MPM2D - Day 0

I will be teaching grade 10 academic math this fall (along with grade 10 applied and grade 12 advanced functions) for the bazillionth time, but it will be different as I decided to spiral through the curriculum as I have done in MFM2P for the last two years (click here to learn more about spiralling). I have always incorporated activities in my classes, but have been intentionally adding more over the past couple of years. I will take those activities and add new as I get rid of units and look at this course in a whole new way. There are fewer overlaps between curriculum strands in this course than in the grade 10 applied course, but I think I have found a way of organizing the cycles that makes sense and will help students be more successful. Here are the curriculum expectations (standards) for this course:

CURRICULUM EXPECTATIONS

Analytic Geometry:

• Model and solve problems involving the intersection of two straight lines.
• Solve problems using analytic geometric involving properties of lines and line segments. Verify geometric properties of triangles and quadrilaterals using analytic geometry.

Quadratic Functions:

•   Determine the basic properties of quadratic relations. Relations transformations of the graph of y = x² to the algebraic representation of y = a(x - h)² + k.
• Solve quadratic equations and interpret the solutions with respect to the corresponding relations. Solve problems involving quadratic relations.

Trigonometry:

• Use knowledge or ratio and proportion to investigate similar triangles and solve problems related to similarity.  Solve problems involving right triangles, using the primary trigonometric rations and the Pythagorean Theorem.  Solve problems involving acute triangles, using the sine law and the cosine law.

There are also the mathematical processes to consider:

The mathematical processes that support effective learning in mathematics are as follows:

• Problem solving

• Reasoning and proving

• Reflecting

• Selecting tools and computational strategies

• Connecting

• Representing

• Communicating

I decided that my first cycle would be all about relationships. Students will do activities that allow them to collect and work with data and they will look at patterns to help establish important relationships right away. As always, time is flexible with any of these activities and things never go according to plan! But I have a plan anyway.

Day 0: The Crow and the Pitcher
I stole this from Pam Wilson who blogged about it here. 

I bought some great, tall cylindrical glasses (pictures will be in Tuesday's post) and more marbles and created this handout (update: the handout now includes homework). I have different sized marbles so if a group finishes early they can experiment with larger marbles or combinations of different sizes. By the end of the class, I will put some water in my glass and have each group determine the number of marbles needed to fill it. Then we will see which group came closest by actually adding marbles until the water reaches the very top of the glass. It should be fun.

I love doing activities on the first day, not only because it is a great way for the semester to begin for the students, but also because I get the opportunity to observe my students. I did not teach any grade 9s last year, so I won't know any of them. I will learn their names as I circulate and also learn who the extroverts are, who is quiet, who thinks they can sit back and let the others do the work, who is enthusiastic, who is a perfectionist...

Day 2 & 3: Visual Patterns
I have often professed my love for visual patterns and particularly for Fawn Nguyen's site: visualpatterns.org. I decided to spend at least two days working through linear and quadratic patterns. I made this handout (made = stole pictures and formatted stuff). The first three pages are the patterns students will work on in class and the last two will be their homework. This will help set up the mindset of seeing more than one way to solve a problem and will hopefully challenge some of the high flyers that are used to not having to do too much thinking.

Day 4: Solve Me (Balance Benders)
No handout on this one yet, but we will be spending time here, having fun while solving equations.

That's the plan for my first week. After that we will do ropes, frogs, Desmos, some 26 squares and more. Stay tuned!

Better Qs

Last week, Sam Shah tweeted this:

I immediately replied because I was at Rachel's session, and at Dylan Kane's session and at Robert Kaplinski's session, all of which were on questioning. My #1TMCThing was:

(I'm going to let go the fact that I can't seem to get those two tweets to be the same size, but know that it is really annoying me.)

What were Sam and Rachel planning, you ask? A most awesome collaborative blog found here. There are already a number of posts, so check it out!

