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. 

Friday, October 13, 2017

Discovering Proving Triangles Congruent VNPS

In Accelerated Geometry, I am trying to get the students up to the boards a lot to discover and Geometry is lending itself nicely.  (#VNPS)

I was introducing the Triangle Congruence Theorems and did not just want to tell them.  Instead, I had them in groups of threes at the boards with one marker, one ruler, and one protractor.  My notes to read to them: Triangle Congruence Theorem Lesson.  We practiced our notation as I orally gave directions on what to draw.  Draw Triangle ABC with side AB measuring this, etc.  We went through different scenarios and then compared all 9 displayed around the room.  If they were all the same, we concluded it was enough to prove them congruent.  If not, then it was not going to work.  We also practiced classifying each triangle along the way.  It led to great discussion.  I did not teach how to use the protractor, so they did struggle with that, but I helped and they figured it out. 

We came back to our desks for a recap to get the theorems in our notes and practice using them in proofs. 

I did this in three classes and it went really well.  It took me about 35 minutes to get through it all.

Exterior Angle of Triangle with Geo and Desmos

In Accelerated Geometry, I introduced the students to the Exterior Angle of a Triangle Theorem.  I did not straight out tell them the theorem.  I wanted them to "discover" it using the Desmos activity.  However, the first question was what is the theorem.  Some thought it was all the exterior angles add to 360 degrees - true.  Some thought it was the exterior angle of a triangle is greater than each far angle.  True, too.  So, I drew a picture on the board and we discovered the connection that way, then we dove into practicing with Desmos.  I loved seeing them sketch their pictures:

Linear Regression: Legos Desmos

In Accelerated Algebra 1, we are learning linear regression.  I had notes from last year to add more practice and Desmos Legos fit in beautifully on a shortened class on a Friday.  I love seeing the kids make their predictions, sketching their graphs, using their equations to make predictions, and discuss Legos.  Then, we clarified what y =0.112x meant - did it mean 12 bricks for a dollar or 12 cents per brick?  I extended it to the current largest lego set the Millenium Falcon set.  It has 7541 pieces.  We used our equations and came up with about $840, so when we googled and found out it was $800, it was a steal!  Some non-lego lovers couldn't image spending that much time and money on Legos but some really appreciated it.  One student was talking about his $3,640 piece Lego set and another asked, "How do you know how many pieces? Did you have to count?"  He said, "Nope, it says it on the box?"

Also, love the new Desmos dashboard.  I did anonymize the students and they were intrigued with their mathematician.