Posts tagged desmos
Cycling Back to the Beginning
It’s the last week before the holiday break.  When I teach grade nine math my goal is to always wrap up the teaching of curriculum before the break.  I do this for two reasons.  First, so that we can spend two weeks engaging in review activities to help prepare for the final exam, which in this case is the EQAO.  The second reason is so that we can play around with a final performance task that is a bit more open than usual.

I had no idea if this plan would hold up now that our grade nine course team was trying a blend of project based learning.  When I step back and think about what our team has accomplished over these four months, I’m pretty pleased.  We started the semester with a question that was very loosely defined, “Can we teach Grade Nine Math using projects?”.  We took a risk and dove in.

After playing with Barbie Bungee, Dandy Candies and some intentionally frustrating algebra problems we decided on our next focus:  We wanted to use ratios to help drive home with the class the need for more formal algebra.

A respectable ratio
We started with an activity that asks students “What is the ideal Mullet Ratio?”  This is an activity that I first saw via Jon Orr on twitter but I’ve come to learn has travelled to us from Matt Vaudrey in California.  In this activity students are asked to determine what is the ideal length of “party” to “business” in a mullet.  It’s silly, students laugh, then they start debating, and then they calculate to justify if their opinions are correct.  The two days we spent on this activity were hilarious.


Of course, we needed a suitable project to go along with ratios.  We know from past experience that there are often challenging ratio problems on the Grade 9 EQAO.  The team wanted to spend time working on different ratio problems in order to set our students up for success in January.  We decided on introducing the class to Nana’s Chocolate Milk, another three act task by Dan Meyer.

We adapted things slightly to allow for students to complete a formal project.  We asked our students to find their favourite recipe and then intentionally mess it up. They then had to “fix” their recipe and prove to us that they ingredients were still in the same ratio.  We even asked them to think back on their work with linear relationships and create some graphs and equations for their recipe.

Bacon is ALWAYS the denominator


This one impressed me
After the students finished with “Nana’s Favourite Recipe” we realized that we needed to dive into the Analytic Geometry strands of the curriculum.  We spent a good two weeks doing some formal instruction with our classes as this is probably the most formal component of the course.  At the end of the two weeks we challenged our classes to create their own drawing in Desmos to show off what they have learned.  We asked for drawings with 8 different lines, since that’s all our classes knew how to do with equations.  We were surprised by the level of depth our students went to.  One boy in my class asked me how to draw curved lines.  When I wouldn’t tell him, he didn’t give up, rather he did some research on his own and then shared his knowledge with the class.  



We have spent the past week trying up any loose ends or curriculum expectations that we did not quite cover.  For the final two days before the break we will ask our students to play with cup stacking, running a project that is heavily influenced by Alex Overwijk and his Thinking Classroom.  By the end of the week students will have created models of different cup stacking strategies, analysed them and extrapolated from their data.

That's some good cup stacking!


What came out of our experiment has been an unintentionally spiralled course.  Algebra and abstraction skills became what we dialed down on but we didn’t spend all that much time on the details.  Our students felt the need for the mathematics, asking for more efficient ways to do things.  When we presented the cup stacking activity to them they were already searching for ways to create equations and models.  

There were many days where the students led the class, posing interesting questions and then answering them.  The teachers became facilitators of great discussions, parachuting in on different groups when they needed assistance or a push to go a bit deeper with their learning.  Some days were great, other days were disasters.  On the bad days, the team would go back to the drawing board, talking about what we could do better in order to help students uncover the curriculum.  We tried something new and learned a lot in the process.  I can’t wait to do it again next semester.
Ignite the Spark
Last year, Halton was able to send 25 teachers to the 2017 OAME Conference.  There was lots of good learning and discussions during the three day conference.  What many realized was that there wasn’t much of a secondary conversation after the conference.  People were inspired, but what was lacking was a way to share that inspiration with other teachers in the board.

Enter Janet Juby and Laura Gatey, who were inspired enough to propose a Halton Mini-Conference in order to promote sharing.  Part of this mini-conference was a series of Ignite talks.  If you aren’t familiar with the concept, participants get 20 slides that auto advance after 15 seconds, giving you five minutes to speak about one topic.




Constructing an Ignite talk is a challenge, as you are forced to be very purposeful with what you decide to share.  I spent my five minutes speaking about Risk Taking and why I think encouraging our students to be risk takers is so important.


I was much more inspired by the other nine Ignite speakers.  I was left with a list of things I want to learn more about.


Tammy Knetchel validated my feelings about Interleaving and Spiralling.  She made me wonder what Interleaving might look like in other subject areas.


Erin Kinsella spoke about the need for Wellness in our classrooms.  The more I explore the ideas of Wellness, the more I see it is linked closely to Community Building.


