As we finish up the weeks 24-27 with a focus on integral calculus we must prepare for the unit 6 test. In the video below I will walk through 4 questions students have been asking in the last few weeks. You might already know and feel confident with some of this material other parts might be useful to help you review.

by Ellen Lawsky – Pamoja Math HL Teacher

I had the good fortune to spend spring break with my 5 year old granddaughter. While we had many adventures each day, her favorite activity was playing the board game CandyLand with me. The goal of the game is to be the first to get your figure to the candy castle. After shuffling a deck of cards each player chooses a card. The card indicates how many spaces you are to move. My granddaughter’s method of shuffling the cards was to put them on a table and just mix them around. Amazingly each time we played, she won.

Many people would say she cheated. I choose to say she was strategizing. She would look at the board, compute the number of spaces she would have to move to reach a desired spot, leave the room, stack the shuffled cards in her favor and return, always declaring that she just “happened” to get a “good” card. She understood the cards needed to be shuffled but then felt compelled to rearrange them in her favor.

I subscribe to a math and science journal called Quanta. This past issue had a very interesting article about “smooshing”, a way of randomizing a deck of cards. Persi Diaconis is a professor of statistics at Stanford University in the United States and has won the prestigious McArthur Award. He and I attended elementary school and religious school together. So I was excited to read about his current research.

Persi started his professional life as a magician and at some point moved on to the study of mathematics and statistics. He is interested in randomization.

“Smooshing” is the way a 5 year old would randomize a deck of cards – put them out on a table and just mix them around. Persi is exploring questions about smooshing. He proved that if you smoosh long enough, even cards at the edge will get mixed in. Persi is interested in the following questions: Does smooshing mix the cards? (He says (proofs) yes.) How long does it take? Is there a relationship between the size of the deck to the amount of mixing time needed? To answer these questions and others Persi is using ideas from a relatively new field of mathematics call quantitative theory of differential equations. Here is a link to the article. I would be interested in your response to it.

What is most interesting to me is that looking around you – even at things that 5 year olds do – can lead to interesting and profound mathematical questions.