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Julia Robinson Math Festival Returns: May 29th!

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Our June 2020 Julia Robinson Math Festival was canceled like many major in person events. Now, in partnership with the national JRMF organization, Julia Robinson Math Festivals are back! We are offering an online festival for 3rd to 8th graders. Some key information:

  1. The event will run on Saturday, May 29th, from Noon to 2PM Central Time. Register here.
  2. The festival will be online, using the Gather.Town platform. Each participant will have an avatar and will be able to roam around the virtual festival, entering rooms by choice. Gather.Town has functions that allow you to connect to friends (so you can stick together, or find each other across the festival).
  3. Roughly speaking, the festival is for 3rd to 8th graders. Older MC2 students can email info@mathcirclesofchicago.org if they are interested in helping us host the festival.
A Screenshot from Gather.Town

Gather.Town will allow us to better simulate the environment of an in person festival–it will be the first festival every using this technology!There will be puzzles throughout the virtual space along with a variety of math circle like activities in individual rooms. The space will be geared to engage a range of students, with levels for beginners and more experienced math circlers, along with activities that will be facilitated in Spanish as well as English. It promises to be a fun experiment in conducting a high-agency, collaborative math virtual math world. Join us!

Have a Week or Four? Summer YSP at UIC & UChicago!

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Many MC2 students over the years have participated in UChicago’s Young Scholars Program. That program continues, but has now expanded to UIC! The key differences between the programs:

  • UChicago YSP is a 4 week commitment starting the week of July 5th, serving 7th to 12th graders. Their website should be updated with the Summer 2021 application soon.
  • UIC YSP is a series of four 1-week programs, the first starting on June 28th. You can participate in as many or as few as you’d like! Students must currently be in 9th to 12th grade (aka Rising 10th to 13th graders).

My colleague Will Perkins at UIC shared the following detail for UIC’s program:

This program is a fun introduction to exciting topics in mathematics, applications of mathematics, and the work mathematicians do in education, research, and industry. Each of the four one-week sessions will focus on a particular area of mathematics, not covered in a typical high school curriculum, and its applications to science, technology, and society.  The program is free to participate in and students may sign up for as many of the four sessions as they like.  Any student who was in high school during the 2020-2021 academic year is eligible to apply.  The program will take place in-person on UIC’s east campus and participants will follow the UIC Covid safety guidelines.Every day students will learn something new, get hands-on practice solving problems and exploring new topics, and hear a guest speaker describe their work and how it relates to mathematics. Students will learn what it’s like to major in math in college, learn about how math is used in different careers, and meet fellow students excited about learning math.

The program is run by UIC faculty, and instruction will be provided by UIC faculty and graduate students.

Each day will run from 9:30am to 3:00pm and the daily schedule will include

9:30-10:30: arrival and mathematical lecture
10:30-10:45 break
10:45-12:00 small group problem solving
12:00-1:00 lunch break
1:00-2:00 invited speaker or video
2:00-3:00 small group activities
3:00 dismissal

The topics of the four sessions will be:
Week 1 June 28 – July 2: Probability, games, and statistics
Week 2 July 6 – July 9: Number theory and cryptography
Week 3 July 12 – July 16: Graph theory
Week 4 July 19 – July 23: Algorithms and social networks
Each of the four sessions is independent and students may apply for as many or as few sessions as they want.
For more information and for a link to the application, see our website here: https://willp.people.uic.edu/YSP/

So Many Online Options

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MC2 continues this winter and spring online; for the moment we hope we’ll be back in person this summer. In the fall, when it seems almost certain that our in person sites will re-open, we will maintain our online sessions to provide access to students who couldn’t participate otherwise. Like many organizations, we’ve found that one of the few silver linings of the pandemic is that we’ve learned to adapt to the online setting to further our mission.

Online options provide greater access to great programs everywhere. Our colleagues across the country provide a range of opportunities:

1 The Julia Robinson Math Festival

Prior to the pandemic, JRMF’s main activity was to support groups across the county to hold local in-person math festivals. MC2’s festival takes place every June, for example. Since March JRMF has undergone a remarkable shift. Their weekly webinars introduce a new activity every week.

