Paging Doctor Math: Nardo Ring

Today's task comes from Dane Ehlert and his page of 3-Act Tasks. I have been messing around with his Nardo Ring task since last year when I was at the University of Northern Iowa, and I finally got to implement my adaptive version with my 8th graders. This task was interesting for most students because they had never heard of this track (and neither had I). The ideas of fast cars, or in my case slow cars racing is exciting, and many students took a few minutes before getting started to do a little research on the track. Having tasks that are interesting for middle school students helps with engagement, which in turn makes the math content more meaningful. See exhibit A and exhibit B for more examples of tasks that middle school students enjoy. I also like the implementation of Desmos, even if it isn't a major part of the task. I use a lot of the Desmos Teacher activities, but I don't use Desmos for much more than that. I was happy to find some other uses.

Here is what the students saw upon entering the classroom:

The Nardo Ring is a high speed test track in Italy. Use this link to Google Maps to get an idea of what it looks like...

Nardo Ring

Today, witness a race between my old high school car, the Chevy Celebrity, and the new Shelby Cobra Mustang (pic one and pic two). As you can tell from the pictures, my old ride will need a slight headstart to keep this race close.

Chevy Celebrity Speed - 40 mph (if it doesn’t fall apart first)

Shelby Cobra Speed - 90 mph

Race Track Specs

How to Use This Map:

The large orange dot is the Shelby Cobra, which is at the starting line and finish line. The large light blue dot is the Celebrity, which is where the head start is at. You can take the slider on the left hand side labeled r orange and move orange line to see the angle it makes with the starting line, or the green line (the angle measurement is also displayed on the right hand side).

Map

Q1- Who wins the race? Use appropriate minutes and seconds to convey you answer.

Q2- At what degree does the Celebrity need to be placed at so the race is a tie (or as close to a tie as you can get)?

Q3- How much less space is contained inside the track at the old 1910 Los Angeles Motordrome than the Nardo Ring? The Motordrome is 1 mile around the track.

A few of the tougher spots for students on this task:

1. When finding the degree that the Celebrity should start at for the race to roughly be a tie, many students figure out how many degrees the car would take to get to 5 or so minutes to match the Cobra, but not where the car should start at on the track. It took a lot of conversation to understand that those numbers were not the same thing.

2. Finding the radius of the track that is 1 mile around was difficult because students had to use decimals without whole numbers to eventually get the circumference to be 1. I think if the track would have been 10 or so miles around, the radius would have been easier to find and made more sense, but there isn't anything wrong with using decimals. 8th graders should be able to do that.

3. Some students had to do a triple conversion of degrees being equal to miles being equal to minutes, which was different. Normally my students set up ratio tables for percentages and proportional relationships, but not normally in groups of three.

Some of the reasoning I really enjoyed from this task:

1. A few students also related the degrees of the track to fractional pieces of the track like 1/8th of the track or 1/16 of the track to help with conversions.

2. Students were all over the board on what information was used to solve the problem. For instance, you can find the time for both cars by only using the miles per hour, but some students ended up using miles per hour and degrees.

3. We were able to have a nice discussion on some of the variables that we did not factor into this race (like time taken to get to top speed for instance). These are valuable discussions that let students know that math isn't always as simple as it can sometimes be presented.

Enjoy the student work...especially the ones you can actually read without straining your eyes!