# Geometry of Numbers

The theme of this week’s lesson was geometry of numbers.  The goal was to get the kids to think about the different ways that one can arrange some fixed number of identical objects.  To that end, we had two activities: one involved the kids recognizing a number from a geometric representation of it, and the second one had the kids arranging the objects themselves.

The props for the first activity were an empty candy box (with holes) and Mancala stones.  One of the adults would arrange some number of stones in a nice pattern (without the kids looking) and then open up the lid in front of the kids for about a second.  The kids would then have to identify the number of stones in the pattern.

It was interesting to see how the kids had different approaches towards solving the problem.  Some would try to count the stones during the brief moment that they had for looking at them.  However, if the number of stones was greater than 3 or 4, this approach generally did not work too well.  Others would try to remember the pattern, such as three rows with four stones each.  Once the lid was closed, they would then do the calculation in their heads and come up with the answer.    Some kids would give the correct answers with fairly large numbers of stones (8-10), but when asked how they came up with the answer they would say “I just knew” or “I just guessed.”

Another interesting thing to note is that success in this activity was not always correlated with age.  One four year old boy did better than most of the six year olds.

For the second activity, the kids each got 8 snap cubes and had to make a flat figure out of them.  They then had to draw (by coloring in squares) an identical figure on graph paper.

This proved to be a bit more challenging for the younger kids.  However, with some guidance, everyone was able to draw at least one such figure successfully.  One 6 year old girl drew a scaled-up version of her figure: each cube became four squares on paper.  A few other kids tried to do the same but were unsuccessful.  Similarity and scaling seem like good future topics.