## Thursday, October 19, 2017

### Quadratic Card Sort on Desmos

In Accelerated Algebra 2, we are having a Desmos Day with Quadratics.

I dressed up in Desmos and one student told me "It was like I was sponsored by Desmos."  Proudly!

I first collected information from a Google form as a lesson opener.  We have recapped Algebra 1 Quad stuff - graphing from all forms and the start of solving.  I wanted to see where we are and how to move forward (formative assessment).

I learned quite a bit from these 8 questions.  I put my thoughts into a powerpoint for the next class's opener (using formative assessment to change teaching).  I do have one student who is still unsure of how graphs are transformed and I will definitely reach out to her.  The biggest area of unsure students is Inverse.  This was new this year, so it makes sense and we will be revisiting it.

Question 1: They understand the Zero Product Property and how it is used to solve quads by factoring.
Question 2: A few divided by zero and threw away an answer. NO!
Question 3: Write a quadratic tangent to the x-axis - one did not know what they meant (need to clarify vocab), otherwise, pretty good. And, they gave me answers in all forms.
Question 4: When would a quadratic have no solutions - got two possible correct answers and good connection to the graph in understanding this.  Next class is imaginary numbers and complex solutions.
Question 5: Write a quad in standard form with an x-int at -4.  Mostly correct.  A big problem was form - some wrote in factored form.
Question 6: Write a quad in standard form with x-int at -1/3 and -5.  Again, an issue with not writing in standard form.  But, for the most part okay.  Interestingly, a good amount of kids stayed with the fractional form.
Question 7: This one had mixed results - looking at the reflection:

Question 8: What are you still unsure of from the previous unit.

Then, I was going to try 3 Desmos Activites.  Silly me, too ambitious as usual.  The first one was more powerful than I anticipated.  Desmos Quadratic Card Sort.  It asked the students to sort quadratic equations.  All but one of my students sorted by the form of the equation - vertex and standard.  Then, in slide 3, a Desmos student sorted them into three piles.  It took the students quite a while to figure out how she sorted.  It finally took them away from just seeing the form.  It turns out she sorted by how many solutions - 0, 1, or 2 solutions.  Then, it asked them to sort another way - what, a 3rd way?  Most did it by the value of a - was it positive or negative, was it reflected over x.  Some did was it vertically stretched or compressed (still looking at a).  The original student who did not look at form, originally looked at reflection and this time now looked at form.  I read their responses and shared the analysis with the class.  It made them think for sure.

I love that I can see there progress, comments, thinking, and mistakes (as them fix them live!).

Love it.  Try it!

Desmos Activity 2: Factoring Sort - We did not have enough time to get very far (we could have used an hour period) but it did reveal some misunderstandings.  One important one was students were putting a sum of 2 squares under a difference of 2 squares.  I went around individually to each student and showed them their answers on my computers and what they did incorrectly.  Another mistake was not to realize once you pulled out a GCF it was a different of 2 squares or a perfect square trinomial.