Problem Solving : Which phone contract is best?

I’ve been thinking a lot recently about problem solving.

The new maths GCSE introduces a lot of it, and some of the sample questions I have seen include almost Fermi-like questions.

I’ve always liked problem solving, I particularly like the Dan Meyer stuff, but I’ve not written much about it. So here is an example of a problem solving lesson I’ve created.

Problem Solving Lesson : Phone Contracts. 

Equipment required: 
Graph paper
A3 paper

Prior Knowledge Desirable:
Linear graphs

I simply showed students this slide.


We talked about it for a while. I have obviously had to massively simplify the problem. I was upfront with students about this. We talked about contracts and a little about data, texts and things like WhatsApp meaning that they didn’t really need minutes. This time was important. These questions about the validity of the task I think helped draw out thinking and were useful in getting students into the task. It’s important not to shoot students down when they ask them.

We then talked a little about how the task seemed simple. But it’s deceptive.

The real question comes in how we present our answers. Students started to ask questions. How long does the average person spend on the phone? Do different users have different needs? This last question unlocks the potential of the task.

Which phone is best for which person? How many minutes do you have to be on the phone for before buying the initially more expensive phone is the better option? How can I show this information clearly? 

Students came up with a variety of responses. Not everyone used graphs. Some went around and surveyed other pupils to find out how long they sent on the phone. I liked that idea.

Not all answers/conclusions were of high quality, you can see a selection of student work below, but I’m OK with that.

I will look at these and give feedback next lesson. Hopefully they will gain confidence in this sort of task.

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