Teacher Appreciation Week

Room Service

Teacher appreciation week is a big deal at my school. The different clubs and organizations feed us breakfast and lunch almost every day. It’s amazing!! I wanted to do something a little different this year with my Student Council. I saw the idea for room service on Pinterest last year and tucked the idea away for this week. I created the door hangers in PowerPoint using fonts from www.dafont.com/. (All files and fonts linked at the bottom) I printed them on bright yellow cardstock and had the students cut them out. We stayed after school on Friday and put them on all the doors so the teachers would be greeted with their menus on Monday morning. The door hangers were collected on Tuesday, and the students delivered the treats on Thursday. We loaded the snacks and an ice chest with all the drinks on a cart, and we pushed it around the school. The students filled each order from the cart. It worked great! As you can see from the photos, the teachers were very appreciative!




Triangle Congruence Sandwiches

I love teaching triangle congruence theorems.  It’s really one of my favorite parts of geometry!  But until this year, I just presented the theorems, and we practiced them.  Nothing exciting at all!  But this year, I had the awesome chance to experience a lesson taught by a fellow geometry teacher in our district.  At a Saturday PD day, Adrienne (who I get to call a friend now AND who finally joined Twitter!! (@Mrs_math_martin)) presented this lesson to us. I fell in love and was so excited to get to teach this to my math class. I knew it would really help them “get” the triangle congruence theorems.  It was just the spark this lesson needed!

I have no idea where the lesson originated from, but the activity we used can be found here:  https://www.sophia.org/tutorials/123-124-in-class-activity-fast-food-factory

I have a small class, so I split the students up into groups of two, and each group had to make one of each of the seven triangles.  This took all of one class period, and about 15 minutes of the period the next day.

*Note- if you use the linked assignment, one triangle calls for a side length of 12 inches.   You can either have 12 x 12 paper on hand, or you can have the students change the measurement to 11 inches.  We went with 11 inches because I just had plain 8.5×11 paper. Still worked perfectly! 🙂

After all of the triangles were made, we taped them to the board and had a pretty lengthy discussion about which “sandwiches” were appropriate for the restaurant to keep on their menu, and which were not.  Then I had the students guess how this related to triangles and they figured out that S stood for side and A stood for angle, and HL meant hypotenuse leg.  This lesson led beautifully into the introduction of the congruence theorems.  I still have the triangles taped up now as we have been referencing them throughout the week as we worked through the unit.


Nothing about this lesson was difficult to prepare and it wasn’t “flashy” by any means, but it did a wonderful job taking the congruence theorems and making them relevant for my students.  It is a keeper in my book!

Ode to Desmos

No surprises here – I love Desmos.  I have used Desmos for about two years now, but it seems like every time I use it, my love grows stronger.  Desmos.com is the only way we graph in Algebra 1, it’s our most popular choice in Algebra 2, we have had a ton of fun with the geometry feature in my geometry class, and I use the activities with both my middle school and high classes every single chance I get.  My students know and love Desmos, too. But it is so much more than just a graphing calculator.  This week Desmos has been particularly useful in my classroom…for discovery purposes.

On Monday, we began our unit on polynomials in Algebra 2.  My students did a little work with polynomials in Algebra 1, but just adding, subtracting, and multiplying them.  Not graphing.  But now, the time has come, and I am so happy that I have Desmos is my toolbox.

One of my favorite things to do to introduce a lesson is play a polygraph. I like doing this BEFORE they have any formal vocabulary.  So on Monday, my students played this polygraph: https://teacher.desmos.com/polygraph/custom/560c53f3441172070b2621f9
(H/t to @mrbenzel)

This particular class has an odd number of students, so I played too. It was challenging for me to ask questions without giving away too much vocabulary! This is a shot of some of the questions they asked.  I would be lying if I said this was an easy game for them. They had a hard time coming up with questions that helped them eliminate quickly, but I really enjoyed reading their questions and I think they did an awesome job for not knowing anything about the graph of a polynomial.

polygraph polynomials

On Tuesday, we began talking about the types of polynomials.  I gave them the notes on the types of polynomials and an example of each one. Then, I led in to what the graphs look like.  I even wrote myself a note in my textbook LAST YEAR to use Desmos, and use Desmos we did.  I had them graph each “example”, and I added another example of each type.  I had them type each equation in, then turn them all off.  We turned on one polynomial at a time, and I had them “notice and wonder” things.  Then I had them turn on just the even degree polynomials.  Then we turned those off and turned on the odd degree polynomials…more notice and wondering…and of course they noticed the end behavior of each type.  It was perfect – exactly what I was hoping for.  Then we predicted what would happen if we made each leading coefficient negative.  And then we did it, and their prediction was correct.

