Monthly Archives: February 2014

Guess and Check

Kids really like guessing games.  However, when they are very little they cannot tell the difference between random guessing and estimation based on partial information.  For example, you might play a game with them where you show them some number of objects and ask them to “guess” how many there are without counting.  When they inevitably then ask to give you a problem in return, they will hide their objects from you and ask you to solve the analogous problem.

As they get older, they will be able to make the distinction, although they may still enjoy games of both types.  Whereas the pure guessing games can be amusing, the games involving estimation are both fun and teach a valuable life skill.

To practice estimation, we played a simple game in our last class. In a large room, a stuffed dog was placed some distance away from where the kids was standing.  The task of each child was to predict how many steps it would take him/her to reach the dog.  Overall, the kids were quite good at estimating the number of steps.  Occasionally, someone would say a really large number, like 100, but this was mostly done for general amusement and did not reflect what the kids were thinking.  It was also amusing to see how some kids really wanted their predictions to be accurate and they would adjust the size of their steps as they were getting closer. (We tried to control the size of the steps that the kids took and suggested that they they put one foot in front of the other but it didn’t always work)

At some point, it took two kids an identical number of steps to reach the dog, even though one of them was standing noticeably closer.  When we asked the kids to explain how this was possible, a few immediately pointed out that one of the walkers had larger feet.

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Geometry with Geoboards

Last Sunday we also played with geoboards.

We first asked the kids to make a triangle, and it turned out that they come in many varieties:

ImageImageWe then had them build quadrilaterals.  Here’s a sample:

ImageWe briefly discussed some terminology such as square, rectangle, parallelogram, trapezoid, convex…  The first two were of course familiar terms, and a few kids had heard of a trapezoid but many would struggle to define them if asked to describe the difference.  Some kids would also make comments such as “I made the largest quadrilateral possible” or “I made the smallest one”.  We did not yet discuss the concept of area with them, but I think that we will in the near future.

We then moved on to slightly more challenging assignments.  We would tell the kids to make a figure with exactly one interior point, or exactly five points on the boundary.  For the older kids we eventually would put conditions on both interior and boundary points.

Not surprisingly, geoboards are a great tool for introducing and exploring basic geometry concepts.  In the future, we also hope to use them to continue with the theme of geometry of numbers.