This page describes an in-class activity used to teach 4th grade elementary school students the mathematics behind tomographic imaging. It requires knowing addition of whole numbers, including perhaps adding three numbers together. In this activity, we teach tomographic imaging as the solution to addition problems. We've tried this activity with 4th grade students, and they were both interested and engaged. We believe that this was set to the right "level" for fourth graders.

The activity starts by introducing students to the two main topics: engineering, and imaging. This introduction uses the presentation slides 1-11. Then, there are two activities:

First, we present slides 12-27. Then, we hand out worksheets for the Magical Squares activity. (Magical squares are also on line, and perhaps even easier on line than on paper, because the addition is done for you.) The 2x2 worksheet with hint is the easiest. The 2x2 worksheet without hint is more difficult, students may need to erase and fix their answers to get to the right solution. The 3x3 magical squares are significantly more difficult. You can give them a hint or two to speed up the activity; or you can let them try to solve it if they are able. After finishing, we don't want to leave them with the impression that engineers do these activities to find the image, in particular, since we said in the slides that there are 250,000 pixels in the desired image. We mention that engineers program computers to do the work for them, so that the image can be calculated quickly. We used a total of 25 minutes for this activity.

We let students participate in, and experiment with, our radio tomographic imaging testbed. This is substituted by watching videos of the experiment, one indoor experiment, and one through-wall tracking experiment, with the radios outside of a house showing that radio tomography can image and track a person inside of the walls. The demo is presented as a science experiment, with which they can set up a particular experiment (where people actually are located in the network), and record observations (what the estimated tomographic image displays).

Here are links to the presentation and the worksheets we use.

- Engineers and Imaging Presentation (pdf)
- Magical Squares Worksheet 2x2 with Hint (pdf)
- Magical Squares Worksheet 2x2 (pdf)
- Magical Squares Worksheet 3x3 (pdf)
- Magical Squares Worksheet 2x2 Solutions (pdf)
- Magical Squares Worksheet 3x3 Solutions (pdf)

Alternatively, you might want the raw files, if you are interested in modifying the activity.

- Engineers and Imaging Presentation (ppt)
- Engineers and Imaging Presentation (odp)
- Raw graphics files for worksheets in svg and odg formats (zip)

Many thanks to the members of the SPAN lab who have helped with this activity: Jessica Croft, Dustin Maas, Joey Wilson, and Yang Zhao. Please give us your feedback if you use this activity, we'd love to hear from you. Email Neal Patwari at first initial last name at ece dot utah dot edu.

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