This poster is about a visualization of concept that is usually only handled symbolically. The idea of a ‘power’ or ‘exponent’ is a leap in many senses and is good example of mathematical notation being efficient. It is one thing to teach students that 43 means 4 x 4 x 4, it is another altogether to understand the implications of the exponential. This poster is an image of 43 and an invitation to see exponents at work.
There is plenty to notice about this diagram and, as ever, it is always great to hear what things students spot that you had noticed or thought of. This can be very revealing. What might anyone say about the different sizes of the dots and the fours? Will anyone spot and try to explain the 3 in the picture? How many dots are there altogether and what does this number represent? What would happen if we extended the diagram? How does each ‘4’ relate to the ‘4s’ that stem from it?
There is fun to be had in creating some of these images and looking at each others. It is great to see how creative students can be with the idea.
Here is a construction a student made as a video based on this idea :
I’d be surprised if during a conversation about this image somebody doesn’t ask how many yellow dots there are. Here we come up with a nice example of the difference between the nth term and the sum of the first n terms. This can be a nice lead in to the summing of geometric sequences.