Friday 29 May 2015

MFM2P - Day 75: Measurement

We started with a Daily Desmos-style warmup, where they had to determine the equation of the line through the following points:

This is the work they did:

Notice that we found the y-intercept in two ways. Some of my students are more comfortable with the numeric solution, while others prefer algebra. We talked about the circumstances when the algebraic solution would be better. We then put our equation in Desmos to see if we were right:

I handed back the work they had done yesterday figuring out how much wood they would get from the General Sherman tree. We looked at the volume using a cylinder and a cone after discussing the different ways they could have calculated volume (I did mention frustum, too):

The actual volume is shown here, and the cone looks like it gave a closer estimate:

We then built on that with this:

I tasked them with calculating how many board feet they had, based on their calculations from yesterday.

That seems like a big number, but none of us really had any perspective on how big it is. A little Googling found this:

That is a lot of houses!

They spent the rest of the period working (individually) on this task.

Thursday 28 May 2015

MFM2P - Day 74: General Sherman Tree

We started with this warm-up:

I discovered many misconceptions my students had about buying and leasing cars. One student worked out how much it would cost to buy it and was shocked that it didn't work out to $19 000. You will see interesting things in their work:

The third group was trying to figure out how many miles you would need to drive for the prices to be the same. There was a lot of good discussion that came out of this warm-up (which you don't see here). At the very least my students now have some idea of the difference between leasing and buying.

Next, I showed them this picture:

I put them in (not-so-random) groups and gave them these instructions:

Each group worked on a whiteboard and was given 6 squares (-ish) of one colour of paper and an envelope (which stayed with the whiteboard):

They took the squares of paper with them as they went around the class to read each other's questions and choose the best one from each group. Here are their questions:

Lots of good questions, and very few off-topic ones. We did not really come to a consensus on the best question so I steered them toward the group that had "How much wood would you get from it if you chopped it down?". I asked what information they needed and they said they needed the circumference, the height and the weight. I asked why we needed the weight... and we decided that we didn't. I showed them this:

We had 15 minutes left so they had to individually figure out how much wood they would get out of this tree. Some wanted to know more about what the product would be - firewood, 2' by 4', etc. I told them they could choose. Many had trouble starting so I asked what shape the tree was, which was enough to get them going. They didn't like not having one diameter to work with - I did like that they had to make decisions and provide support for those decisions. And I didn't let them leave until they were able to hand in some work.

Wednesday 27 May 2015

MFM2P - Day 73: Quadratics

We started today with this visual pattern:

They fairly quickly recognized that it was quadratic (not linear), but struggled with how to find the rule. We looked at the number of rows and the number of helmets in each row for steps 1 - 4 and then noticed a pattern:

I had promised my class another Kahoot today so that's what we did next. It is called "Quadratics #2" (my user name is "maryatwest"). I looked at the results of yesterday's quiz to choose what questions to ask today. Here is a quick overview of the questions:

They were a little less focused on the math today, compared to yesterday, with lots of students guessing as soon as the question came up <insert my sad face here>. Lesson learned - one Kahoot is plenty in one week!

The rest of the class was spent working on the quadratic handout from Monday or on this quadratics review sheet for those who had finished the previous handout.

Tuesday 26 May 2015

MFM2P - Day 72: Quadratics

I decided to skip today's warm-up as I had made a Kahoot for my class. I'm fairly certain that I can't share it unless you have a Kahoot account so I will tell you that my username is "maryatwest" and it is called "Quadratics Vocabulary". I made it public so if you are interested, you should be able to get it. Here are the 11 questions (sorry about the inconsistent formatting):

That took about 25 minutes. They really enjoyed it and got into it (for the most part - there were a few who don't get into anything we do...). We went over each question right after they answered it so there was learning going on, too. I gave them the rest of the period to continue working through yesterday's handout while I ran around helping them. I promised them another Kahoot tomorrow, if they worked well today. So I'll be making that tonight. I will analyze the data from today's quiz to help choose good questions for tomorrow.

Monday 25 May 2015

MFM2P - Day 71: Quadratics

Monday morning means counting circle! Today we started at 7x + 12 and added -12x + 48. There were a few mistakes along the way, but they didn't struggle as much as I thought they might. I helped with some strategies along the way, like adding 50 then subtracting 2.

We returned to quadratics today with this handout. It starts with a review of the vocabulary associated with quadratics, then works through all that we have done.

I circulated and helped them get going and talked about the axis of symmetry over and over to help them find symmetrical points. They are remembering and starting to put it all together. We will continue with this tomorrow.

Friday 22 May 2015

OAME 2015: Rethinking Math Class

Last Thursday, at the OAME 2015 math conference, I presented a double-session entitled Rethinking Math Class. I am going to try to recap it here, as best I can, with links to everything! So expect this to be a long post...

First, we played Quadratic Headbanz, which I have blogged about here

Given that 64 people had signed up for my session I had to make a second set of headbanz. As my original set featured equations I decided to make the second set with graphs which you can get here. As it turned out these ramped up the difficulty level for both the person wearing it and the person answering questions. This is a great activity with students and teachers, alike. It was especially good given that my session was right after lunch! It is fun, but gets at the vocabulary and skills you want students to know and each interaction can help struggling students get better at asking and answering questions. This is what it looked like:

Next I talked about warm-ups. This took a long time because there is so much good stuff out there to work with! I have blogged about warm-ups here and with my files, here.