end behavior polynomials

The whole idea of them discovering the end behavior with Desmos was SO MUCH BETTER than just giving them the notes. It’s fun to manipulate the graphs and watch how they change.  They were satisfied with the end behavior, but they had many questions about WHY each graph looked like it did.  They wanted to know where the relative maximum and minimum points came from.  In their words – what makes the humps?  The best way I knew to explain it was to let them see it.  So, I took the 3rd degree polynomial that we had just graphed and made a few different forms of it taking away terms each time.  I had them graph each one on the same graph.  This is what I had them graph:

different terms in a polynomial


This was cool!  They could really see how each term changed the graph.  To me, this is the kind of exciting, beautiful math that Desmos is made for!  The real-time results just don’t happen as authentically with a hand-held calculator.


After the rest of that lesson, and the conclusion of the lesson on Wednesday, it was time to play polygraph again. We played the exact same one.  Take a look at this:

polygraph 2nd round

This makes my math teacher heart SO HAPPY!  They learned so much vocabulary in two short class periods. They were able to apply what they learned from the Desmos graphing calculator to describe graphs in a whole new way!  This is why I love polygraph.  Even they commented on how much easier it was the second time around.

Desmos also played a huge role in my Algebra 1 class this week.  I teach 8th grade math and Algebra 1 in the same year to my 8th graders, so they have done very little graphing up to this point.  We are about to begin graphing linear equations, but we have been talking about functions and domain and range.  This problem came up in our Springboard lesson on “more complex graphs”.  A graph like this is not something I would have normally introduced in Algebra 1, but as this is my first time using some Springboard lessons AND because I knew I had Desmos… I took a chance and showed them this “complex” graph.

I let them look at it for a few seconds, and I simply asked what they thought.  Almost immediately a student very confidently told me that the lines would eventually meet.  “Awesome…let’s find out where” was my response.  So we popped that bad boy into Desmos and I had him come up to the board to find the intersection.  LOTS of zooming and scrolling and zooming and scrolling and zooming and scrolling led to him and his classmates deciding that maybe they won’t ever meet.  THAT was a fun moment to watch as a teacher.  That literally would not have been possible without Desmos.  His ability to come stand in front of the class and manipulate the graph to his liking with the whole class watching- that was Desmos magic.

On Tuesday, I introduced them to graphing horizontal and vertical lines.  Once again, we used Desmos.  I gave them equations like x = 3, y = 6, x = -4, y = -11, x = .5, etc.  I had them turn on all the x =  graphs, and then the y= graphs.  They were very quickly able to see which equations graphed as horizontal lines and vertical lines.  Simple, but so, SO effective.

On the same day, I also introduced graphing lines using the x- and y-intercepts.  I gave them three equations and had them tell me what the x- and y-intercepts of each line were.  We “noticed” things about the intercepts, and their observations led right in to the idea that we solve for the intercepts by setting either x or y equal to zero.



All of these brand new things my students learned this week were made better by Desmos.  I genuinely feel that students retain information so much better when they are able to make discoveries themselves, and when they are able to “play with” the math.

All of this to say thank you. Thank you to the amazing and inspirational team at Desmos. Thank you for creating a product that has elevated my teaching to a new place, far beyond where I was nine years ago when I started.  Thank you for keeping your product free.  Thank you for supporting and loving teachers.  From all of us, thank you.

Parabolas in Action!

Last week, as I was going through my upcoming Algebra II lessons, I saw “Modeling with a Parabola” was coming up.  I had to look through the lesson to refresh myself on what the book was doing…which means that when I taught it last year, it was dry and forgettable!!  I knew it could be better.  So I did what I always do when I have a math question – I took to Twitter:

It wasn’t long before I got several replies– thanks everyone for the help!!– but one stood out to me as being fun and easy to implement:

[Side note:  I was fortunate enough to meet Todd at Twitter Math Camp this summer!  Had I not gone to Cleveland, Todd may have not ever followed me on Twitter, and I would not have learned about this awesome activity!  Life lesson- put yourself out there and connect with people!]

I was excited to read this response, because it seemed easy enough.  But I was also nervous because I had never done it before and I was worried that the switching back and forth between the video, Desmos, and my Promethean board software to draw the curve would be confusing and that with all that technology, something was bound to go wrong!  So I told my students on Monday that I had a fun activity planned, but it may not go perfectly, and I was gonna take the risk. They were totally ok with that!

