For my MFM2P group this followed the Perimeter activity I did with the 26 Squares manipulatives (partially pictured at right). For my MPM2D group, this was their first introduction to working with the 26 squares manipulatives. For both groups this was their first introduction to Quadratic relations and parabolas.

**Predict**: *What is the relationship between side length and area of a square?*

**Create a table of values:**

This was done in their groups at their boards.

I had to encourage groups to count the grid on their squares. Many were calculating the side length times 4, while others were trying to square the side length but doubling instead. For each of those groups, I redirected them to our physical squares cut out w/ grids [pictured at top of post] & asked them to count the area of a 2×2 square, then a 3×3 square, and so on.

**Graph**: Back in their seats students were given this handout & asked to graph by hand the data from their table.

**Linear VS Quadratic**: Students were asked to choose which type of relation they thought this was.

And why:We then discussed the shape of the graph being a curved line & the first differences being not equal (which only some students had pointed out).

**First & second differences**: Groups were sent back to their boards & their table of values with this prompt:

We discussed that second differences being equal means this is a Quadratic relation; a new key term for us. The black writing on the whiteboard above is my own addition during the class discussion.

**Desmos & Quadratic regression**: Back at their seats, individually students used Desmos to perform a quadratic regression on their table of values. They had this prompt on their handout from earlier:The 2P students had practiced performing a linear regression with Desmos the day before during the Perimeter investigation. The 2D students had mostly never seen Desmos before. I walked around helping students that got stuck or couldn’t find where they’d mistyped something & gotten an error. The result was:at which point I did some direct teaching about how to use the a, b, and c value determined by Desmos to write out an equation for the relationship between side length and area. I also introduced the word *parabola* to them while we looked at the graph from Desmos, zooming in & out.

In their groups at their desks they had 4 application questions to work on:and this became the homework for the MFM2P class as we ran out of time in class.

**Key features of a quadratic graph**:

With the 2D students I had time left to do some direct teaching about y-intercept, x-intercept / zeros, vertex, max/min, & axis of symmetry. Their homework was on Khan Academy to identify these key features given an equation that they could graph using Desmos.

For my 2P students this lesson came a few days later with class time to work on the Khan Academy exercise set.

* My reflection*: I wish I had asked at the end of the activity for students to restate in words the relationship between side length & area.

Folder w/ handout & Pear Deck interactive slideshow here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

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