What do you notice? What do you wonder? Notice All the red ones - - PowerPoint PPT Presentation

What do you notice? What do you wonder?

Notice

• All the red ones are prime numbers
• If you go down all the even numbers will be orange
• The greens go diagonal - all divisible by three
• Colors based off prime factors
• All the solid colors are prime numbers - except for one
• They stopped after red - there are only a set amount of distinct colors
• The number of segments are the same as the number of prime factors
• 1 is white - it’s composite so it doesn’t match anything - not prime
• Each color represent a number so if you multiply those numbers you get that
• number. If you go to 40 it’s 2x2x2x5 = 40

Wonder

• Why are all the prime numbers greater than 10 red?
• Why multiples of 7 are purple - where did the purple come from?
• Why didn’t they do white for 1 instead of gray? There should have been a lack
• f color instead of bland color.
• Why did they stop at 60?
• Can we find patterns when you’re looking at only one color? What is the

pattern for the number of sections colored? Is there a way to find that pattern?

• Why the column of three there are quite a few prime numbers?
• What would it look like if we continued this pattern?

Mathematics is not about following rules, it’s about playing -- and exploring and fighting, looking for clues and sometimes even breaking things.

• Dan Finkel

Session Outline

• Introductions
• What is a Math Circle?
• Open Middle, Open Ended
• Resources

• Exposure to advanced

mathematical topics

• Developing problem

solving skills

• Sharing of mathematical

culture

A National Movement … Math Salute!

Kittitas Valley Math Circle

• Dr. Brandy Wiegers, Director
• Drs. Emilie and Brent Hancock, Coordinators: Elementary Programs
• Dr. Dominic Klyve, Coordinator: Spanish Program
• Ms. Linda Graf, Dr. Janet Shiver and Dr. Allyson Rogan-Klyve, Coordinators:

Adult/Community/ Parent/Guardian/Teacher Program

• Teacher Program
• Summer Camp
• Starting Circles with

students What does building a math community look like in this area?

Long term goals for this program

Math Circle Core Value: Foster Problem-Solving Habits of Mind Math Circle problems are facilitated in ways that promote authentic mathematical experiences wherein participants maintain agency in driving exploration of disciplinary

• mathematics. Participants engage in

mathematical discourse and develop the habits of mind of mathematical thinkers and problem solvers (e.g., pattern-finding, conjecturing, experimenting).

Math Circle Core Value: Build a Community of Mathematical Thinkers and Problem Solvers Math Circles connect participants to the broader community of mathe- matical practice. They provide a space for participants to develop math- ematical passion, identity, and a sense of belonging in the discipline.

Math Circle Pledge

I solemnly swear (or affirm) that if I already know the answer to the math problem I will not yell it out loud but instead will challenge myself to take a different approach to the problem

• r think more generally about the problem

so our whole Circle can experience the joy of learning.

Math Circle Core Value: Explore Worthwhile Mathematical Tasks Authentic mathematical problems are just that, problematic. Math Circle tasks provide “low-floor” access to essential disciplinary questions, with “high ceilings” that connect to important and deep mathematical ideas. The problems are often open-ended and sometimes even open questions in the field. These problems are also open-middle, providing participants choice in solution strategies, representations, and other components of the problem-solving process.

Session Outline

• Introductions
• What is a Math Circle?
• Open Middle, Open Ended
• Resources

The Locker Problem (20 min)

At a (very) large high school, there are 10,000 lockers all on one wall of a long

• corridor. The lockers are numbered, in order, 1, 2, 3, …, 10,000, and to start, each

locker is closed. There are also 10,000 students, also numbered 1, 2, 3, …, 10,000. The students walk the length of the corridor, opening and closing lockers according to the following rules:

• Student 1 opens every locker.
• Student 2 closes every second locker.
• Student 3 changes the state of every third locker, closing it if it is open, and
• pening it if it is closed.

⋮

• Student 𝑙 changes the state of every 𝑙th locker.

After all 10,000 students have walked down the corridor, which lockers are open? Which students do we send down the corridor if we only want prime numbered lockers open?

Math Lessons

Presented by Paul Zeitz in SIGMAA- MCST 2009 JMM presentation

Lesson Plan A Lesson Plan B

How far can a pullback car travel? (20 min)

Induced Variability

On your table are several of the same toy pull-back cars. The company that makes these pull-back cars wants to put a label on the package to say how far you can expect it to go forward after you pull it back. What should they advertise on the label? Justify your claims. As you solve this problem, represent any data your collect with a data display on a large sticky sheet.

Representing variability in the world around us

Natural Variability Measurement Variability Induced Variability

Groth, Randall E. "Royalty, racing, rolling pigs, and statistical variability." Teaching Children Mathematics 22.4 (2015): 218-228.

Bringing Math Circles into the Classroom

Explore worthwhile mathematical tasks Supplement, without overburdening, existing curriculum Foster problem-solving habits of mind Teaching through problem solving helps develop the habits

• f mathematical thinkers and problem solvers

Build a community of mathematical thinkers and problem solvers Provide a low floor, high ceiling space for participants to develop mathematical passion, identity, and a sense of belonging in the discipline.

• Exposure to advanced

mathematical topics

• Developing problem

solving skills

• Sharing of mathematical

culture

A National & Local Movement

• Tacoma:

○ Mathlete Coaching Project. ○ South Sound Math Teachers' Circle.

• Seattle:

○ Math For Love Math Teachers' Circle. ○ Prime Factor Math Circle. ○ University of Washington Math Circle. ○ Washington Experimental Mathematics Lab. ○ Seattle Julia Robinson Math Festival

• Teacher Program
• Summer Camp
• Starting Circles with

students What does building a math community look like in your area?

Long term goals for this program

2:00 - 3:30 today in Hotel Murano Venice 3

• Dr. Brandy Wiegers

brandy.wiegers@cwu.edu

• Dr. Emilie Hancock

Emilie.Hancock@cwu.edu