Unicorns, Elephants and Numbers

The other day I asked some of my young grandchildren to tell me the difference between a unicorn and an elephant expecting the answer that was obvious to me. Instead the answers I got were:
"Elephants are grey, unicorns are white."
"Unicorns have a horn on their heads, elephants have trunks."
"Unicorns are a bit like horses, elephants are not."
"Elephants are bigger."

So I tried a different track and asked where would you find unicorns and elephants and was told that elephants were in jungles and unicorns in forests. It took one more question for the penny to drop.
"Where could we go if we wanted to see an elephant?..."
"The zoo."
"..and a unicorn?"
"Ah elephants are real and unicorns aren't!"

In their minds eye they could easily see both elephants and unicorns and could give descriptions of both with equal clarity and draw them.

It is pretty obvious to see which drawing is of the elephant and which is of the unicorn.

How about numbers? Which of the following are drawings of a one and which are drawings of five?



This is not a straightforward as it seems. The flower could be either one or five depending on how you think about it. Perhaps the flower stands for five as that is the number of petals but as it is a single flower then maybe it represents one.

How about the   surely this must be a five since you throw this and move five spaces. Suppose, however, the game is different and you throw three dice and roll

Then among these you rolled one five, so if counting fives   represents one, the one dice that shows five dots. It all depends whether we are counting particular dice or dots. This may be obvious. The important thing is that when teaching and learning maths it is important to be very clear on what is being counted. Perhaps, surprisingly or not, what are usually being counted are numbers themselves. Over a series of posts numbers will be considered as objects as real as unicorns only with more magic.