I wanted to share this task because my students were very proud of their work, and they should be recognized…because they’re awesome.

I want to say first that this was inspired by a post that I saw by Mary Bourassa. So thank you Mary!

The task was to first create a rough sketch of a drawing which they think would contain some parabolas, lines, a circle and a triangle, and then to use mathematical equations in DESMOS to create their good copy. The rule was that they can only use things that we’ve learned in class, unless they could explain to me the mathematics behind something else they’re using. I’ll show come cool examples of these situations when I go to the examples.

Once the art was complete, students had to submit two things along with their artwork:

**The Equations page:**

They had to select 15 equations from their sketch and identify where I can find them. the 15 equations had to include a variety of:

- Parabolas in Vertex and Factored form
- Lines (horizontal, vertical, and slanted)
- Circles (one was sufficient, and it was allowed to be centred and the origin)

**The Calculations page:**

Students had to submit some calculations to me:

- Show algebraically the lengths of the sides of one triangle in your artwork
- Show algebraically all of the angles in that triangle
- Determine algebraically the point of intersection of two lines in your artwork
- Determine algebraically the point of intersection of a line and a parabola in your artwork
- Show me how you convert one of your parabola equations to standard form

**The Interview:**

Finally, students were given the chance to explain their thinking orally. Individually, they were asked questions like:

- (I’d point to a parabola in their artwork) Tell me an estimate of the equation of this parabola in vertex form, and explain your choices.
- What would the equation look like if I wanted to make this parabola look like (then I’d draw for them a new parabola similar to theirs, but slightly different)
- Describe using transformations the parabola here…(point to a parabola)
- Why did you choose to use the Cos law here (pointing to their calculations)

I’d usually ask two questions about their artwork, and one question about their calculations.

Their summatives were amazing, including all aspects. This is the actual assignment that we gave them.

**Here are some interesting examples:**

I love how this student used screenshots to identify where the functions are on the Equations page!

This student went ahead and learned how to create ellipses on her own. She said that she just assumed that if you multiplied the bracket by a number, it would stretch or compress the circle because that’s what it does to a parabola. She also felt that it was important to colour in the artwork, so she did it by hand!

This student’s artwork had a title. “Nonno” – Grandfather in Italian. When I saw the rough draft, I told her to not be married to the details because she may not be able to fit it all in, but I obviously underestimated her.

A few students exported their image into PAINT and then used the fill function to colour in the final product. I was amazed at the amount of effort that went into this.

Some were just fun to see…

And others were very interesting artistically. When I saw the rough copy, I had no idea that the final product would be this awesome…

So thanks to my students for doing these for me, and if you’ve got any ideas or modifications, please let me know!