Enhancing Mathematics Rigor Through Problem-Based Tasks: NCDPI Insights

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/curriculum/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. AgendaAgenda • 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

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