mathcoachblog

Today’s class opener features the first of many times I hope to expose my classes to the rich site MathMunch.  In this week’s post, the site discusses Alex Bellos’ “Favorite Number” survery, and my classes participated by sharing their favorites on a combined dot plot. Before showing the video below, I asked my classes why they felt certain numbers would be deemed “favorites”, while others may not feel the love.  The class agreed that 7 would probably be the most popular overall, with one astute observation that 7 tends to provide an anchor to interesting lists: 7 days, 7 seas, etc, and seems to have some interesting mathematical properties – like its primeness.

The students had many reasons for having a favorite number:

It’s what I wear for sports.

It’s my birthdate.

My favorite multiplication fact when I was little was 8 x 9 = 72, so 8972 is my favorite number. My dad played it in the lottery once and I won $200

In the same post, the Math Munch gang expresses appreciation for Bellos’ book The Grapes of Math. So, what’s on your math classroom bookshelf? Here are some favorites I keep around for stories, and for students to check out after assessments:

 

 

Outliers – by Malcolm Gladwell

Journey Through Genius – by William Dunham

The Wisdom of Crowds – by James Surowiecki

In Code – by Sarah Flannery

Count Down – by Steve Olson

As students entered today, each group found on their tables the mystery envelope…{cue Law and Order music}.

Inside each evenlope were 36 cut out pieces of paper.  Yesterday we had discussed sample spaces, theoretical and experimental probability involving 2 dice, using applets and online resources to think about similarities / differences, so these pieces were not unfamiliar.  Instructions for the pieces was provided on the board:

Arrange your pieces into a 6×6 grid, so that no duplicate red die appears in any row or column, nor any duplicate white die.

Groups immediately gravitatied towards this task, and after some initial misunderstandings over the directions, got down to business looking for patterns. One student who was a Sudoku fan became quite obsessed. I let this problem hang through the period, just having them stop when we completed notes or had class problems to do.  Many students felt they were close, but couldn’t quite solve the puzzle. Half-way through the period I reminded students that it is often helpful to think about a smaller problem before tackling a larger one. What if you just looked at the dice numbered 1 through 4 – can you complete that problem?  Learn from smaller steps – then tackle the big ones.

If you want to try this task on your own, cut out the pieces from the picture above. Then come back here and visit for the solution.

OR if you just want to know how it end….you unadventurous soul…then keep reading…

We’ll wait for you to come back.

THE BIG REVEAL

The problem I gave today is an interpretation of the 36 Officers Problem, a problem often credited to Euler.  Instead of dice, the Officers challenge is to arrange 6 ranks and 6 regiments into rows and columns.  My alma mater, Muhlenberg College, hosts a high school math competition every February – with a free t-shirt to all who attend. For the 36th year of the contest, the shirt features the 36 Officers Problem, and gave me inspiration for today’s activity.

As for the solution….here’s the thing….the 36 Officers Problem is impossible.  It’s do-able for all other numbers of rows and columns (except 2), but is impossible for a 6×6.  Some examples of solvable squares appear on this untamed blog, and I’d love to have others contribute their thoughts and or/resources.

Classes today were presented with a multiple-choice question as they found their seats –

This summer, Mr. L met a math teacher who has won competitions involving:

A) Reciting digits of Pi

B) Multiplying 5-digit numbers quickly

C) Drawing perfect free-hand circles

D) Finding really large prime numbers

Only one of the above choices is correct, and the class voted on which one they believed to be true. The “pi” option received the plurality of votes.  The video below then reveals the correct answer –

And this is how my classes “met” Alex Overwijk, a World Freehand Circle Drawing Champion, and a fine math teacher I had the opportunity to meet at this summer’s Twitter Math Camp.

After some lively discussion over how one apires to be a proficient circle-maker, and why a World Championship even exists for it, some deeper math ideas emerged, in particular…

How would we judge the roundest circle contest?

One student suggested using a compass to make a similar, perfect circle. Piggy-backing, another student thought we could then somehow measure the “white space” between a drawn circle and a perfect circle?

But what radius should we use? And how do we determine the center of an imperfect circle? So many great questions. To close the opener, I shared how calculus – a few years  down the road – will provide some structure for finding unusual areas.  Always fun to provide some math seeds for experiences down the road.