2 Museum of Math

When MoMath reopens it’s well worth a visit (11 East 26th St. in NYC). In the meantime, they have a wide variety of virtual programs, from social gatherings for tweens and teens to Family Fridays (think origami) to summer camps and more.

3 Art of Problem Solving

AoPS has been the premier online math enrichment site for many years. For students interested in taking math courses that go beyond the standard curriculum, it’s the place to be. AoPS is also a platform for the math contest community–their Community Forums have a wide variety of discussion topics.

4 MathCommunities.org

The American Institute of Mathematics provides links to their own programs (e.g. ‘Math Mondays’) along with those of their partners.

Survey Says: Thank You Teachers

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As MC2 has expanded over the last five years, we’ve kept an eye on our surveys. We don’t want to increase enrollment at the expense of lowering the quality of our programs. I’m happy to say that the fall results are in, and 92% of our students Agree or Strongly Agree with the statement, “Overall I am very satisfied with my experience in math circles.” 84% said MC2 made them more interested in math.

Given that we’ve been online, it’s a testament to our teachers that these satisfaction rates are so high. Our students wrote things like, “I really liked the kindness of everybody,” “My teachers were great, that’s the only note I wanted to share. I had a fun time!”, and “The teachers were really nice and made me want to come to the meetings!”

We survey our teachers too. 98% agreed that, “I am highly satisfied with my work as a Math Circles instructor.”

Peyton Morgan, pictured here, led 8 MC2 sessions at 3 sites this fall.

I think the number 2 reason why we do our work well is that we have the right values–empowerment, inclusion, access, student agency, and the promotion of student collaboration. But the #1 reason for the quality of our work is that we have over 60 teachers that are committed to these values. Many of these teachers lead very busy lives, yet make the time to teach MC2 sessions on late afternoons and on weekends.

Moreover, we managed to have three teachers at almost every online session this fall. This could have been an overwhelming financial burden to our organization, but many of these teachers taught voluntarily. I particularly want to thank the undergraduate and high school students who stepped up when we made a plea for volunteers in September so we could meet the demand for our online programs.

It’s the time of the year to give thanks. Thank you to our teachers, without which MC2 wouldn’t exist, but more importantly our teachers are the reason why MC2 is so good at what it does!

 

Our Fall Plan

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Planning for our fall sessions is happening in earnest. We will, of course, be online, so we have a lot of planning to do. Last spring when we went online we held only a limited number of sessions at three program levels; this fall all five of our program levels will meet again. Some key things to note:

1. Fall Registration

Pre-registration for our fall programs will open the week of August 31st. Our lottery will run on September 19th, and remaining spots will be available on a first come first serve basis. Students who were enrolled in our spring in person programs can re-enroll at the site they were assigned to in the spring.

2. Offerings

Although our sessions will be online, we will continue to use our site names–in effect, a site is really a grouping of sessions taking place at the same time.

  • Back of the Yards sessions will continue to meet Saturdays at 10AM; UChicago and Payton will meet Saturdays at 1PM (with a 2nd round of Haynes-5/6 sessions at 2:30PM).
    • All Saturday sites will hold Haynes-5/6, Brahmaupta-7/8, and Cantor-A1/Geo sessions
    • Kovalevsky-A2/PC sessions will be part of our Payton site (but not UChicago)
    • Euler sessions will be part of our UChicago site (but not Payton)
    • When we return to in person sessions, we will again hold Kovalevsky-A2/PC and Euler at both Payton and UChicago.
  • Our after school sites will all meet at 4:30PM.
    • Mondays: Morgan Park, Haynes-5/6, Brahmaupta-7/8
    • Tuesdays: Bridgeport, Haynes-5/6, Brahmaupta-7/8
    • Wednesdays: Little Village, Haynes-5/6
    • Thursdays: Lane Tech, Haynes-5/6, Brahmaupta-7/8, and Cantor-A1/Geo sessions
    • (Our Pilsen site will resume when we go back to in person meetings)

All of our Haynes-5/6, Brahmagupta-7/8, and Cantor-A1/Geo sessions will meet for 75 minutes. Kovalevsky-A2/PC and Euler online sessions will be 90 minutes. You can find the meeting dates for all of our sites here. You can find descriptions of our program levels here.

