Quadratic Card Sort

My grade 10s have been working on quadratic relations and I thought that a good way to help them consolidate all their learning was to give them this card sort. I first saw this years ago in the NCETM's Improving Learning in Mathematics and I made some slight adaptations.

I started by giving the students these two sets of cards:

and they began cutting them out and matching the standard form to the factored form:

Immediately, there were lots of great discussions on factoring, too many almost to track!

When I saw that a group had made the correct matches, I then gave them these cards about the intercepts:

I had debated about whether I should label these with 'x-intercepts' and 'y-intercept' but then thought it would be better for the students to figure out this themselves (which they did!)

When these matches were made, I then gave them the seven graphs (created with the help of Desmos)

Lots of good connections were being made now as students used the factored form and the intercepts to make their decisions. They were then ready for the next set of cards which were the maxima or minima.

These were matched quickly: the graphs helped a lot but I was able to get students to check that each vertex lay halfway between the x-intercepts.

Finally, I gave the cards with the vertex form:

I have not done vertex form with them yet so I was curious as to how they would manage with these. But by using a bit of intuition, they matched the y=(x–5)^2–9 equation with the card that said 'Minimum: (5, -9)' I could then ask groups to expand and simplify the vertex form to see that it matched the standard form of y=x^2+10x+16.

As they beagan to match some of the other vertex form graphs, I could hear some groups making conjectures along the lines of 'Look at the co-ordinates of the vertex, make the x one opposite of what it is but keep the y one the same and then look for that equation.' In doing so, most groups came up with a full set as shown: 

At this point, I was able to get the class to see that when we write an equation in vertex form, it allows us to immediately see the co-ordinates of the vertex which, for some problem solving situations, is important to know. They will learn more about this in the next unit.

Finally, each set of cards purposely had a blank template so I challenged the students to create their own set of cards. I wish I left more time for this though as most groups did not have enough time to complete a full set of cards (a sample is shown below):

If you would like to try this yourself, the cards can be found here.