Posts tagged Burn Math Class
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.
No, I'm Not Listening
Students say the best things when they think I’m not listening.  It’s pretty funny actually, if not more than a little frustrating.  Students can be having excellent conversations about mathematics but as soon as I come over to listen they get just a little bit self-conscious and the conversation ends.


I’ve gotten really good at listening from far away.


We’ve been dabbling in project based learning with our grade nine academic classes this semester.  After our first project, we introduced our students to Dandy Candies.  This activity has been around for awhile.  I first was introduced to it at the 2015 OAME conference when Dan Meyer ran it with a packed room.  Since then, I’ve used this activity on and off with my classes, but never as a project.


The premise is pretty simple, show students the video of a preset number of small cubes assembling into packages (prisms) of various dimensions.  Then ask them some questions about what they’ve seen.


“What do you notice?”
“What do you wonder?”


As the person responsible for steering the conversation, I try my best to guide them to the questions I really want them to ask.  Except this time my thunder was stolen!  Apparently, after doing only one previous project, at least one student in the room was wise to my plan.


“I bet Mr. Mitchell wants us to figure out which arrangement uses the least wrapping paper”, said one student.  The entire classroom kind of gasped and went quiet.  Then there was an explosion of conversation at each table group.  This is a win.  Here I thought I’d have to trick my class into asking the right questions.  Somehow, they did it for me.




We spent a week playing with Math Cubes, calculating surface area and preparing a final report on which arrangement of 48 and 128 cube sized candies would need the least wrapping paper or in math speak, had the least surface area.  Then we spent the following week diving deeper into Surface Area and Volume calculations.  Students showed us their understanding in different ways.  It was fun!




It has now been 7 weeks of project based learning and curriculum wise, the grade nine team was all over the map, covering linear relations and geometry without having developed some of the other tools that would make solving these problems easier.  This was on purpose, we were creating a need in our students for them to ask us for better tools.


Up to this point, I haven’t once mentioned the word algebra to my class.  But it was time to introduce them to some more formal methods of problem solving.  Todd Malarczuk provided us with a simple mini project to drive home the need for algebra.




Students were presented with some pictorial representations of different algebraic equations.  You’ve probably seen these puzzles floating around your Facebook feed.  You may have even witnessed some of the arguments that they create.  Well, it wasn’t surprising that the same thing happened with our students, arguments everywhere!  Yet as I roamed around the room observing how the students were working, listening but not listening, I heard some comments that convinced me this was working.


“Drawing apples in my notes isn’t very easy.”
“If a bushel of bananas is four, do we need to know what one banana equals?”
“I wish there was an easier way to do this”

We had created a need in our students for something more efficient.  They wanted to know how to calculate what a coconut equaled, without us having to convince them that they needed algebra.  It was difficult, but by giving students the time to struggle; to try and fail and learn, we had created a community where risk taking was valued.  It wasn’t taboo to ask questions about the math we were learning or wonder about where we were headed.  Students owned their own learning, without us having to tell them that the learning was important.
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?
What Are We Reading?

Let’s put all the cards on the table before we get into our book list. When we say “reading”, what we really mean is “what pages do we look at after putting the kids to bed”. It’s hard to fit in reading, for professional growth or for fun into a day that is full of work and family. And yet, we try, as we imagine most of you do to.

Given the nature of this project, reading for professional growth has become more important to us. For sure we still try to find the time to read for pleasure but that time is shrinking as we get closer to launching The Shift. Certainly, if we are going to be the conduit through which innovative teaching practices are shared we better have some evidence to fall back on.

We both started by reading Most Likely to Succeed: Preparing Our Kids for the Innovation Era. This book was the basis for the companion documentary Most Likely to Succeed, which was screened twice last semester in our board. The documentary itself was attended by over 500 Halton staff and prompted many great conversations in our schools. The film was even shown to students from Milton District High School. The book itself asks, among other things, how should classrooms be changing to reflect the skills needed to be successful in the 21st Century.



We have also moved on to the book Open, by David Price. Open wonders how we’ll work, live and learn in the future. How can our schools evolve in a world where many companies give away their products for free? Likewise, sharing in the 21st century seems to becoming the norm so how can our classrooms and professional relationships reflect that? Certainly we can continue to teach using our current model, which is formal (pre-determined time and place), linear (follows a curriculum) and transmitted one way (teacher to student). Open imagines an education system where learning is social and knowledge is gained as the task or project demands.




At least one of us is reading Burn Math Class (Hint: It’s not Matt). The author, Jason Wilkes,
describes a reordering of the math curriculum where students start with addition and subtraction and create their own mathematical facts based on experimentation and failure. At its core, the novel stresses removing the emphasis on memorization of procedures and instead have students construct methods that make sense to them.


Being a wide-eyed fan of his TED brilliant talks, we have picked up Sir Ken Robinson's Creative
Schools: The Grassroots Revolution that Transforming Education. As we are looking to SHIFT education at HDSB, the promise of direct call to action in this book has brought this one to the top of the "next read" list.


Finally, both of us are looking forward to reading Hacking Assessment: 10 Ways to Go Gradeless in a
Traditional Grades School. Neither of us have opened the cover yet but we can’t wait to dive in. Both of us struggle with the question “What is this worth?” or “Is this getting marked?”. Hacking Assessment is about shifting everyone's thinking away from grades. School should be about the learning, not about the number attached to that learning. We can’t wait to start this one!

It is important to remember that no one book or idea is the magic bullet for our schools. Rather, the synthesis of ideas is important, especially when each individual educator thinks about their strengths and areas for growth. Reflection, as always, is important. We can picture a classroom where project based learning is the norm, each student is learning something different so that they can be successful on their own project and the curriculum is delivered in a way that makes sense to each individual student. More than that, each student engages in the classroom not because it is worth a mark but because they want to learn that material. We aren’t there yet, but we are working on it.

Want to learn with us? Consider joining Innovators Mindset, a book club with a twist! If you are an employee of the HDSB you can join in the discussion and get a free copy of the book. Over the course of five evenings the book will be discussed online. Participate from the comfort of your own home, or meet up with friends and collaborate as a group.


We look forward to participating in the conversation.