Of course, online sites are equally accessible to anyone with a computer and wifi not matter where you live–keep two things in mind when you rank your choices: (1) Once we return to in person sessions, you can re-enroll at the site that you last attended; (2) your personal schedule. That’s it–you’re welcome to attend at any site that fits your schedule!

3. QED, Chicago’s Youth Math Symposium

We are committed to holding an online version of QED this year. Our anticipated date is December 5th, although this may change depending on circumstances. As our plans become firm we will share more information!

4. New Site

Since 2015 we’ve added 5 sites as we’ve grown to serve nearly 800 students in our academic year program. Adding one new site in the fall has become a habit, and our plan had been to add a new site this fall until Covid made that a near impossibility. However, once we are able to return to in person meetings at our current 8 sites, we will immediately add a new 9th site: ‘Online’. Our mission is to create opportunities for all children in Chicago to build a passion for mathematics, and it’s clear that an online site will provide access to more children than ever before!

5. Math Circles in a Box: MC2iaB

Last year we piloted a new program: MC2iaB. MC2 sessions were held in after school programs in Little Village Academy and Goudy Elementary. This year we are expanding to 15 schools across the city, with an emphasis in the Back of the Yards, Little Village, and Austin communities. We provide teachers at local schools math circle plans, workshops, and coaching to help them develop as math circle leaders. If you know a middle school teacher who might be interested in participating in the MC2iaB program, have them complete this form.

Math Circles at Home: Flips & Tools

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When spring math circles were suspended in March, I started sharing some ideas for at home, independent math circles, posting them here until our summer camps started. From here on out I’ll post one idea each month where math circles don’t meet. Send any ideas you have to info@mathcirclesofchicago.org. Thanks!

Flips

Did you know that 1089 is a 9-flip? Let me explain.

1089 x 9 = 9801. See? Multiplying 1089 by 9 results in 9801, which is 1089 ‘flipped’.

  • There are other 9-flips. Find one. Are there more?
  • There are also 4-flips; numbers that you can multiply by 4 that result in ‘flipping’ the number you started with. Find a couple of 4-flips.
  • Are there other kinds of flips besides 4-flips and 9-flips? Are there any 5-flips or 7-flips? If not, why not?
  • Think about extreme cases. There are a lot of 1-flips. What is true about all of them? Can you have a 2 digit flip (like, say, a 19-flip)? Why or why not?
  • What other questions about flips could you ask?

Tools

How could you approach the flip investigation?

  • Guess and check. It gets us through life most of the time.
  • Try a spreadsheet. This is sort of like guess and check on steroids. You can collect a lot of data fast and get a feel for what it takes to find/create a flip.
  • Do some initial analysis. Take 9-flips. Multiplying by 9 results in a number much bigger than what you started with. That limits what numbers you might have in the first and last digits of the number you are playing with. With 4-flips, you have more options….
  • Use Algebra if you know some. Suppose I have the number ABCD, where D is the digit in the 1s place, C is in the 10s, B in the 100s, and A is in the 1000s place, so that ABCD = 1000A + 100B + 10 C + D. How does that compare with DCBA? Of course, it’s better not to have too many variables, so use your analysis to narrow things down a bit. If you have a 9-flip, what number do you think will be in the left-most decimal place?

(Thanks to A. Gardiner’s Discovering Mathematics: The Art of Investigation for introducing me to Flips!)

Math Circles at Home: Adding Boxes

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Suppose you place two numbers in a row of boxes like so:

Then we generate the next number by adding those first two boxes together.

We continue in this fashion to complete the row:

 

 

On the other hand, suppose I give you this:

What numbers should be in the boxes between the 5 and the 16?

Some follow up questions:

  1. A simpler case: If there are only 3 boxes, and I give you the first and the last boxes, what goes in the middle?
  2. What happens if I switch the first and last number?
  3. Can you give a general rule for finding the numbers between the first and last box when there are 5 boxes?
  4. What if you had 4 boxes? Or 6? Or n? Can you come up with a general rule for finding the numbers in between when you have any number of boxes?
  5. If the first and last numbers are whole numbers, will the numbers in between be whole numbers? If not, under what conditions will those numbers be whole numbers?
  6. How can you change the rules? What questions could you ask then?

