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 of 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
Long term goals for this program ● Teacher Program ● Summer Camp ● Starting Circles with students What does building a math community look like in this area?
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 or 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 opening it if it is closed. ⋮ Student 𝑙 changes the state of every 𝑙 th 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 Lesson Plan A Lesson Plan B Presented by Paul Zeitz in SIGMAA- MCST 2009 JMM presentation
How far can a pullback car travel? (20 min) 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. Induced Variability
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 of mathematical thinkers and problem solvers Build a community of mathematical Provide a low floor, high ceiling space for participants to thinkers and problem solvers 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
Long term goals for this program ● Teacher Program ● Summer Camp ● Starting Circles with students What does building a math community look like in your area?
2:00 - 3:30 today in Hotel Murano Venice 3
● Dr. Brandy Wiegers brandy.wiegers@cwu.edu ● Dr. Emilie Hancock Emilie.Hancock@cwu.edu
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