Author: Ben Gordon

This type of activity is known as Rule. Please read the guidance notes here, where you will find useful information for running these types of activities with your students.

I really like this activity of Ben’s. Mode from a frequency table is not something I have ever spent a significant amount of time on with a class. It tends to get no more than a passing mention before I crack on with teaching my students how to work out the mean. And yet, I have certainly seen my students make “daft” mistakes with regard to the mode – mistakes that could have been prevented had I put more thought into my teaching.

I like the way this activity starts off with two non-examples. This is often a good way to hook students into the activity. Imagine you are student who has only encountered the mode from a list of data. It is perfectly understandable that when presented with Question 1, you believe it to be true. When I then indicate it is false, you are not only a bit perplexed, but your mind is also turned on. “What on earth is going on here?”, you ask yourself. Then the second question also turn out to be false. But when Question 3 turns out to be true, so long as you are given sufficient time to reflect, and maybe discuss with your neighbour, then you may start to piece together what is going on. Question 4 may confirm this.

And then Questions 5 and 6 incorporate boundary examples – examples that push a concept to its outer limits.

Ben then made a really smart move. Questions 7 onward involve numbers for the data types. Had numbers been involved from the start, there is a danger that students’ would not so clearly have been able to focus their attention on the aspect of the examples that really matter. By giving them the opportunity to do this in the first 6 questions, Ben is then able to turn up the difficulty/noise in subsequent questions.