I chose about a dozen or so people to do a counting circle. We started at 49 and counted down by 7. We talked strategy along the way and stopped so that they could figure out what we would be at 7 people along the circle and again shared strategies. I noted that you can do these with fractions and expressions, etc. They definitely help set the culture in my classroom where it's okay to make mistakes and we value each other's ideas.

I showed off Andrew Stadels' Estimation 180 site a little and I had participants estimate his height with reasoning. We also looked at this one together:

On to Visual Patterns. I love visual patterns. We do them every Wednesday and they take longer than some of the other warm-ups, but that is because there is so much rich math that can be drawn out of them. We did this one together:

We looked at the pattern in the number of black squares first, then looked at the number of white squares. I did not take a picture of what we came up with, so my challenge to you is to try to see how the white squares are growing in at least three different ways. You can check out my post here to see what I did with my students.

Next up: Always-Sometime-Never. Here is the one we did, which I showed without the "answer" first.

I really like how these push you to think further as you need to consider many cases.

We then talked about Math Talks and how good they are at helping students develop their number sense.

I then showed off the Solve Me site, which has lots of balance bender type questions.

I am working with my grade 10 applied students to have them solve these puzzles and then write down the algebraic equivalent. They need to make the connection and see that they are doing the algebra already, just in their head.

I also briefly mentioned and showed the Daily Desmos site which is filled with graphs that students need to try to recreate. The latest ones are all a little crazy, but if you search you can find simpler linear, quadratic and other more curriculum-aligned ones.

Then we got to have a little more fun with Which One Doesn't Belong?

I showed the logo you see above and asked which one didn't belong. Different people came up with a reason for each of the four not belonging, which is how all the sets on the WODB? site and designed. We then worked on the following incomplete set:

It was great to see groups trying to come up with a fourth graph that made this a solid WODB? set. There were several answers that groups created and the ones they found that turned out to not work generated some of the best conversations.

I think the vast majority of math teachers in Ontario have heard of and love Desmos. I wanted to highlight the fantastic activities that they have created. These go from linear to rational functions and truly engage students in meaningful mathematics.

We put those activities on hold while we did a little speed dating. It was too big of a group to rearrange the desks to properly speed date, but we improvised and they did 5 minutes of factoring. The idea here is that each student factors the expression on the paper they chose and therefore become the expert on how to factor that one. Then, they show only the question and factor their partner's question and because they are each the expert, they can provide help if anyone is struggling.

I then provided "play time". Teachers could try one of the Desmos activities (I had codes for them to try four of the activities) or do any combination of the following activities. I will briefly describe each or provide links to blog posts. I feel that reading a blog post about the activity will give you more insight into what to expect if you choose to use the activity yourself.

Speedy Squares
Students first figured out how long it would take to build a 26 by 26 square out of linking cubes. They then used their times to figure out the relationship between number of blocks and time. They designed a simple house and calculated how long it would take to build it out of blocks, with a little help from the Lego My House app.
I blogged about it here and here.

Barbie Bungee
Let's give Barbie a thrilling bungee jump without letting her get hurt! Students develop a model and use it to determine the number of rubber bands needed for a particular height.
I blogged about it here and the handout is here.

Matching: Linear & Quadratic
This activity has students matching up word descriptions, algebraic expressions, tables of values and area models. I love this one - it comes from Shell Centre for Mathematical Education and is available here.
A brief blog post about it is here.

Matching: Combined Functions
This is an old OAME activity - I believe it starts on page 57 of this document. It is great for getting students thinking about combining functions in MHF4U.

Cup Stacking:
Students, using only 10 Styrofoam cups, determine the number of cups needed to reach their teacher's height. They can then find other relationships based on how they stack the cups and the types of cups used. They can solve systems of linear equations if you start one stack of cups higher than the other. Lots of good stuff in this one.
I blogged about it over several days starting here.

Marble Roll:
This is how I start my MPM2D course. Students have to find the relationship between the height of a ramp and how far a marble will roll from the base of the ramp. I haven't blogged about this one (!) so here is the handout.

Tying Knots:
Students first determine the relationship between the length of rope and the number of knots, then figure out how they can have the same number of knots in two ropes to produce the same length.
Since I don't seem to have blogged about this (yet), here is a link to Alex Overwijk's post and my handout (that needs work).

I started by looking at cost vs. mass for various sized boxes of Smarties, then cost per Smartie. On day 2, I explored the amount of air in a box of Smarties and have students construct their own box that will minimize the air (or maximize the Smarties, depending on how you look at it). 
I blogged about it here and here.

Intro to Calculus with Desmos:
This was my day 1 challenge to my Calculus & Vectors classes. I blogged about it here.

Log War:
I don't have any recollection of whether I made these myself (they look like I did). I'm pretty sure I stole the idea from someone else - sorry I can't properly give credit. Here are the cards as pdf and doc.

It was fun to present to and work with such an enthusiastic group of math teachers. I hope you found something that will help you rethink your math class.