Practical Cumulative Frequency - Some thoughts

Another lesson based in the hall this week; this time cumulative frequency. Went quite well considering it was bottom set Year 9! I can see this working better with pupils  who have a reasonable attention span (my Year 9 second set would have been the proof had my intern not been taking them for the cumulative frequency). Equipment today was:

1) 6 metre rulers
2) A big ball of wool
3) Sellotape
4) Scissors
5) Blu-tack
6) Printed axes numbers (I had the numbers 1 to 30 and heights from 140cm to 190 cm)
7) Bean bags (one per person).
8) Flipchart paper

We set up two rulers taped to the wall one on top of each other to create a 2 metre high line, one at each end of the hall, and ran the wool across between them at 10 cm intervals (starting at 140 as no one in the class was below 130 cm tall) to create a way of seeing how many people were in each group, and also set up a big axes on the floor by blu-tacking the printed numbers down at intervals using the final two metre sticks to measure the intervales (I used 20 cm going up and 1 metre going across for the heights, which seemed OK). 

Once the measuring station and axes were set up, they lined up in height order between the two rulers and numbered off (there were 23 in my bottom set, so numbered 1 to 23). We then draw a frequency table (flipchart paper) by looking at how many people were between the lines, or below the lowest line (or above the highest line). What was great was that I could then throw out things like, "Raise your hand if you are below the 170 cm line" and then after a pause, "How could we tell this from the table we just drew?" From here the concept of cumulative frequency was born.

Once that was clear I had each person in turn, from 1 to 23, come and place their bean bags at the correct point on the axes, creating what was actually quite a good cumulative frequency curve (Year 9 bottom set remember!). We talked about the shape, explaining why it appeared the way it did, and even got as far as looking at median and quartiles; first doing it from the line, with everybody raising their hands and then putting them down in pairs, leaving one person, and then breaking the line in half leaving that one person on their own, before doing the same with each half to create the quartiles; and then seeing how we could see that from the graph by walking along from those peoples numbers to where they had placed their bean bag, and then down to read off their height. I am hoping that following this up with a classroom based lesson tomorrow, starting with the same table, that we will begin to really understand how cumulative frequency works and how it is represented.

Any practical lesson like this has it dangers and pitfalls, and there were times that some kids were standing around whilst other did bits (my TA was invaluable with supporting the creation of the measuring station and axes in particular), but on the whole I would say the lesson was quite successful and would certainly run it again.