Teaching Geometry - Pythagorean Theorem #VNPS

My students are very confident with the Pythagorean Theorem.  They learned it prior to my class and we have used it in class without a formal introduction.  Today's lesson was to include Pythagorean Triples (new), more difficult problems with sides measuring square roots or binomials as well as Pythagorean Inequalities.

Again, we were up at the boards.  I gave them this list of triples without telling them what they were.  I asked them to write what they noticed.



They had so many different noticings I wanted them to share, on the spot I decided to have them do a gallery walk.  In their groups, I asked them to circle the classroom and read each other's remarks.  When they got back to their spot.  I asked them to share out something they noticed about what someone else wrote.  I liked this.  One group in the first class noticed the last four.  So, in my other two classes, I asked them to notice about the last four as well.  Some noticed it added 3, 4, and 5 when you went down the list.  Some kids noticed it was 3*7, 4*7, and 5*7, etc.

 







After this, we did these board problems.



And, Google Slide Lesson: Pythagorean Theorem

They did well with the regular Pythagorean.  No one tripped up when I gave them a hypotenuse instead.  We struggled with squaring the binomial - only one group per class got it wrong.  We learned from their mistakes.

I finally, we drew a triangle from the triple 5, 12, 13.  I asked if it was a right triangle and how they knew that and then I asked what would happen if we changed the 13 to a 14.  They quickly grasped that it would now be obtuse and that was our inequalities.

Student work

Back to desks to recap and practice. 

Teaching Geometry - Geometric Mean #VNPS

I taught geometric mean years ago.  I did it with the different ratios within the triangle.  I did it with two numbers.  I wanted to have my kids discover it at the white boards and understand how to set up the ratios, so I started researched.

It was our first lesson as a new class with new students in the new term, so I wanted to get them used to my memes, so I showed this as my title of my slides and I got them up to the boards.



In the process of researching the lesson, I learned two things:
1.) You can find the geometric mean of more than two numbers.  You just need to take that root.
2.) The geometric mean is the middle number in a geometric progression.

Here is the google slide lesson: Geometric Mean

I guess I just never really thought about #2 before but it made sense and I could relate it back to Algebra 1 when the students learned about geometric sequences.

When I introduce a new subject, I like to connect it to something they already know.  Naturally, that would be arithmetic mean.  We started with this:



I asked what they thought Geometric Mean might do.  We worked our way to this:



They did come up with the idea of multiplication.  I gave them two numbers and they had it.  They could calculate the geometric mean.  Then, I explained we would use proportions in similar triangles and use the geo mean to help us find other sides of the triangles.

Most of my whiteboarding (#VNPS) is oral, but I gave them this picture.

Here is my script for the board work.



I asked them to classify it to orientate them with the picture.  I asked what "h" was and it took a bit but we got to the altitude.

I had them pull apart the three triangles so the right angle was in the left corner.  That was tough, but we got there.

Then, I asked them to write the ratio of short leg to longer leg.

I forgot to take a picture of that one, but here is a picture of student work for hypotenuse to short leg:


And...voila...there it is staring at them - that diagonal geometric mean.  At least one group in the class had that aha moment and found the geometric mean.

We moved onto the second ratio and set it up.  And, a student taught me even more about the Geo Mean:
3.) The three geometric means are the three altitudes of the triangle!!!

I also thought of them as the altitude and the two legs, but yes, they are all altitudes.  How cool!

They set up the other ratios and found the geometric means within the proportions.  We came back to our desks to recap with notes and did a practice sheet.

I was happy with their work and their understanding.

January...it's the new September (#mtbosblog18 post 1)

My 1st blog post in the #mtbosblog18 challenge.  I challenge you to blog on the 18th of each month for the year 2018!

Our school does semesterization.  Some of the courses are only one semester long and it works for them.  For math, we are a full year long.  This means on Tuesday, Jan 23rd after we finish our midterms, we start fresh with term 2 and this means new classes, some new kids, and new periods.  So, if a student had me first term, they might leave and go to a new teacher or they might stay with me but have new classmates and a new class period.  This new term I will have 117 students - 53 returning and 64 new students for 55% new.  That's a lot!

In September I do a lot of getting to know the students from day 1.  Unfortunately, I don't have that precious time to repeat it.  I will hand out an index card and collect the new students' birthdays so I can add them to my weekly birthday board.  I will do another escrapbook like I did last year.  I make a scrapbook style page about me - pictures and my hobbies and then I share it with the class to make their own slides.  I love this!  It is a great way to get to know the new students but to get a chance to learn about the students who have had me all along.

Here is my page this year:


I am a To-Do list person and I love to check things off and feel accomplished.
Keep in mind I teach 3 different classes, Algebra 1, Algebra 2, and Geometry.

Here is my list:

• Update my canvas pages
• Update flippity.net for my random groupings at my VNPS
• Make new Jan/February seating charts (I change each month but both are short, so 1 will do)
• Make new email groups - this means looking through each kids' demographics to see if their email includes a middle initial (this takes a LOT of time!)
• Print class lists and keep printing until day of because they might change
• Copy my Assignment Sheet 11 for each class (Long term assignments due each cycle)
• Make and copy my new calendar and syllabus for the new unit for each class
• Make a new poster for the 2018 challenge
• Update my Deltamath groups (I use this site for practice problems every now and then)
• Put my old lessons away in binders
• Make my escrapbook page and make the classes google slide show and share (once I get email lists made)
• Organize new student birthdays
• Replenish classroom supplies - new board markers, new paper, etc
• Wash my whiteboards
• Clean my computer desktop
• Prepare 1st day lesson for each class, hopefully 1st week of lessons
• I administer the AMC math test on Feb 7th, so I need to make sure I send an email to the PTA to get parent volunteers to help with that.
• We have a math team competition on Jan 24th, so I need to make the teams for that and book the bus.
• Figure out Equatio (first I have to find it. I know I have it, can't find it though)

Keep in mind this all has to be done while midterms are happening which includes grading all of my exams, analyzing results, and recording results, plus providing extra help sessions to students. 

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.

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.

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 

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....