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.

Wednesday, September 13, 2017

Quilt Coloring to Bach

I love hearing about Math on a Stick that happens at the Minneapolis State Fair.  This year Annie Fetter @MFAnnie had kids coloring quilt squares.  I loved the idea and brought it to my classroom.  I went out and bought fresh packs of crayons because I wanted everyone to use crayons.  I decided to have my three Geometry classes color them in our 20 minutes after lunch block time.  Not many had time to finish, but some did and they are continuing to bring their finished quilt squares in.  I wanted to do it this week because Back to School night is tomorrow (Thursday, Sept 14th) and I thought we could make a quilt on my closet door to display for parents.

Quilt Pattern here

The word "crayons" brought up some debate in my Geometry class.  Is it "cray-ons" or "crayns"?

Even though they were new boxes, I still ended up with some broken ones because some kids color really hard.

There is a square within the square that I asked the kids to start with first, make the pattern there and then repeat in the other three quadrants.  The first square was no problem, but then it was hard to replicate - did they pick up the right crayon, did they color in their correct part.  It was harder than I thought it would be.

The hardest part was fitting the crayons back in the box.

I found some Bach music to listen to while we were coloring.  It was so nice and peaceful.  At first, some students thought it was weird or stupid but then they all got into it.  We could have used another hour to color at our leisure.

I think we all enjoyed our coloring time and we ended up with a beautiful quilt:

Thursday, September 7, 2017

Geometry #VNPS Desmos Day 4

Day 3 in Geometry was a summer assessment on a summer packet.

Day 4 we moved into learning about the Distance Formula and the Midpoint Formula.  Kids "know" the distance formula.  They have used it.  They may forget what is added or subtracted, but it comes back to them.  I wanted them to see where it came from, so I had them up at the boards #VNPS and walked them through these instructions to graph on a coordinate plane, work their way to the Pythagorean Theorem (which I let them try to spell out and most of the students thought it was the "PythagoreaM TheorM" - so we corrected that misunderstanding.)  I had them solve it for C and replace with x s and ys.  They finally saw the connection between the Distance Formula and the Pythagorean Theorem!

Here is a picture of group work:

Then, I made a Desmos activity that started with some thoughts on the Distance Formula and the Pythagorean Theorem.  It moves into asking them to figure out where the Midpoint Formula comes from.  Next, I brought a map of our town, Hopkinton, into a coordinate plane and asked them to find a distance.  Then, I did the normal "If somebody walks this way around the corner and somebody takes a shortcut, how much does the shortcut save?"  It took a lot longer than I thought.  I purposely did not put the fire station on a nice integer point, so they were struggling to figure out what decimals to use and then oh my, having to work through the distance formula with decimals was tough.  But, they did understand that they could have used the Pythagorean Theorem or the Distance Formula.  Most opted for the Distance Formula.  Then, I had them find a midpoint and that was a little easier. 

One question I asked that I liked was about the Distance Formula and "Name two mistakes a student might make when using this Distance Formula."  Here is a snapshot of some results:

Here is a picture of my Desmos Hopkinton Map slide:

Meeting Spot: Midpoint:

Thanks for reading.

Geometry #VNPS Day 2 Vocab

On my second day of Geometry, I had the students up at the boards for #VNPS to learn about points, lines, planes, angles, rays.  I read this as they drew and wrote notations.  I was going to have them shift and look at others to correct, but we just had the groups correct their own.  It was great discussion.  I asked them to draw a line, they drew a segment.  After we realized it needed arrowheads to be considered a line, I asked them to write the notation.  They wrote it with a segment on top.  They realized they had to have the arrowheads on this as well.  I am hoping the making of mistakes and fixing them along the way will make it stick better than me saying, "This is how you draw a line. This is it's notation."  It took longer than I anticipated.  I wanted them to return to their seats and then write it in their notes, but instead, I asked them to take out their phones and take a picture and for homework to write it into their notes.  They could take a picture of their own group's work or another.  It was fun to see the Geometry Paparazzi form around the neatest work and snap pictures. 

Here are two examples:

Thanks for reading.