## Sweet Division

Today I had a great conversation with Katie about divisibility.  It all began when we opened a small pack of skittles.

Katie: There are candies of 5 different colors.

Me: How many are there of each color?

Katie: 3

Me: So how many skittles are there total?

Katie counts by 3’s and arrives at the correct answer.  I then take the skittles and arrange them into a 3×5 grid; I use this to show her that she could have just added three 5’s, a much simpler task for her since she can do it without actually counting.

Katie starts eating the candies.  When she has eaten 3 of them, the conversation continues:

Me: Can we split the remaining skittles evenly between the two of us?

We proceed to do it.

Me: What if Zoe came along; could we then split them evenly among the three of us?

Again, it works out.

Me: And now what if daddy came along?

Wow, we can still do it!

But then we discover that if a fifth person comes along, then we can no longer split them evenly.  We further figure out that it works for 6, but not 7 or 8.  I then ask Katie whether there are any other numbers that 12 is divisible by.  She is not sure, so I point out and explain that every number is divisible by 1 and by itself.

Katie seems excited because she understands and she wants to talk more math!  I am excited too, because even though this is not the first time the subject comes up, it’s the first time that Katie is showing this much interest.  We go on to play around with a few more numbers and then I tell her about prime numbers.  She doesn’t seem tired or bored, and keeps asking me for more.  I love it when she gets into such a state of mind!