Stephanie Briggs shared a story about her teaching philosophy and her desire to convince others that thinking is always greater than memorizing.


Lindsay Kueh nailed a talk about coding in math classrooms.  She made me want to diver back into coding and find ways to incorporate it into my classrooms.


Sheri Hill asked us why we are so excited about Fridays and asked how we can use play to engage our classrooms.


Todd Malarczuk encouraged us to jump on and off the various educational bandwagons at will.  Find the things that work for you, leave the other things behind and grow your own personal pedagogy.


Virginia Houston told the group about having students build their own Escape Room and show off their own learning by creating something.


Aaron Neal speaking for Michael Szarka, who was absent due to illness, stepped in and improvised a talk from Michael’s slides.  He did a great job convincing us that it’s ok to ask What If?


Matt Coleman joined the math world for a day and talked how we can gain longer periods of time with our students by Hacking the School Day.


What I really loved about the Ignite talks was how everyone focussed on personal inspiration, the teacher’s journey, their philosophy, their “why”, and not necessarily a strategy.   Passion was on display all day long!
From Why to Barbie Bungee
Back when I started down this ever Shifting road, I learned that good Innovation starts with identifying a WHY.  Why might I want to let students access technology in class?  Why is building a positive classroom culture so important?  I spent the summer thinking about the direction I wanted to take my classes this semester and why I wanted to take them that way.  Neil deGrasse Tyson summed up my thinking pretty well.



I’ve noticed that try as I might, the students I encounter lack a spirit of creativity.  It seems that many times they would prefer to be presented with the answer rather than seek out an answer on their own.  Thinking is difficult.  Many students say they enjoy learning, but that the stress of grades and assessments turn passion into anxiety.


I want to change that.


In May, I was fortunate enough to be able to attend the Ontario Association of Mathematics Educators (OAME) annual conference in Kingston.  I saw lots of great pedagogy that has been put into action and enjoyed many great conversations about how we can move our practice forward.  I felt empowered to try something new and with the course team at my school, we decided to forge ahead with some project based learning in our Grade 9 Academic Math classes.


The course team decided to start with a week of community building, because nothing pumps the brakes harder on curiosity than a week of prerequisite skills worksheets followed by a quiz.  We had fun and laughed by playing team pictionary on our first day of class.  We did some problem solving activities around the game Skyscrapers.  We debated how tasty a banana really is by playing around with Desmos Pomegraphit.  We ended the week by playing Battleship and talking about situations when plotting points might be important.


All in all, in four days we didn’t do much traditional math but the class was primed for our first project, Barbie Bungee.  This is a project that has made the rounds with math teachers for years.  I had heard about it, but never had the chance to try it with a class of my own.


The premise is simple: tie an elastic around Barbie’s legs, drop her, measure how far she drops, add an elastic and repeat.  Then figure out how many elastics are needed for a very high drop and try to get Barbie as close to the ground as possible.


On Day 1 we started with a Desmos Activity followed by a teaser video of some Barbie’s not having much fun.  




We polled the class with various questions: What do you notice?  What do you wonder?  Doing this allowed us to slowly introduce the project and steer the class into asking the real questions:  What makes the “best” Barbie Bungee?  We ended class by defining the “best” bungee as being the one that takes Barbie as close to the ground as possible without physically touching the ground.


On Day 2 we pushed forward by asking students to sketch what a relationship between the number of elastics and the distance Barbie falls might look like.  This prompted some good discussion on what we expected to happen with our Barbies as we added more elastics.  Then it was time for the actual challenge to start.  Without leaving the classroom, students had to build bungee cords for their dolls so that they could be safely dropped from the top of the doorframe.  It was a bit of a disaster, but the teaching team expected that.  Our students hadn’t really been shown the tools to be successful at this activity.  We were, to borrow a phrase, “creating a headache” so that students would feel the need for the math.





After watching our students attempt this initial challenge with no real plans, we pushed pause on Day 3 and did a more formal type of lesson.  We reminded our students about Scatter Plots, and discussed some ways they could use this concept to help them with their Barbies.


No Barbies were harmed...
Given this knowledge, we started Day 4 with a better plan.  Students knew to start small, measure the distance Barbie falls with one band, then two bands, then three and try to find a pattern.  We wanted our students predicting, given that we had not yet told them the real height of our Bungee Jump.  By the end of the period all groups were ready to test their Barbies and were told that the drop on the last day of this activity would be 520cm, or 5.2 meters, or two stories.


Day 5 was the big day, a time to test our students calculations in the real world.  There was a lot of excitement and smiles.  Perhaps not surprisingly, there wasn’t much anxiety.  This was, for all intents and purposes, a test of the students work and knowledge over the past week, yet none of our students approached it this way.  They were eager to have their Barbie’s jump, and disappointed when we told them they couldn’t refine their bungee cord after their failure.  And there were many failures.  

