# Walking a Z-score #tmc14

Standard

I was super excited about spending time with experienced Statistics teachers this past week at #TMC14.  On our first day together, we discussed, well, I listened mostly, what big ideas students seemed to struggle with.  A couple of teachers shared that their students could compute a z-score, but for whatever reasons, this past year, they had trouble explaining what the score actually meant.

My thought is to use something similar to  students plotting points on a number line.  Suggestions are welcomed.

Materials:
Tape
Post-its
String/yarn 2 colors, one shorter, the other at least 6 times its length.
Markers
Ziploc bag

Inside each bag I will include mean score, and standard deviation on an index card along with a list of data values from that sample,  a string length to model 1 standard deviation, another string length for our axis.

Students will layout their “graph” with a longer string as the axis, taping the ends down.   What I heard others saying was that students wanted to report a probability for the z-score.  My initial thoughts are to keep it 1 dimensional and maybe alleviate this misconception.

They will place a post-it for the mean value label on the graph, use the standard deviation string to label data values occuring at each sd on the graph.

Next, they will locate the other data values on the number line and place a post-it.  I will ask them to come up with a measure of each data point using the sd string as their unit of measure.  Some discussion about what their estimates represent and my hopes that after plotting and sharing, someone will develop the z-score on their own.

Next, they will practice calculating z-scores and add to the data post-its.  They will choose one of the z-score post-its.  Next they will stand at the mean and estimate the location of their data value by “walking” on the number line, using the standard deviation string as their measurement device.  If everyone in the group agrees with the locations, the post-it note is placed on the graph.

The next team member repeats the process with another data value and so on until all z-scores have been placed.

Snap picture of each groups model.  Share out with class.  Discussions as needed.

Quick-write reflection as the exit ticket for the day.

Just getting some ideas down, definitely some revisions to come.

I am new to statistics, so I value any feedback from seasoned teachers.

### 2 responses »

1. I like this as a conceptual introduction. When I do z-scores, I use the Ultimate Frisbee simulation as the context, but the core problem is finding a way to combine two completely different stats into a combined score (such as speed and catching percentage). To do that, you can compare each value in a set to its average and see how far away it is compared to others (the z-score). Repeat for another set of values and now you have two unit-less numbers that could be added. The context doesn’t directly explain z-scores but helps students understand why they are useful.
Also, I teach them far away from when I teach normal curves, that way they understand them separately from normal probabilities.

• This will definitely help me…getting ready for the why / how it’s useful. Thanks!