The first thing I did was film two students throwing a ball in front of my board.  It took a few tries to get it right.  I filmed in slow motion as Todd suggested because it is way cooler! 😁

Then, I uploaded the video and used the “desktop annotate” feature on my Promethean board software to plot the vertex of our parabola and a few other points in the path of the ball.  Next, I opened Desmos and we moved the coordinate plane around until we found some nice points for the vertex and one of our plotted points.  We found the coordinates and at this point my students did not know how to find the equation of the quadratic using only a point and a vertex, so I showed them.  We worked together to find the equation, then went back to Desmos to graph the equation.  I traced the parabola, then we opened up the video again to see how we did!  Here’s the video of us watching it for the first time:

It was so neat to watch the ball follow the path of the parabola that we used algebra to create!  It wasn’t perfect, but it did lead to some authentic conversation about human error and how we could have made it better!  Here is another video:

After this, we also learned how to create the equation of a parabola when given a set of data using quadratic regression.   We used Desmos, of course.  Because life with Desmos is better!

All-in-all, it was a win in my book!  It was the same lesson I taught last year, but it wasn’t dry, and it (hopefully) wasn’t forgettable!

Points, Lines, and Planes, OH MY!

Full disclaimer:  This lesson is not my own!  A colleague from another school in our district told me about it, and then modeled it for us at our Back to School District-wide PD.  I was SO excited to try it!!  With good reason, too – it was amazing!!

So the lesson starts off with guided notes (linked at the bottom).  These aren’t anything new, it just happens to be what my colleague used, so I used it too.  We filled out the “undefined terms” section, then I passed out the playdough.

First I told them to make a point.  We went around and looked at all the points created.  Most students made a ball…others made shapes WITH a point. So that was our first discussion.  Then we filled in the guided notes on point.

Next was a line.  When I instructed them to make a line, every single one of them did the exact same thing… rolled a playdough snake.  And then I said, “I’m still waiting to see some lines.  I don’t see any lines…” It only took a little student-led discussion for them to figure out that I wanted arrows on the end of the lines.  This led to discussion about lines and the guided notes.  I ad-libbed a bunch of knowledge about lines, just like I normally would.

Next we talked about planes, did the notes, etc.  I told them they could think of their desktop as a plane.

They did not previously know the definition of collinear, but they worked together to figure it out. And they did it without any instruction from me!  All I did was instruct them to create two points that are collinear.  THEN the fun started.  I asked them to create two points that were NOT collinear.  We know it’s impossible, but boy did they try!  It was so funny!  And I walked around with meter stick and made a line with it through each of their two points.  “Nope, they are collinear…Nope, those are collinear…”  It didn’t take long for them to realize that any two points make a line.  Next we did the same for coplanar.  And creating three points that are not coplanar.  One student even went so far as to stick a point on my bulletin board halfway across the room.  And I still made a plane through them! (2nd picture below)

I knew this lesson was a winner when one student who was really confused about the plane started moving her third point around with her paper.  She exclaimed “Oh!  I get it!”  (1st picture below)  I don’t think I’ve ever had my students be able to really GET points, lines, and planes this well on the first day.

We only got through line segments today, we will continue the rest tomorrow, but I am calling this a win!

I am excited to figure out how else to use the play dough.  I know I will use play dough and dental floss to show cross sections, but please share if you have any more ideas!!

Here is the file for the worksheet I used:

Points Lines and Planes with PlayDough

First Day Fun!

I love the first day of school!  Because I teach the same students year after year, the first day is a reunion day for most of us.  This year, I only have two students that I’ve never taught before.  Everyone else I already know!  For one group, this is their 5th year in my class, and another group is starting their 4th year with me.  Because of that, there is no need to spend time getting to know me or my classroom.   We just skimmed the syllabus.  I did add something new this year on my syllabus, so I had to talk about that for a few minutes.  I decided to add a section where I told the parents about Twitter and how I was also blogging this year. I have them choose to what extent I can share pictures of their children.  I am very anxious to see the responses I get there!   After all of the housekeeping stuff, we did two activities I’ve never done, but I was so excited to try!

A few weeks ago I exchanged a few tweets with Bob Janes (@mrjanesmath) about the 4-4’s activity.  THEN, at our back to school PD week, our middle school curriculum coordinator shared it with all of us.  I was ready to try it!  So we did.  And man, was I blown away!!  I teach 6th grade, 8th grade, Geometry and Algebra 2.  Here is how three groups did:

Shout out to 3rd hour for finding ways to solve for all numbers 1-20!  Because I had never done this activity, I wasn’t sure what was going to happen!  Turns out, I was thrilled!!!  They did excellent!!  My favorite thing about this activity is that it worked for all the different levels I teach!  I love comparing the work of an Algebra II student with a 6th grade student.  There were some super conversations happening today… on the first day of school!  Win!!

