Data Management and Probability

This week we discussed data management and probability. The main thing to remember when teaching data management is the quality of the data (i.e. is it meaningful and accurate). One way the data can be made less meaningful is if the sample size is too small. For example, if we only sample 3 people in a class of 45 then the results of the sample will not apply to the entire class.

I'm going to organize this post similarly to my week #9 post in that I'm going to outline several strategies/activities that can incorporated into lessons for data management and probability.

Terminology: Probability Line

It's important for students to understand the terminology that's used when talking about probability. Below is an example of a graphic that could be posted in the classroom for students to refer back to regularly. 

MathIsFun.com (2014). Probability Line [Online Image]. Retrieved from: http://bit.ly/1MpzS9B 
Having an anchor chart in the room like this one will help students remember key words and hopefully will cue them to previous lessons about probability. 

I would also include the following companion chart with the one above, because it indicates that all the probability must add to 1. 

MathIsFun.com (2014). Probability Line [Online Image]. Retrieved from: http://bit.ly/1MpzS9B

Comparing Theoretical and Experimental Probability

Experimental probability: the ratio of the number of times an event occurs to the total number of trials or times the activity of performed. 

Theoretical probability: the number of ways an event can occur, divided by the total number of outcomes. 

The activity would be to first establish a theoretical probability (for example using a dice and establishing that there is a 1/6 chance of rolling any of the numbers) and then testing that probability. Use a table to mark every time one of the numbers is rolled (see below) and then establish the experimental probability after a set number of trials (for example 30). 

MacCuish (2015). 

Probability With a Pair of Dice

The following worksheet requires students to work out theoretical probabilities in a very interesting context. It doesn't give students baby-steps to get the answers so students who are struggling may need a lot support for this type of assignment but advanced students will be challenged in a good way by it. I would suggest having students work in groups and create the groups so there is a mix of abilities in each group. 

Math-Aids.com (2009-2015). Probability With a Pair of Dice [Online Image].
Retrieved from: http://www.math-aids.com/Probability/


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