1. Implementing Problem Based Tasks to Increase Rigor in the Mathematics Classroom

2. Message from NCDPI about CCSS This following video from Dr. Atkinson will assist you in understanding the process and timeline around the common core legislation. http://www.ncpublicschools.org/movies/curri culum/home/atkinson-common-core.mov http://www.ncpublicschools.org/movies/curri culum/home/atkinson-common-core.mov

3. Outcomes Participants will: Learn a new definition for rigor Consider how real-world problems support rigor Solve and discuss a Problem Based Task Document analysis and discussions

4. Agenda Discuss/explore RIGOR Solve a problem with partner or small group Record findings, print and submit to document participation

5. What is rigor? When you hear that your math program must have RIGOR, what do you think that means? Turn and talk with others for 2-3 minutes

6. What is RIGOR? Did you say that rigor means something like HARD? Or CHALLENGING? There is a new definition of RIGOR that helps us think about concrete steps that we can take in our mathematics classrooms

7. New Definition of RIGOR Rigor - pursue with equal intensity conceptual understanding procedural skill and fluency applications

8. Example of Rigor Conceptual UnderstandingProcedural Skill and Fluency Application Explaining the graph of a linear equation – demonstrating an understanding of what it shows. E.g., “When x increases, y increases twice as fast – that’s the 2x. When x is 0, y is already 1. That’s why you need +1.” Solving and graphing a linear equation e.g., y = 2x+1 x y 0 1 1 3 2 5 Use linear equations and their graphs to compare options and make a choice e.g., which is a better phone plan for a heavy user?

9. What does RIGOR look like? Take 5-10 minutes to discuss and complete with others Draw a picture of 3 divided by ¼ Calculate an answer to 3 divided by ¼ Describe a real world situation where you divide 3 by ¼

10. What does RIGOR look like? What kind of visual representation of 3 divided by ¼ did you come up with? Do you think being able to draw it shows CONCEPTUAL UNDERSTANDING?

11. What does RIGOR look like? How did you calculate 3 divided by ¼ ? Do you think being able to calculate shows PROCEDURAL SKILL AND FLUENCY?

12. What does RIGOR look like? What real world situation did you describe for 3 divided by ¼ ? Do you think being able to describe in terms of a real world situation shows APPLICATION?

13. Did you come up with any of these? Drawings – 3 bars or 3 pies cut into 4 pieces each Calculations – “invert and multiply” 3 x 4/1 = 12 Real world situation – How many quarter pounders can you make out of 3 pounds of hamburger? Did you come up with similar drawings, calculations, real world situations? Discuss as a whole group

14. Providing Opportunities for Rigor Attend to the balance of concepts, skills, and application Look for opportunities that provide all three Engage students in problem solving that includes the application of skills/procedures in meaningful contents – this supports concept development

15. Walch Problem-Based Task Each task is aligned to the CCSS standards / the NC Standard Course of Study. Each task will engage students in the Standards of Mathematical Practice. Problem-Based Task 2.8.1: Jai’s Jeans Jai is shopping for jeans and finds a style she likes so much that she may buy more than one pair. The jeans cost $50 each and are on sale for 30% off. Write an expression for the sale price of the jeans in such a way that the original purchase price is still evident. Then, write a function rule for the expression and simplify it. Use this function to find out how much money it will cost if Jai buys 4 pairs of jeans.

16. Walch Coaching Questions Each Problem-Based Task will have coaching questions. Problem-Based Task 2.8.1: Jai’s Jeans Coaching Questions What is the original price of the jeans? What is an expression to represent buying x pairs of jeans at the original price? How would you calculate the 30% discount?

17. Next steps Turn and talk – take 3-5 minutes to discuss  What are my next steps for considering rigor in my classroom?  How will using Problem Based Tasks help?

18. Review a PBT for Opportunities to Support and Enhance Learning Work with a partner, or in a small group Select one of the Problem Based Tasks located on the intranet Review/solve and discuss Identify aspects of rigor: skills, concepts, application

19. Find a Walch PB Task Directions Goto my.cms.k12.nc.us Click departments Click STEM (Sci, Tech, Eng & Math) Click Middle & High School math Look under: Algebra I folder Look for North Carolina Problem-Based Tasks Look for Math I, II & III Workbooks

20. PRINT, COMPLETE, and SUBMIT Attach a copy of task with your work Describe opportunities for: Conceptual understanding _______________________________________ _______________________________________ Procedural Skill and Fluency _______________________________________ ___________________________________

21. PRINT, COMPLETE, and SUBMIT Application______________________________ _______________________________________ What will you have to do to support opportunities for conceptual understanding, procedural skill, and applications ? This may include instruction, problems, discussions in addition to the selected PBT

22. PRINT, COMPLETE, and SUBMIT your work to document your participation Think about next steps for using Problem Based Tasks (PBT) in your classroom. No need to do everything at once (conceptual understanding, procedural skill, applications)! But do consider all the opportunities that PBTs offer

23. Contact Information Joanne Whitley Joanne.whitley@cms.k12.nc.us Michael Pillsbury Michael.pillsbury@cms.k12.nc.us