Dividing by Zero

I found this on Pinterest and now use it to help my pupils remember the rules regarding division and zero.  It seems to work!

I also like to show them a silly meme like the one below to help the rule stick in their heads.  A search for 'divide by zero' on Google Images brings up loads of these. I do apologise to my pupils in advance for the bad language, which I think makes it more memorable.

I was very pleased when one of my pupils recently wrote this in a test. It's nice to see that some of them pay attention!

Most calculators give the message ‘Maths Error’ when a number is divided by zero.  It’s crucial that pupils understand why. For teaching ideas, I recommend this excellent blog post 'Why can't you divide by zero?'.

We use this understanding when solving equations like this:  x² - 5x = 0. A common mistake is to divide by x to get x - 5 = 0. This incorrectly gives only one solution (x = 5). Knowing that we shouldn't divide by x because x could be zero (unless we're told otherwise) allows us to understand why the correct method is to factorise ie x(x-5) = 0, giving the two solutions x = 0 and x = 5.

To stretch your students, try this interesting activity about the value of 0⁰, Evaluating a Special Exponential Expression from Illustrative Mathematics.

It's interesting that throughout history, many great mathematicians (including Euler) have argued that division by zero gives infinity. Most modern mathematicians take it as undefined.  If you want to do some background reading on the ‘history’ of dividing by zero, I recommend this article - it's an enjoyable read.