Wow, it’s been a month since school started. Evidently, I’ve been busier than I realized…but it’s time to get back into regularly reflecting on my teaching.

Over the summer, I saw an interesting statistics task as an introduction to variability:

Rank the following from most fair to least fair:

My students’ prior knowledge only consisted of how to calculate the mean. I gave this task in order to introduce variability and create a need for a numerical measurement of how spread out values are.

After giving my students three minutes with a partner, here’s how everything sorted out:

I asked the group how they defined “fair” in this task (since I never defined it for them). They decided that the more uniform that the distribution is, the more fair.

The entire class agreed on allocation A being the most fair, allocation D being the next most fair, and allocation B being the least fair. The real problem came with ranking the order of allocations C and E. I opened the floor for debate and there were good arguments for both allocations. My students then turned to me for help. They wanted a way to settle the argument. So, we discussed standard deviation:

…and we practiced calculating…

My students then went back and calculated the standard deviation for each of the allocations and re-ranked them:

My hope was to create a need for standard deviation. My students decided that standard deviation is a measure of how spread out data is **from the mean**. They also concluded that the larger the standard deviation is, the more spread out the values are. This task lead to a great 45+ minute statistical conversation…hopefully, I can find some more good tasks for future concepts.

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## Published by corycloud

I teach math.
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