Why did I agree to be a contributor? Plainly because I know that I need to work on asking better questions. I hope that participating in this collaborative blog will give me that push to try harder. Of course I feel completely overwhelmed by it all right now, but I haven't started school yet, so I guess that's okay.

If you would like to work on asking better questions, become a contributing author. The instructions are on the blog. And if I haven't convinced you head on over to Sam's blog post about it.

Warm-Ups 2.0

Back at the end January, I created (i.e. compiled from all the great stuff out there) a set of warm-ups which I used in one of my classes last semester. Each student received a duo-tang* on the first day of classes with all 18 weeks of warm ups. These did not leave the classroom.

I have updated my warm-ups to include Which One Doesn't Belong?, Open Middle, along with better balance benders. There are also now quadratic visual patterns thrown in from week 6.

Here is the DropBox link to the Word file. Please feel free to edit them to better suit your needs!

*Apparently the term "duo-tang" may be a Canadian thing. This is what I am talking about:

To Those Considering Attending TMC16

In a recent conversation, a teacher whom I respect greatly, said "Maybe one day I'll be brave enough to register for TMC". This is an amazing teacher, who has deservedly won every award possible, who gives workshops around the country and is among the kindest, nicest, most genuine people I have every met. How could TMC seem to intimidating to this person? I went to Twitter Math Camp for the first time in 2013, knowing no one, rooming with a complete stranger (who turned out to be lovely) and really not knowing how or if I really fit in with this community, so I understand the anxiety leading up to TMC, but I still went. I wonder if the community has grown so strong in the past few years, that it seems to be more intimidating. Well, let me shatter that for you. The teachers at TMC are the most welcoming and kind you could find anywhere. The teachers whose blogs we all read are down-to-earth people who are, just like you and me, trying to get better at what they do. They will sit down for a meal with you and give you a hug when you fix their tech issue. TMC is an experience - one that is at times overwhelming, but one that is always positive. There are times on Twitter when some express opinions that bash something that another teacher makes work really well in their classroom - I find this very unfortunate. In my three TMCs, I have heard none of this. It's just really positive. I have met so many great people through TMC - people that are now friends for life. I have connected with teachers who really push me out of my comfort zone and make me think about teaching in ways I would not have on my own. Meeting and having conversations with these people in real life really strengthens my on-line connections. It's much easier to jump into a Twitter conversation when you actually know someone in that conversation. It's about community (as Lisa said), and TMC strengthens your sense of belonging to this amazing MTBoS community we have. So I urge those of you who didn't make it to TMC15 to make plans to be at TMC16 - you will not regret it. 

TMC15 - Morning Session: Activity-Based Teaching

I teamed up with Alex Overwijk this year to offer a morning session at Twitter Math Camp on something we are both passionate about: activity-based teaching. We had a fantastic group, 30 strong, who jumped right in with us. 

Day 1:
After quick introductions we started right away with an activity. We showed this picture:

and asked them what questions came to mind. Al brought the original picture from National Geographic so everyone could look at it up close. Look really closely - that speck at the bottom is a person! Next, they formed groups and came up with their group's top three questions with justification for choosing them. After that the groups snowballed around the room - they chose the top question from each other group's top three and wrote why they chose it, then put it under the desk so as not to influence other groups (I was supposed to take envelopes - that's what we do in class - but forgot to pack them). Then each group got back to where they had started and read what the others had chosen as the best question and why. Each group then chose and wrote what they deemed was their best question on the blackboards surrounding the classroom, along with all the reasons for having chosen that one. Here is what some of that looked like:

We then moved into a discussion of what makes a good question. Co-creating this criteria in the classroom helps students learn how to ask better questions. Here is the list we created:

Not every question has to hit all of these criteria, but it is something to strive toward.

Next, we talked about criteria for a good activity. Each criterion was written on the board and then everyone had 5 votes for the ones they valued most. Here is the list, in order, based on those votes:

As [optional] homework, we asked them to read Al's blog post on 26 Squares, found here.

