Cheerio Stacking Race

Today in grade 9 we were working on graphing linear equations, remembering y=mx+b, and next looking for intersection points and interpreting their meaning.

We started with x+y=5 and talked about how sometimes we just know some points that are on the line because they work. E.g. (2,3) works because 2+3=5. We made a list of points and graphed them. We talked about the special points which are on the axes, and named them.

We next looked at an equation that was more complicated 2x-y=4

We found the x and y intercepts and plotted them to make a line. We noticed that the graph had a rise of 4 and a run of 2, and started with a y intercept of -4, so we could make an equation. We also determined the y=mx+b form of the line by isolating y. We realized quickly that the slope of 4/2 is the same as the slope of 2/1 or just 2.

Next we looked at the graph of both the lines, and noticed that there was a point where they crossed. That is the only point that is on both lines.

To give ourselves a context for what intersection points are, we participated in a cheerio stacking race.

Students each determined their cheerio stacking speed, in cheerios per minute. We used non dominant hands just to make things interesting. Once they knew their cheerio per minute speed, we tried to set up a photo finish between the slowest in the group and the fastest in the group with both having a full skewer of cheerios. To do that, the slowest person needed a head start of a certain number of cheerios.

We used graphs to help us figure out the head starts. We knew that we wanted both people to have a full skewer at the same time as the fastest stacker. We used the fastest stacker’s data to draw the red line. We know a full skewer is 54 cheerios, so we want that to be our intersection points. We know the slow stacker’s speed, so we can use their slope to count backwards from that intersection point, and we can extend the line to the axis to determine the head start needed.

Some groups had more luck than others when testing their head start numbers. Some people had gotten better with practice, or they’d calmed down so hands weren’t as shaky. Some had maybe been cheating a bit the first time, so they had misrepresented their speed. Most of them ended up with a pretty close photo finish even if it wasn’t exact.

I was particularly proud of how they were willing to try something new, work together, figure out what information they needed, and how to figure out a head start. Also at the end of the class materials were cleaned up and put away without issue which is not always the case when it comes to cheerios! Thanks grade 9s 🙂