Box on!

Summer Opportunities & How to Multiply 9 Digit Numbers in Your Head

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Like MC2, a number of summer programs have now committed to running their camps online:

1. MC2’s Camps

Our lottery runs on Friday, 5/15. Camps will run the weeks of 7/13 and 7/20, serving rising 6th to 13th graders.

2. The Stanford Summer STEM Institute

This camp runs from June 21st to August 1st. It consists of a research and data science bootcamp, a masterclass lecture series, and  a guided research project. Rising 9th to 12th graders. Admission is on a rolling basis, so apply ASAP.

3. Wolfram High School Summer Camp

Wolfram has reached out to MC2, and they are looking to recruit more female students. The camp runs from July 5th to July 18th, and participating students will get an opportunity to learn the Wolfram programming language, engage in special computing topics like natural language and machine learning, while also having individual project time.

4. MyChiMyFuture

Mayor Lightfoot will be launching the MyChiMyFuture website on May 11th. You’ll find links to summer programs offered by Chicago out-of-school providers. This site will be a clearinghouse for the summer and beyond, from camps to online challenges to meet-ups!

 

Now, how do you multiply 9 digit numbers in your head?

First, and yes, this is a trick, one of the numbers has to be 142,857,143. But the other one can be anything you’d like! Here’s an example:

142,857,143 x 358,246,974

Steps below will be written out, but with practice you can do them all in your head.

Step 1: Write the chosen number twice: 358,246,974,358,246,974

Step 2: Take the number from step 1 and divide it by 7, moving left to right. That’s it! In this case:

35/7 = 5

8/7 = 1 with remainder 1, which you connect to the 2, the next digit
12/7 = 1, remainder 5, which you connect to 4, the next digit

54/7 =7, remainder 5

56/7 = 8

9/7 = 1, remainder 2, etc.

etc.

So, 142,857,143 x 358,246,974 =

51,178,139,194,035,282

Works every time!

 

Math Circles at Home: The Opposite of Times Tables

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When my children were in primary school, I found that multiplication times table tests were far less common than when I was their age. At least, teachers were less likely to give them. Other parents, however, worried that their kids wouldn’t get enough ‘practice’ and wouldn’t be ‘fluent’ in single digit multiplication. So they’d time their children completing times tables at home.

This, to me, encouraged flippancy, not fluency. In the short term, flippant memorization of multiplication facts might work, but in the long term it’s a disaster.

There is a place for (fluent) mastery of multiplication facts. So, if not times tables, what then?

Do math with your children instead. Give an actual problem to be solved, where the practice of ‘multiplication facts is built in. Try this:

Numbers can be partitioned in many different ways:

7 = 3 + 4 = 1 + 1 + 5 = 2 + 2 + 2 + 1 = 1 + 1 + 1 + 1+ 1 +1 + 1 = etc.

For a given number, take the numbers in one of its partitions and multiply them. Out of all the possible partitions of that number, what’s the biggest product you can get? Can you come up with a rule that guarantees the largest product?

In this investigation, you’ll find you have to do a lot of multiplication, more than if you completed a times table. But now you will multiply with a goal in mind. You’ll need to organize your work, make conjectures, consider simpler cases, connections between cases, and, most importantly, you will be doing this work with a purpose.

And all those things are sorely missing when you do times tables.

Math Circles at Home: Trapezoids, Hexarights, and Reptiles

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With school back in session (online), here’s a simple math circle activity to try at home when you need a break. 🙂

  • A trapezoid is a quadrilateral with at least one pair of parallel sides.
  • A hexaright is a hexagon with all sides at right angles.
  • A reptile is a polygon that can be divided into four congruent pieces, all similar to the original.

This figure at right is a trapezoidal reptile; note that the horizontal sides of the trapezoid–both the ‘big’ original along with the four ‘little’ copies–are in a 2:1 ratio.

 

Show that the trapezoids and hexarights below are also reptiles. From there, try to make up a new reptile of your own!