Day 2:

We started by talked about 26 Squares which, over the course of about 3 weeks, allows students to see linear relations, quadratic relations, Pythagorean theorem (sum of squares), similar triangles and right angle trig. You can read more detail via the link to Al's blog above. Perhaps this is a good time to mention that I blogged every day in my grade 10 applied (MFM2P) course last semester so if you want more of a day-to-day breakdown, start here.

We did another group activity called Serial Position Curve. Al and I had come up with a list of 20 words which he read. No paper/pens or devices allowed - everyone had to remember as many as they could. Then they had time to write down as many as they could. Such focused students here!

We then counted how many had written each one and I put that into Desmos to show number of words vs. position of the word in the list:

Here are the words, in case you were curious:
hat, fork, golf, nose, horse, glass, belt, canoe, watch, book, shirt, phone, tent, ball, truck, foot, pencil, gum, ring, skate.

The relationship looks somewhat quadratic and can be used to ask questions about the features of a quadratic in context. My students get pretty good at telling me what the vertex means, not in terms of "it's the lowest point", but "the fewest people remember the word in position 12". We came up with a number of good questions to draw out the math. We also talked about what this means in terms of memory and how this can be used in real life.

We also did a 2nd run with a new set of words, only this time at the end Al "burned" everyone's short term memory. Here is my data and graph and this is what Dylan Kane did with it:

I think we spent some time just talking about spiralling (I wrote this after TMC14 as an overview) and answering questions to finish off day 2.

Day 3:

We started day 3 with me saying that although I have jumped off the edge of the cliff with my grade 10 applied classes, I still teach with units in other courses. I have been incorporating activities in my classes for, well, forever, but have made a much more concerted effort in the past few years to add meaningful activities where they make sense in each of my classes. I find this more difficult the higher the grade, but continue to look. I often find that matching activities work to help consolidate learning. I'm pretty sure I showed a few examples of other activities - this blog post likely highlights most of them.

Initially Al and I thought we would have everyone in the group create an activity of their own, but we changed the plan. I had started a Google spreadsheet to collect activities as I thought this would be more helpful in the long run. The intent was that this way we would all share with each other and everyone would have a starting point if they wanted to add activities to their class(es) this year. Well, the one-and-only John Stevens ran with this and turned it into the MTBoS Activity Bank which is searchable and all kinds of awesome. We populated it with 68 activities during that morning session and everyone can submit their own using the link at the top of the Activity Bank page. This is such a great example of "together we are better"!

A huge thank you to the participants in our morning session for making it so great. Apologies from me for not contributing as much as I would have liked. I know we will all stay connected throughout the year and support each other in our journey to make our classrooms better for all our students.

Post Script:
Since TMC15 I have decided to go against the flow and will be spiralling my grade 10 academic class this fall. I'm very grateful to have the full support of my principal. My plan is to blog every day to help me reflect and perhaps provide something useful to others along the way.

TMC15

I wrote this yesterday but, after reading Sam Shah's post, would like to preface it. This is not really about TMC15 itself, but more about my evolution since first attending TMC13. My point is that I wouldn't have done all these things were it not for TMC. That is pretty awesome. And my friend, Mark Sanford, mentioned that someone told him that what I have done is evolutionary, not revolutionary - it takes time and no one should expect to get there (wherever there is) overnight. I'm still not sure that I'm making a lot of sense, but I wanted to add that in.
- Mary

I feel so fortunate to have found this incredible community of math teachers. As I sit on the plane flying home after three days of the most meaningful professional development one could ever wish for, I want to attempt to distil what makes TMC so unique and special.

I, like many of you perhaps, joined the math-twitter-blog-o-sphere slowly, lurking at first, bravely tweeting at no one and eventually writing my first blog post which I did not think anyone would read. Since then, my professional world has changed vastly.

