What good is a bunch of empty boxes? Last week, it was great to teach proportional relationships. I had my students all bring an empty box or bottle that had unit conversion information on them. The first thing that I asked my students to do was to enter the conversion information onto a table on Desmos table. As you can see below, the student started by entering the information from the package: 10 oz. and 283 grams.

The next thing that I had the kids do was to enter at least 2 more points that would be true based on the conversion information that we had. Most of my students cut the amount on the package in half, or divided it by 10. At this point, we stopped to talk about the fact that the points the students were graphing were forming a straight line.

Next, I had students put (0, 0) on the table, and see if it fell on the line. Then we talked about why this point would be on everyone's line, even though they had different conversions.

Finally, I had students trace along the line, and find the point where the x-value was 1. We talked about what this point represented.

This simple activity was a great way to introduce proportional relationships, and some of their important characteristics.

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