the fudge in an open box that has no top but is covered in colorful plastic wrap.

17. Fiddles Fudge Factory 1. What are some possible ways the fudge can be packaged into rectangular boxes? 2. What are the dimensions of the box that uses the least amount of material?

18. Fiddles Fudge Factory 3. Thelonious Fiddle wants you to make templates for at least three boxes. Since he will have each box cut from one rectangular piece of expensive material, he would like for you to show him what each box will look like when it is unfolded 4. List the mathematics that you know or used to help you solve these problems

19. Fiddles Fudge Factory • Read through the problem once more • Talk with your partner: • What do you know about the task? • What exactly does Thelonius want you to do? • Work with your partner to complete items 1-3 • Talk with those around you to do number 4

20. What mathematics did you use to solve the tasks? In what ways was being able to visualize or to draw representations of your ideas helpful? Where in the K-8 curriculum are students likely to learn this content? In what other settings could the tasks be situated? When might these be helpful? Debriefing Theolonius’ Tasks

21. How did you begin to think about the first task? How did you record the possibilities? What possible configurations did you discover? What are the dimensions of the box using the least amount of materials? Does everyone agree? Is there more than one possible answer? Debriefing Theolonius’ Tasks

22. Nets for the Candy Boxes • What nets have you created? Explain what the dimensions are as you share your nets? • Is one net more effective than another in terms of left-over paper? Explain or demonstrate why you say this

23. Contexts & “Naked Numbers” • Students need practice to develop “automaticity” with processes • What other questions/ tasks would you pair with this investigation? • What might be the next task?

24. ‘IN’-formative assessment • Also called classroom assessment or formative assessment • Supports learning as teachers recognize student’s misconceptions as well as what students understand • Supports teachers in making decisions both “in the moment” and in planning

25. ‘IN’-formative assessment • Ongoing process to close gap between learner’s current state and desired goals • Strong research base supports effectiveness of formative assessment • Includes feedback to students • Relates to mathematics in task • Tells what is good/correct • Suggests what students need to rethink

26. Comments on Student Work • Which student’s thinking do you feel you know the most about? Why? • If this set of papers represents the class as a whole, what lesson/task might you plan next?

27. Return on the Investment • Why is it important to invest time in using student work to understand their thinking and then plan “next steps” in instruction? • What are the advantages in working with colleagues to plan tasks, examine student work, and plan future instruction based on what you observe?

28. Processes: Ways to Learn • Problem solving • Reasoning and Proof • Representations • Connections • Communication What’s new? Goal 6 in Curriculum Standards focuses on these processes

29. We’ve Come “Full Circle”

30. Basics for the 21st Century Our students will face a different kind of competition as workers Workers need mathematics content knowledge and confidence in themselves to use the mathematics in routine and creative ways Education must meet their needs

31. Basics for the 21st Century WE are preparing the workers for the 21st Century Basics include understanding of mathematical concepts, procedural fluency, strategies for solving problems, and ability to communicate thinking.

32. Thanks for joining us in this movement to improve mathematics teaching and learning in North Carolina!

33. DPI Mathematics Staff Partners for Mathematics Learning is a Mathematics-Science Partnership Project funded by the NC Department of Public Instruction. Permission is granted for the use of these materials in professional development in North Carolina Partner school districts. Partners for Mathematics Learning

34. PML Consultants

35. PML Writers Please give appropriate credit to the Partners for Mathematics Learning project when using these materials. Permission is granted for their use in professional development in North Carolina Partner school districts. Jeane M. Joyner, Project Director

36. 2008 Mathematics Curriculum Standards LEA Leadership Team Professional Development Day 1 of 6 Spring 2008