I had a double lesson with my year 8 on Friday morning, and we were looking at averages, and moving on to averages from a frequency table. Several were away due to the snow, and the class were in a rather hyper mood. Fortunately, the lesson I had planned fed very well off this energy.
In the previous lesson we had used this Averages Collective Memory to jog their memory about what they averages were and how they worked. They really enjoyed this activity, and we ended the lesson with a few quick questions on calculating the different averages. They were all pretty confident with this.
To start the double lesson, I gave out the mini whiteboards, and we had a go at the Averages Activity. I started simple, with 5 numbers, and they had to find the averages, then made it 6 numbers and we discussed the median again. After a couple of these, I only showed them 4 numbers, and gave them the mean. After a little complaining ("that is so mean of you sir!"), and a bit of discussion, they all worked out how to do it.
Next, I hid 2 numbers, only showing them 3, and gave them the mean and the mode. After a bit more discussion, they all managed to work out the missing numbers, and the other averages. Next, I didn't give them any numbers, just the four averages, and they had to work out the 5 numbers. Some of them looked a bit blankly to start with, but I didn't want to jump straight in to help, and their friends turned round and explained how they could start. They all got there, and I revealed the numbers, which they all got correct. Finally, I did the same, but with 6 numbers. This time they all made a quick start, but there were a few disconcerted members of the class when they got different answers to the others. We talked our way through the problem, and realised that in this instance there were actually two different possibilities for the data (4 numbers were fixed, but the last two could have been 5 and 14 or 6 and 15). We discussed how we didn't have enough information to actually determine for certain which it was.
After this starter, we go on with the main activity for the lesson. I handed them out two Magic Sticky Notes (see this blog post by Mr Collins for a detailed look at them), one green and one pink, and asked them to write their shoe size on the pink one, and the number of TVs in their house on the green one. They then came and stuck them on the board, and we discussed the problems with having lots of data. We started by looking at the shoe sizes, and we moved them around into an ordered line, but this was still a bit tricky to get a "jist" of the data. Somebody suggested putting all the same shoe size together in a group, so we did that. They noticed that the mode was easy to spot from here, and with a bit of a nudge we turned this into a frequency table.
Now we discussed how to read the averages from the table, by referring back to our groups on the wall. The mode was easy, as was the range. The median was little bit more tricky. They wanted to cross off each end one at a time, but I asked "what if we were looking at the whole school?" We arrived at the middle number, and discussed how we could find it (especially as there were an even number of us), just from how many people there were. Finally, we looked at the mean, and this is where the magic sticky notes really came in to their own. We looked back at the grouped data, and worked out how much each group was worth, we then compared this with the table, and they easily saw why we multiplied the frequency by the data (something classes have always struggled with before).
I then got them to do the same with the TV data, before getting them to come up and go through it at the board.
This lesson went really well, and was definitely one of the best lessons of this school year, as they were all engaged the whole lesson, and really got to grips with why we were doing things. The starter activity got the thinking deeply about the meaning of the averages, and the magic sticky notes were absolutely perfect to show them what was going on. I will definitely be using them again.
Next lesson we are going to consolidate what we learnt on Friday, and they will be getting a homework to do some questions on the Averages from Frequency Tables 10QQI.
I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice.