Teaching the normal model using a z-table

We are just wrapping up working with z-scores and the normal model in my AP Statistics class. In the past, I had students use the empirical rule (68-95%-99.7% of distribution within 1, 2 or 3 standard deviations) and then moved to using a graphing calculator.

This summer, while teaching the introductory statistics class at MSU Denver, I had to teach the normal model a z-table since a graphing calculator was not required. What I discovered was that using the table made the conversions among raw scores, z-scores, and percentages was much more transparent to students and, hence, more understandable. I decided that I needed to bring this experience to my AP classes.

I started through the z-score and normal model unit as I have in the past, including showing students how to find cumulative probability and z-scores from percentiles. Then we started working through an ten-part problem that required using the empirical rule and explicit values. I showed students how to read a z-table and asked a few questions to confirm they could find a percentage from a z-score or a z-score from a percentile. I then told students they could not use their calculators to work through the problem; they had to use the z-table.

There were a few questions as students started working through the problem parts but all readily picked up on how to make use of the table. But, more importantly, students started getting a better feel of how to transition easily between a raw score through a z-score to determine a percentage or vice-versa.

For the assessment on this unit, it was interesting to see that more than half the class asked if they could use the z-table, which was, of course, okay to use. I regret that I did not see the value of teaching to use tables earlier. If you are like me and have not previously taught using the z-table and just worked with technology, I highly recommend spending some time using the z-table in your instruction. You may be pleasantly surprised, as I am.