We worked neatly through the worksheet almost entirely, only pausing when we encountered the issue that A) The Pizza Hut app doesn’t work through the college network and B) In the UK Pizza Hut cut their personal pizzas into 6. I decided for the sake of speed to look it up myself for them and tell them the prices (see below for how this affected the second group) and that we would use the ‘cut into four’ picture rather than the cut into 6 reality. (Bad decision? – Maybe, but I wanted to reduce confusion as I predicted, correctly, the students found the information overloading as is, without differences in the diagram and actual information)
I did one thing slightly differently, we built a table for calculating different values we needed to help organise the information. This part of the lesson was actually the part that students told me they liked the most, once they had built the process to find the areas and percentages they could follow it through several times – they preferred following routines over the exploration part of the lesson.
The table gave us a place to go for the percentages needed for the graph at the start of next lesson:
And we could wrap the task up with finding the 50% crust/delicious interior, and the 0% cheese and why there was no 100% topping etc.
As I said above the students preferred following routines to exploration, and when I questioned a few students they told me that they would probably have preferred a worksheet of circles to having to make decisions about compartive pricing. They also struggled to see the link to the exam they are taking soon, without me giving them explicit examples of exam questions. I find it terrifying and somewhat depressing that even after almost 9months in my class they are still only concerned with whether it is directly linked to an exam question.
Class 2 (Observation lesson)
This time around I decided that I would avoid the looking for prices problem and give the students the prices on the sheet to start of with. I was concerned with this group that they would be less inclined to answer questionsd and make observations and explorations than the previous group, so I used much more directed questioning. I also produced a sheet for them to calculate the the areas and percentages on (this had unforseen consequences) and gave them examples of exam questions which assessed their skills for them to have at the end of the lesson.
The first part of the lesson went much more smoothly than before, however we ended up running out of time when working on the table.
I think is for two reasons
1) There was no pattern – previously the students were able to notice that they could use the previous step total area to help them work out the next step cheesy area; I lost this when I added the ‘in between’ sizes like 9″ and 13″.
2) Weaker students got lost with all the information they had to use and arrange; despit ehaving the table I ended up with students confusing the different areas they needed to use to find percentages, or where to record things. I could have solved this by differentiating my sheet better – perhaps filling in some lines partially for weaker students to work on so they did not have to hold so much information in their heads at once, or by pairing them with a stronger student to check their work.
As it was this delay meant we could not finish the table in the lesson. I decicded to wrap up instead by reflecting on the tasks they had completed using the exam questions. there were certainly no complaints about relevance when they had exam questions in front of them comparing the price of unit areas and the percentages of shapes.
On reflection, using a task such as this with classes that are un used to working in this manner is always going to be challenging, and it was strange for me to hear students to be flipping the ‘when will I ever use this?’ question on its head to ‘will this be on my exam?’. I also feel I did not make enough of the discussion questions provided by the lovely people at Mathalicious – and this was for a two reasons:
1) I have not successfully built a group work culture with the classes; I could blame a lot of things, the fluctuating attenance, the class size, the ability range, but it boils down to me not setting the expectation early enough. This really hit home that the collaborative work and discussion culture MUST be established early and MUST be pervasive across the year.
2) Time. I just didn’t leave enough time to do them. Both lessons went over 1hour 10mins, and next time I do this I will ‘budget’ for 2 lessons!
It was a whole lot of fun though, and I recommend this task to anyone doing circles with their group!