Feb 28, 2016 - Math Circle 2.0

Odd and even number pattern

We sorted numbers 0 to 20 on the table and then examined the odd and even pattern of numbers.  We continued the pattern even with 21, 22, and beyond.

Grouping of objects

We borrowed a bunch of Ellie's toy animals and grouped them.  We grouped them many ways:  Anya's likes and dislikes, humans and animals, water creatures and land creatures.

Probability

The students did an experiment with coins to determine how many flips it takes to get a "heads."  Sometimes it took 5 tries, other times it took only one try.

Doubling numbers

Cookie Monster starts a cookie eating marathon.  He eats one on Sunday, two on Monday, four on Tuesday.  He then eats twice as many cookies as the previous day.  The students made the pattern to Thursday and figured out that it would be a challenge - even for Cookie Monster.

Raw egg and hard boiled egg experiment

Darrin made a hard boiled egg and got it mixed up with the raw eggs.  We made an experiment to determine how to find the hard boiled egg.

For next time....

If a b and c are cities, if 4 roads go from a-> b and 3 roads from b->c, how many roads go from a->c

Constancy, Odd ones, and Symmetry Feb 14, 2016 Math Circle 2.0

What are there more of: rectangle or triangle blocks?

Based on experiments by Piaget, used by Zvonkin in his math circle.

First we lined up 8 rectangle and 7 triangle blocks. Which are there more of? It was clear that there were more rectangle blocks. Then lined up 7 of each in rows of the same length. Then, it was clear that there were the same number of each. But when I spread the triangles apart (see below) and asked "are there more triangles or rectangles" most thought there were more triangles. But then they thought about it 

Then I pushed all of the triangle blocks together. Which were there more of?

Which is longer?

After working on the 'what are there more of for a while, we went into "which line is longer". And we did different permutations of this: rectangles on their long or short edge, triangles on the long or short side. Below, I thought that the rectangles on their long side and triangles on their short sides would make lines of the same length. But, this was not correct. Each triangle is just a bit shorter so when lined up the row of triangles is shorter.

Odd one out

from Zvonkin 

Put together sets of cards. First three, then more. We started easy, like the one below (giraffe, lion, snake):

Later we moved onto more challenging sets with no clear answer:

These weren't as easy as counting the number of legs. For [elephant rhino lamb], the lamb was seen as the odd one because it was furry! For [chicken, eagle, flamingo] all were stuck until one child chose the eagle as the odd one out because it had long claws.

Symmetry

Last, we moved to drawing symmetry. I started with a connect four, trying to have students repeat patterns I made on one side, but it was difficult for them to understand the symmetry. So I went back to some exercises we did last year: I folded a post-it note, and drew on one side, and then students drew across the line of symmetry.

After they had the 'symmetry' down, I tried a more difficult challenge: the original drawing crossed the line of symmetry. This was confusing even though I tried a few permutations.

Admittedly, this one was pretty tough:

Reference: Zvotkin Ch 1 http://www.msri.org/people/staff/levy/files/MCL/Zvonkin.pdf

Feb 7, 2016 - Math Circle 2.0

Third dimension

To review coordinates with three axes (x, y, z) we placed Legos on a grid and asked a series of 'what are the coordinates of the pink Lego?

This was the third time we presented the idea, and now all of the kids more or less get it, but I presented this more as a fact than an open ended puzzle. Will try more puzzle next time, and hope the students recover!

Dividing stones

2x + 3 = 9

3x + 1 = 4

2x + 3 = 15

Splitting coins

Split in 2s and 3s

experiment

Do oranges float in water?

Why does the orange float but the pieces don't?