I have always been a huge proponent of teacher learning. I have given workshops across Canada, the US and Australia where I have had the privilege of interacting with smart, dedicated teachers. I have always been involved in mathematical opportunities outside my school – sitting on the boards of math associations, writing, organizing conference and such. But this group, my little corner of the MTBoS, is different. They have taught me, and continue to teach me, how to be better every day. They push me (because I want to be pushed) to reflect on my practice and realize what next steps will best help me grow. They support, encourage and value, disagree, discuss and give push-back. They are what every teacher needs.

Twitter Math Camp is so special because it allows us to take all the events and interactions of the year past and share them in person. The connections I have made at the three TMCs I have attended are priceless to me and shape the teacher I want to be. This past school year has been important in my efforts to grow as a teacher and demonstrates the effects of being part of the MTBoS. I continued to add good practices to my teaching and felt more confident spiralling my grade 10 applied classes. I blogged regularly (the good and the bad) and really tried to take time to reflect on my work. I read countless blog posts as well as a few books, which sparked ideas and made my classroom better for my students. But in the month of March, when I created the Which One Doesn’t Belong? website, I finally felt like I had contributed something meaningful, and that I really did belong to the MTBoS. Writing that makes it seem so ridiculous – everyone who interacts on Twitter and reads/writes blogs is part of the MTBoS – but for me, it was important. I suppose this comes from growing up in a house where nothing I ever did was good enough. The positive of that is that I always strive to be better and push myself to do more. In continuing to do more and accepting new challenges, I always know that I have the support of this group of amazing teachers from near and far. I am shy and introverted – I’m the one who is sitting in the kitchen with the dog at a party – but somehow I did an Ignite at OAME this year. Saying that it took me out of my comfort zone is a huge understatement, yet I did it and people that I did not know even said nice things after. I could not have done that without having the MTBoS behind me. I, along with Alex Overwijk, led a morning session at this year’s TMC whose participants included brilliant teachers that I respect hugely. And, more frightening to me, I gave a My Favourite, which was a disaster from my point of view, but still, I did it. I also seized the opportunity to learn from the amazing gathering of teachers, so willing to share. I have yet to fully process the sessions I attended, but hope to say more about those in a separate post. I will say that they inspired me to think deeply about teaching mathematics – something that I admire so much in others, but did not believe I could do.

As those who attend TMC will attest, a large part of what makes it extraordinary are the times after the sessions are done for the day. I feel so fortunate to have met and spent some time getting to know many of the west coast teachers that I had previously only known on Twitter. I could not have imagined better company for dinners or having more fun afterwards. So this blog post is really my way of saying thank you. Thank you to those who had the vision to create TMC and to those who make my experiences there so valuable.

Exeter Conference - Day 6

Today is the last day of the Exeter Math Conference. We have shortened classes and everyone leaves by 1 pm. It has been a fantastic week - lots of interesting and fun math, great company and really good food (including a lot of ice cream!).

The participants in my class have been amazing - they have jumped right in and tried everything. We have had lots of productive discussions and really learned together and from each other.

We started by looking at a couple more examples of warm-ups: Would You Rather and Open Middle. My Thursday blog posts from this past semester have write ups about Would You Rather warm-ups. I am looking forward to adding some Open Middle questions to my warm-ups for September.

I had saved the Barbie Bungee activity for today and they loved it. The idea is that you have to determine how many rubber bands to use to make a bungee cord for Barbie so that she has the biggest thrill possible without getting killed. 

We decided to drop from the 2nd floor (which is actually 2 flights of stairs up) of the science building. I measured the height, which was about 7 m, while my participants were working on their models. And then the challenge was on. I dropped each of their Barbies and am happy to report that they all survived the experience! This is a really fun activity. I have blogged about it here and here.

I had one last thing to show which is my day 1 of calculus activity. I have my students recreate a set of Desmos graphs. Some are to refresh the students on polynomials and some use animation, which is not something that my students have played with before.

The blog post, including a video, is here. If you want a link to the actual file, please email me.

And with that, my week at Exeter comes to an end. I really hope to have the opportunity to do this again next year. You can find information on this amazing conference here.