The point of this project wasn’t really to build the “best” Barbie Bungee.  The point was to get kids excited about math class, to get them to think about math class, and to let them have some fun in math class.





At the end of the week the students had learned a lot by doing.  They’ve explored scatter plots, collected data, and made informal lines of best fit.  They were assigned to visibly random groups at the beginning of the week and met people they wouldn’t have otherwise worked with.  


Could my class do well on a formal test about scatter plots and lines of best fit?  Probably not at this point in the course, but this is why I reject testing as a sound form of evaluation.  When a student completes a test and fails, what have they learned?  When students dropped their Barbie’s and they hit the floor, what have they learned?  I’d argue that students that have iterated their way through the bungee jump project have learned much more from their own failures than those who fail a test.  From my point of view we brought some joy into our curriculum and lets students learn through a bit of discovery.  It’s working for us so far!

So that’s my why, what’s yours?
Teaching and Learning with Desmos
Me and my math classmate and helper Nikolina
The other day, Jamie asked whether I wanted to become a student again for a math period.  All for it, I grabbed my laptop (as I was told I needed it), and ran for the portable.  You see, Jamie was doing a little recording of Stephanie Briggs’ Grade 10 math class for the upcoming OAME (Ontario Association for Mathematics Education) conference, where Briggs will be presenting on teaching using Desmos with Todd Malarczuk. I had heard of Desmos, the online graphing calculator, because well, Jamie won’t ever stop talking about it!  As an art teacher, I never really knew what he was always so excited when Desmos was mentioned. So here was my chance to see what all the fuss was about.


I settled into a group, hoping that my new math classmates might help guide me through the period.  I have to say, it is a little intimidating diving back into high school math, not having done so SINCE high school *cough* a few years ago.  Briggs introduced the day’s topic quadratic equations in vertex form and did a quick review of standard form and factored form.  I calmly wrote down the equations that she was putting on the board and pretended to follow along.  Really though, I was panicking a little because right from the top, I was lost.  I didn’t know what the formulas were supposed to do, and even what all the letters in the formula meant.  I sidled up to my new math pal, Nikolina, praying that she could help, and she was great.  She quietly explained the formulas we had just written down.


Next, Desmos!  Students seemed excited to get started and they were ready, devices in hand.  We were doing “marble slides” , where you were trying to create the shape of the parabola so that marbles slide down the parabola and pass through stars.  Kind of a like a phone game, but with MATH! The only problem was, I had no idea how to manipulate the formula to alter the shape of the parabola, and we weren’t given specific instructions on what to do.  Frozen, and unsure how to proceed, it wasn’t until I confirmed with my seatmates that it was ok to just start stabbing in numbers and see what happened.  Trial and error, look for patterns, trial and error, look for patterns...  Try, fail, learn. Try, fail, learn.  Now I was starting to get it!  A little journey of self-discovery, which is why Briggs didn’t tell us what to do.  Brilliant!  Slowly I figured out what would happen when I changed the numbers and how it affected the parabola.
desmos_marbleslides.jpg
Then, all of a sudden, Stephanie Briggs paused the activity for all of us.  We were locked out! There was a chorus of collective groans from the students because they were so engaged and invested in what they were doing! With the class’ full attention again, she did a quick revisit of the formulas we were using, asking about what we had learned so far about how the numbers in the formula affected the parabola.  It was an interesting and effective use of a pause in the activity!  After consolidating our thoughts on the process so far, gleaning a bit more understanding in the process, she un-paused the activity, allowing us to get back into sending marbles through our parabola slides.  I was getting the hang of this, starting to gain confidence and have fun with it.  Not bad progress seeing as I was blindly stabbing in numbers only a few minutes earlier. Briggs was constantly circulating through the room checking in with each group individually during the activity.  The whole goal of the activity was for us to discover and develop what vertex form was, which for me and students at my table group, seemed to be sticking a lot more than if we were just told what vertex form was.  

Stephanie Briggs circulating and helping students through the Desmos activity
All in all, it was an insightful window into Math exploration.  I found it a little like the math equivalent of getting a new type of paints that I’d never used before and just going for it and seeing what happens.  I don’t recall that kind of open ended exploration and play in my math classes.  Students are definitely better for it.  Thanks to Ms. Briggs for the lesson, now I can see why they get so giggly and excited every time Desmos is mentioned!


If you want to play Marbleslides yourself you can go here.
If you feel like exploring some of the other Activities provided by Desmos, head over here.
If you want some Desmos activities, organized by course, to use in your class, head over here.