implementing problem based tasks to increase rigor in the mathematics classroom

Implementing Problem Based Tasks to Increase Rigor in the

Mathematics Classroom

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•

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

Agenda

Agenda• Discuss/explore RIGOR • Solve a problem with partner or small

group• Record findings, print and submit to

document participation

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

What is RIGOR?

• Did you say that rigor means something likeHARD?

Or CHALLENGING?

There is a new definition of RIGOR that helps us think about concrete steps that we can take in our mathematics classrooms

New Definition of RIGOR

• Rigor - pursue with equal intensityconceptual understanding

procedural skill and fluencyapplications

Example of RigorConceptual Understanding Procedural Skill and

FluencyApplication

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-1 -1 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?

What does RIGOR look like?

• Take 5-10 minutes to discuss and complete with othersDraw a picture of 3 divided by ¼Calculate an answer to 3 divided by ¼Describe a real world situation where you divide 3 by ¼

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?

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?

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?

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

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

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.

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?

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?

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

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

PRINT, COMPLETE, and SUBMIT• Attach a copy of task with your work• Describe opportunities for:Conceptual understanding

______________________________________________________________________________

Procedural Skill and Fluency __________________________________________________________________________

PRINT, COMPLETE, and SUBMITApplication_____________________________________________________________________

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

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

Contact Information

Joanne WhitleyJoanne.whitley@cms.k12.nc.us

Michael PillsburyMichael.pillsbury@cms.k12.nc.us