The other activity we did was writing a #MathIs tweet. I got the idea from Sarah Carter’s blog (https://mathequalslove.blogspot.com/2012/08/first-day-of-school-plans.html).  My students know I’m all about some Twitter, so it was a fun little activity to get their creative juices flowing.  Pictured below are a few of the tweets I received:

I’m very fortunate that many of my students really enjoy math, and these tweets tell me it’s going to be an exciting year!

Another first day complete!!

Math Menagerie

Day two of the 2018-2019 school year, and I can already tell it’s gonna be my best one yet!

So during Twitter Math Camp, I posted to Facebook about the wonderful experience I was having.  Someone in charge of our district’s professional development saw it and asked if I would present at our Back To School PD week.  We have six days of professional development before our students come back.  This PD consists of several sessions and you pick and choose which ones to attend.  I was flattered that she asked me to present, and I agreed.  On the plane ride home from Cleveland, I brainstormed/jotted down ideas in my notebook of what all I wanted to show the other teachers in my district.  I came up with the name Math Menagerie, because that’s what I wanted it to be.  Just a big “hey this is all the awesome stuff I use” session.  Kinda like a “my favorites” session.  Several of the things that I wanted to include came from seeing the Classroom Chefs back at NCTM two years ago.  I appreciate everything they have done and will do for math instruction!!

Fast forward to today:

I’m not gonna lie:  I was really nervous.  My 9:00 am session consisted of about 20 middle school math teachers.  My 1:00 pm session consisted of 5 high school teachers.  I wanted to show them all the things, including Twitter!  Fun fact – Twitter is blocked on our district’s network, so it didn’t go QUITE as smoothly as I had planned, but we made it work!

So what did I share with these awesome teachers?  I showed them Twitter, #MTBoS, Desmos, Desmos Activities, Which One Doesn’t Belong, Would You Rather Math, Estimation 180, Open Middle, and Delta Math. And the BEST part?  Most of them had never heard of over half of these things!! They were so excited to learn about these fabulous resources!!  I loved every second of them jotting the websites down as I was showing them.  They were curious and ready to use these things in their class!

Some REALLY COOL things that happened during my session:

  1.  I live-tweeted a question that the teachers in my session came up with.  I wanted them to see just how awesome Twitter is!
  2. We got several responses, and we checked them all out together.  They loved the ideas!

3.  They LOVED the Desmos Activities- especially the high school group.

4.  Most of them had only heard of Desmos before, so it was awesome to show them just how great it is.

5.  Every time I showed them a new resource, they shared ideas on how they could use it.  That’s exactly what I was hoping for.

6.  My goal was for each person to find ONE thing they could implement next week, but I know several people are ready to implement MORE than one thing!  Win!!

7.  One of the high school teachers was already on Twitter, but had NO IDEA that there was a whole community out there.  She does now!!

8.  She is officially part of #MTBoS now!

9.  I also asked them to share their favorites, just like @misscalcul8 did in her session at TMC, and they did!  They shared about Edulastic, Quizizz, and Quizlet live.

10.  Two people mentioned Teachers Pay Teachers…and were plum DELIGHTED when I told them the MTBoS crew doesn’t charge! 😉

11.  I left my sessions with what I can only describe as a teacher high.  I was on cloud 9.  This little session that started as an idea on a plane turned in to one of my favorite teaching moments!  Teacher win.

12.  I left with validation that the stuff I do is really cool, and now I’m really pumped to have my students back on Tuesday!


A huge shout-out to these fine folks for helping me process my ideas and plan my session. Each of you played a part in my success today!!

My #1TMCThing

This is it.  Blog post #1.  And my #1TMCThing.  By the last night of Twitter Math Camp, I had a list of things that I wanted to be my #1TMCThing.  A list of things that I was ready to implement in my classroom and school.  Most of the ideas were small things, not too daunting.   But at dinner the last night – that my friend and I invited ourselves to via Twitter…. I love that the inclusiveness of TMC allowed us the confidence to do that – I was telling them about my list, and I was reminded that the #1TMCThing is meant to be ONE thing.  One thing that we commit to.  One thing that we can be held accountable for.  So, four days later after LOTS of consideration, I am ready to declare blogging as my #1TMCThing.  I have no idea how often I will blog, but it is something that I will try this year.  I’m excited, even if it does nothing more than serve as a reflection tool for me.

HUGE shout out to @miscalcul8!!  Thank you for encouraging/pushing me to start blogging, for giving me ideas, for boosting my confidence with tweets about ideas I shared, and for naming my blog!!!  I’m so glad I had the opportunity to meet you in real life!

And the biggest shout out to everyone involved in making Twitter Math Camp exactly what it is.  It was the best professional development I have ever attended – and I’ve attended a lot!  Blog post #2 will by my TMC reflection… hopefully sooner rather than later!