Relative Frequency

I just had another fun Maths lesson worth I think is worth sharing.  We are studying our data handling unit in year 8 and have just started to talk about probability.  Here´s how the lesson went.

Starter:  First, we discussed how theory and actual results are different.  I did a quick experiment where I rolled a dice 10 times and had a student record the numbers that turned up on the board.  Then we created the fraction (3´s turned up 4 out of 10 times) and then calculated the relative frequency.  We discussed bias and why certain number were appearing more frequently than others, and I taught them how to predict results of many trials. 

Main Body:  Students worked with partners to record where the die landed on a target.  I provided students with the following materials:

Students then performed 100 trials to see where their die landed on the target.  I didn´t include the fact that the die might not land anywhere on the target but students just didn´t count that trial if it happened. 

After the groups were done their 100 throws, they calculated the relative frequency of each category and predicted how many times red, white and in between would show up if they three the dice 500 times (relative frequency x 500). 

Finally, we talked about what happens to relative frequency with more trials.  I showed them this great online resource:

http://archives.evergreen.edu/webpages/curricular/2003-2004/doingscience/flash/dice.html

And they saw for themselves that with more trials the relative frequency moves more towards theoretical probability and therefore, the more trials and experiment has the more reliable it is.

We also had time for some UK National Curriculum level 6/7 questions on experimental probability and the lesson flew by.  This was a nice Friday afternoon activity for year 8´s!