Modelling Real-Life Quadratics in Grade 10 Math

Happy first day of October! This post is about an assignment (or “performance task”) I did in my Grade 10 math class last year. It could be done as an in-class activity without evaluation as well. It is based on the following expectation from the Ontario Grade 10 math curriculum:

Collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology or from secondary sources; graph the data and draw a curve of best fit, if appropriate, with or without the use of technology.

Like with most lessons, I started off by looking at what other teachers who had taught the course had done before. In the past, students used imprints of their molars, which fit a quadratic model quite well. They used TI-84 graphing calculators to model the set of the points created by the imprints, which were done on graph paper.

I wanted the task to be a bit more open-ended. I am not a huge fan of TI-84s, so I decided to use Desmos instead. I decided to combine the quadratic modelling with a task my host teacher told me about when I was a student teacher, where students used iPads to do a parabola scavenger hunt around their school and online. Technology-wise, I was teaching at a 1:1 school, so each student had a laptop they could use for the task.

Onto the assignment: students were asked to find or take a picture of a parabola and upload the picture to Desmos:

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I demonstrated how to enlarge or shrink a photo on the screen, and how to move it so that the parabola is symmetric about the y-axis. The next instruction was to estimate 10 points on the parabola as accurately as possible.

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Then comes the cool part: Desmos has its own quadratic regression model.
Yes, it really is so cool. With this one line of “code”, you can easily do your own quadratic regression on any set of points:

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I had students fill out a table to find similarities and differences between their model and two friends’, instructing them to use parabola vocabulary that we had talked about in class (opens up/down, vertical stretch/compression, etc).

Here are some examples of what my students came up with:

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Overall, it was a good day: it was a light, fun activity for the students the day after a test, and it was easy and fun to mark.

If I were to make any changes the next time around, I would have the rubric reflected as a mark out of 10 for each achievement category, where each level is converted to a percentage. I would also try to match up the rubric language with the language that the math curriculum uses for assessment to make it more student-friendly (page 20-21 here).

The full assignment is available here: QuadraticsIIIPerformanceTask

(If you don’t feel comfortable downloading from online, shoot me a message in the “contact me” section and I’ll send it to you by email.)

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