Tuesday, January 16, 2018

Teaching Geometry - Expected Value

I am teaching a new prep this year - Accelerated Geometry, along with Acc Alg 1 and Acc Alg 2.  It is a lot.  I have taught a lower level Geometry course, but a while ago.  I have a colleague who also teaches it, so I have the quizzes (I make different versions). I have the homework.  (I still do each problem).  I have the Do Nows, but have to do them.  And, then of course there is the presentation - the lessons, those are mine and how I run the class.  I have the what and when, but I get to create the how and I enjoy the creation part.

This is where expected value comes in.  I have not taught it before.  I'm not even sure I learned it before.  So, I immersed myself in it. I went down the EV rabbit hole, reaching, researching, reading definitions, real life uses for it, formulas, worksheets, examples.  We have a target example in the book I knew I was going to use but I thought it might not be a good starting point. 



It has the whole area of a circle and the probability of hitting each ring.  I was teaching probability so it should be okay, but I didn't want them to enter at that point and get hung up.  I am all for starting with a challenging problem, but today's lesson was not it.

I also am doing a lot of VNPS - having the kids work at the whiteboards to discover Geometry.  I knew I would be teaching this lesson on the first day back from winter break, so I wanted to have them up and working and discussing, but I just couldn't do it.  I didn't want to force it.  It just didn't fit with that kind of lesson and that is okay.  I felt this topic had to be a whole class, step by step procedure.  That doesn't mean it had to be boring.  I just wanted to slow it down a little and take it one piece at a time.  I also decided to start at a carnival with a card game.  A standard deck of cards because we were familiar with the probability in a deck of cards.

I started like this:



I got them interested.  Some had questions - what do we win?  (I was going for 3Act style, not giving away all the information.)

I gave them some more information and polled the class.  We had some gamblers ready to play.



It went pretty smoothly and seemed to make sense.  I built up to the target.  Now they have seen the idea of EV.  I created a table to organize my work.  I had to consider all possibilities - winning and losing.  And, then it is about multiplying the "prize" by the probability.  Not so bad.  We ended up with an EV of -0.73 and we talked about what that meant.  Did they see how the carnival could rig their games?  Yes, they did.

When I introduced the target problem, I started by saying we couldn't just jump straight to the EV chart.  We had to figure out the probabilities first and that took some time, but again,  they were okay with it. We left things in terms of pi and conveniently pi/pi simplified to 1.  We walked through the problem step by step and they found success.  Then we did a couple more on their own for practice.  I liked the way the lesson went and was happy with it. 

Here is the slideshow if you are interested.

Saturday, December 30, 2017

Books read in 2017

I love reading.  I wish I could press pause and just read when I am hooked into a good book.  Yes, there are some that put me to sleep. But, my friends on Twitter always keep me in the know with the latest and greatest and don't steer me wrong. 

Here is my list of 25 books read this year.  I started to journal about them, just writing a little synopsis so I wouldn't forget them, but that stopped a few months in.  Then, I switched over to the notes in my phone and just typed the title and gave them a thumbs up or down.

First the bad...Sorry, just not my style.
These are some I do NOT recommend.

Grasshopper Jungle - do NOT waste your time.  I wasted enough for the both of us.  Just weird, weird, weird.  Unless I intrigued you, then read it.


The Most Dangerous Place in the World - yuck, snooze fest.


The Futures - just weird.


As Simple As Snow - I liked the way the author wrote.  I even liked the characters.  Just didn't like the story line.


Small Admissions - I am counting this has read but I didn't finish it.  Boring.


Now, for the good stuff, in order of how I read them this year:

Victoria - loved it, read it before the series came on and so excited for it to start back up.


Wonder - going to see the movie on Monday.


The Nightengale - a most read.  I thought the movie was coming out at Christmas but it looks like next year now.  Read it before the movie.  What a great story.


Simon vs. the Home Sapiens Agenda - love this!  And, the movie is coming out called Love, Simon and that is a great name for it.  Read this.


The Radius of Us - great, different.


The Circle - 500 pages, I committed, I read it.  I wasn't exactly happy with it but I don't want to spoil anything for you.  I haven't seen the movie yet.  Not sure I want to.


Big Little Lies - great, don't have HBO but watched the first day of the series.


City of Saints and Thiefs - a must - different - not many YA take place in Africa.  Great story. 


The Hate U Give - second time through.  I read it last year and then chose to read it again this summer for our HS summer reading book club.  I follow the author on Twitter and love seeing how the movie is coming together.


I'll Give You the Sun - love!


Aristotle and Dante Discover the Secrets of the Universe - love this one too!


To all the Boys I've Loved Before - cute, light, easy.


More Happy Than Not - really liked this.  I borrowed from my friend who heard the author speak and really liked it. I bought another book by him called "They All Die at the End" but it was stolen with my backpack so I didn't get to finish it.


The Beautiful List - I honestly do not remember even reading this.  I gave it a thumbs up.  I often read way too fast, I don't remember reading it, hence the attempt at journaling.
(hmmm, can't find a picture of the book.  Maybe it was something else.  Curious? I am still counting it as read).

Turtles All the Way Down - love, love, love!


The Rumor - great - oh, look, not a YA.


