MIRA snowflakes

I have had MIRAs forever and never put them to use.  Today, we made MIRA snowflakes in the 20 minutes after lunch.  It was a quick crash course.  It really ended up being a course in following directions.  We have used compasses before, so we were familiar with that, but the MIRA was new.

Here are my directions:


Here are Period 5's snowflakes.  We ran out of time, but if you notice, they all have 6 parts.



Period 6 has 29 kids and is very loud and energetic.  They did not listen to the directions as well.  You can see - some have 4 parts, some have 8 parts, some skinny in the middle.  They should be skinny at the edge and fatter in the middle.



Thanks.

Similar Triangles at the Board #VNPS

I have been able to get the students to the boards more and more in Geometry.  I love it.  It is a lot of work up front, but the kids are really getting it.  I have all my students at the board at the same time (#VNPS).  I use VRG with flippity.net and project the groups of 3 so they know their different groups each day.  Dare I say, we have reached a great flow in the classroom.  The kids now know how it works and the transitions are smooth.  Today, I heard a student say they love the "board problems". 

I presented on my first year attempting #VNPS last year at #TMC17 and I noted at the end that I wanted to do more with Geometry and more oral and I am happy to say I have done that.  I take a look at the lesson I am to teach that day and then I sort of write a script of the description I will read to the kids.  It is always one student and one marker.  After that student does their part, they "erase the board and pass the marker".  I feel like I say that all the time.  I am lucky that my colleague and I were awarded a grant for permanent white boards and really cool magnetic coordinate planes.  So, I often tell the students to "get in your board groups and grab a graph."  They really like them too.

We go to the boards and go through the problems.  Geometry lends itself so well because it is a lot of  drawing and vocabulary.  With all the students at the boards, I can monitor their work and we can catch mistakes or misunderstandings and discuss them.  I am very picky.  I will state reminders like make sure your lines have arrowheads or make sure you mark your right angles.  The kids have gotten proficient at all the particular details that make up Geometry.

It does take longer than just sitting at their desks and writing down what I tell them, but there are conversations as they build their own understanding, so of course it will take more time.  It is worth it.  As we are drawing things or calculating, I remind them to look around the room.  Geometry also lends itself well to problems taking about the same amount of time.  Students are not held back.  The board is blank when they start, so we are all starting at a low entry point and building our own ladder of understanding.

I will say it is kind of a good exhausting.  With all the movement and taking, there is a lot of energy in the room.  I have my class of 29 first.  Then, my smaller classes, so I know if I can get through them, the rest will be easier.

We will do our board problems, then come back to recap with really brief notes, mostly to get the vocabulary down and to bring it all together.  If time, we will do some practice problems.

Here are a couple of my lessons on Similarity.
In my powerpoints, I cut and paste the answers to the previous night's homework.
I take a screenshot of the flippity.net page so I can have the groups in the ppt.
I keep my Geometry syllabus in a google doc and was able to cut and paste below with all the links.  Pretty cool that it worked.

43	7.1 Ratios and Proportions Geo - Day 43 PPT similarity Geo - Day 43 Board discover similarity
44	7.2 Similar Polygons 7.3 Similar Triangles Geo - Day 44 PPT Similar Geo - Day 44 Board Problems
45	7.4 Parallel Lines & Proportional Parts 7.5 Parts of Similar Triangles Geo - Day 45 PPT Parts Sim Tri Geo - Day 45 Board Problems
46	7.6 Similarity Transformations 7.7 Scale Drawings & Models Geo - Day 46 PPT Scale Transformations Geo - Day 46 Board Problems
47	Review for Quiz 5 on Ch. 7 Geo - Day 47 PPT Quiz 5 Review

Intro to Polygons Lesson

Sometimes I need to remember KISS - Keep It Simple Stupid.  I was introducing Polygons in 9th/10th Geometry class.  I was hoping they came in with some vocabulary and understanding.  I had them right up at the boards for three simple drawings to check for understanding.  It led to great discussions.

Board Problems

We discussed "perfect looking" hexagons vs not for the vocab word of regular.
I asked them to draw diagonals and then had them define a diagonal.
We noticed the number of triangles inside the polygon and saw the pattern to make the formula.
I finished with asking them to draw and name all the polygons they knew.  More great discussions...
Is a circle a polygon?  I had not defined it, so I asked them to and they got all 3 characteristics.
What about a square, rectangle, rhombus, and kite  - are they polygons?
One group came up with dodecagon but asked about how many sides a dodecahedron had so we discussed 2D vs 3D.
Edited to add one girl thought one of them was a "rhododendron"  Too cute.


Then, we came back to our desks for a Desmos card sort to clarify more vocabulary. Which led to more discussion.  I love when the card sorts ask for more than one way to sort things.  Genius!

Finally, a practice worksheet to put it all together.

I had the following meme on my daily agenda.  I guess this has turned into my High5.  Kids look forward to coming to class to see the meme and then it takes a minute but there is usually a smile or a laugh.  A great way to start each class.

Today's - being from Boston - we always sing "Sweet Caroline" at the Red Sox games:


It was a nice lesson for a Monday.  Thought I would share.

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. 

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.