Zenn Diagram - cute, mathy, give it a try


Alex Approximately - good


The Nowhere Girls - Our town library recently formed a book club for adults (and students in grades 11 and 12) who enjoy reading YA.  Right up my alley.  I joined it and this was our first book.  I loved it and highly recommend it.  We have our meeting on it on Jan 22nd. I can't wait to chat about it.


I think my first book of 2018 will be Dear Martin.  Not sure what else will follow, but I will break this year's number.  You can see I love books that are going to be made it to movies, so I think I will google that now.

Saturday, December 16, 2017

A Blogging Challenge #MTBoSBlog18

Do you want to....

Read more mathy blogs?

Write more on your own mathy blog?

Start your own blog?

Then, I have a blogging challenge for you: #MTBoSBlog18

Starting in the new year...2018, on January 18th, I invite you to read or write blog posts.  And, continue on the 18th of each month.  Hence #MTBoSBlog18

If you are not familiar, MTBoS stands for Math-Twitter-Blog-O'Sphere - where people tweet and blog and share or tweet and read and share.

Here is a link to sign up and share your name, Twitter handle, and blog page.

If you don't have your own blog, we still need you to read.  You are our audience.  A lot of bloggers will tell you they mostly blog for themselves and their own reflection, but let's be honest, we are jumping up and down when we get a comment on a blog post.  Or, if someone retweets it, yippee!!!  We need you.  Follow the link for some fresh ideas of blogs to read and comment on.

Need a jump start to get blogging more?  Have every intention to blog an idea but time slips away?  Start typing and then #pushsend on the 18th of each month.  I will share some blog starters below.

Or, have you been reading blogs and keep saying you should start your own because you are ready to start sharing and reflecting?  Then, 2018 is a great year for you.  You will need to decide on your audience.  Mine is other math teachers.  You will need to decide on a platform.  Mine is blogger, but you can do a quick poll on twitter or some research.  Not get too hung up on it, don't let it be a roadblock.  And, a name.  Yes, you need a name and it can be a big hurdle for some people.  Do you want your own name it?  Your passion? Your hobby? Your favorite saying?  Some mathy pun?  Mine is 8ismyluckynumber (which you already know because you are here) but I like that is starts with the number 8.  I just type that into my search bar and it comes up.  Ask for help on twitter if you need more help, but let's set a goal of having it up by January 18th.  That gives you a month.  You can do it!

Need some ideas?  Here you go:
  • A recent good lesson/A recent bad lesson with reflection
  • New tech you like or dislike
  • A group activity and why it went good or bad
  • A podcast or Ted talk you like or disagree with
  • How you make an assessment
  • How you get/stay organized
  • An organizational hack
  • How you organize paper folders or digital folders
  • How you write a conference proposal
  • A recent conference you have attended
  • A school wide initiative or assembly
  • A favorite lesson so far
  • An upcoming lesson that needs a spark added
  • Desmos
  • Geogebra
  • A project
  • Social justice
  • Pedagogy
  • A student survey
  • Extracurriculars
  • Self care
  • Fun
  • Books - educational or for fun - recommendations
  • How you plan
  • Game/puzzles
  • MTBoS
  • Arrays
  • Number talks
  • Clothesline math
  • VNPS
  • Lesson openers or closers
  • Your classroom space
  • Reassessment
  • Review games/activities 




Wednesday, December 13, 2017

The Perfect Storm of Testing

I have been straight out working all the time.  This week is no exception.  I choose to do my lesson plans at school and my grading at home.  Right now, I am in the midst of trying to wrap up all my units with quizzes and tests before our December break on Dec. 22nd.  I was getting confused on which classes had tests and quizzes and scaring the poor students by writing TEST on the board and it should have been a quiz.  No wonder I am going crazy, when you put it all together, it looks like this:

Monday: 3 Geometry Quizzes (73 kids)
Tuesday: 1 Algebra 2 Test (23 kids)
Wednesday: 1 Algebra 1 Quiz (25 kids)
Thursday: 3 Geometry Tests (73 kids)
Next Tuesday: 1 Algebra 1 Test (23 kids)

I make it a priority to grade everything that night and get it back to the students the next day so they can get the feedback and learn from what they got correct and incorrect.  So, that is grading 217 quiz/test in a week.

But, there is more than just grading.  Each time I have a quiz or a test, I precede it with a review day.  For the review day, I have a study guide list of what might be on the assessment.  And, then I have either a review game or a review packet, sometimes both.  Then, there is the assessment itself.  I have to update that each year, type it in, take it to check for time/length, make adjustments, and print.  And, I have extra help sessions on Tuesdays and Thursdays.  Plus with this being the end of the units, that means all my next units need to be ready to go.  I need to have my unit homework and calendars ready to go.

It's exhausting.

But....on a good note, all my grading will be done by break.  I will start a new unit prior to break in each class so we will have a just about fresh start in January. 

I think I can, I think I can, I think I can....

Tuesday, December 12, 2017

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.


Wednesday, December 6, 2017

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

44
7.2 Similar Polygons
7.3 Similar Triangles
Geo - Day 44 Board Problems
 
 




45
7.4 Parallel Lines & Proportional Parts
7.5 Parts of Similar Triangles

46
7.6 Similarity Transformations
7.7 Scale Drawings & Models

47
Review for Quiz 5 on Ch. 7



Monday, November 13, 2017

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.