Wednesday, 28 January 2015

Calculus - Day 1

Update: I turned this into a Desmos Activity Builder which you can find here.

Semester 2 begins on Monday and I want to do something interesting with my 2 calculus & vectors classes. I thought it would be good to have them "play" in Desmos for a class. I want them to have fun but for the work to be meaningful so this is what I came up with, very much in the spirit of Daily Desmos (which I have not contributed to for ages :(). I will randomly pair them up and have them recreate as much as they can of this:


video

Here is a picture of it in case you can't see the video:



They should all be able to correctly determine the equations of the curves, but the animation will be a much bigger challenge for them. I want them to see what is possible with Desmos, yet still within their reach.

I would love your feedback!

Tuesday, 27 January 2015

Warm Ups

August 2, 2015: Update
I updated my warm-up set - the new file can be found here.
- Mary

I finished getting my warm ups ready for MFM2P semester 2! A huge thank you goes out to the teachers from whom I stole, especially Andrew Stadel for Estimation 180, Fawn Nguyen for Visual Patterns (the Visual Patterns are linear until week #11, then a mix of linear and quadratic) and John Stevens for Would You Rather.



Here is the link to my file in DropBox - it is a Word file so please edit to make these work better for you! Also, note that there are a couple of days missing when we don't have school.

Sunday, 25 January 2015

Staples

I decided to create handouts for warm ups for one of my second semester classes. I wanted to formalize some of what I already do to help strengthen their number sense. I plan on doing counting circles which my students really seem to dislike(!). Nevertheless, I think there is great value in doing counting circles, both in terms of the skills and the culture it helps develop in the classroom. We will also be doing more Estimation 180, Visual Patterns, Would you Rather along with balance benders, Daily Desmos, Always-Sometimes-Never and math talks. I created the handout and have filled in the warm ups for the first 5 weeks. They look like this:



There will be 18 weeks worth within the next few days (let me know if you want them - I'm happy to share). I then plan on copying them for each student and putting them in a duo-tang which will not leave the classroom. With the possibility of 24 students in that class, that makes 432 copies. We are repeatedly told not to make any unnecessary copies at school so I began thinking that it might be simpler to send my warm ups to Staples for copying. I looked at Staples prices and this is what I found:


Hmmm. The cost for 432 copies would be $34.56. But the cost for 500 copies would be $30. I see a nice (real-world!) math problem here.

Friday, 16 January 2015

Giving Choice

The more I teach, the more I believe that giving students a choice on evaluations is a good thing. By this I mean, letting them choose the level of difficulty of a question in order to show me as much as they can.

For example, I could ask students to come up with the equation of a parabolic arch, in multiple forms, given certain parameters. They must then decide elements that will make their solutions easier or more complex. Where should I place the axes? Do I want the zeros to be integers? Do I want the 'a' value of the quadratic to be an integer? Students can choose to make their question more difficult and demonstrate a greater understanding of the curriculum expectations. Students who are still learning and not as solid in their understanding can set the bar a little lower, yet still show a lot of good math.

The argument I hear against this doesn't come from students, it comes from teachers. There is no answer key. Every paper is different. However, tools like Desmos make life much easier when I am marking these types of questions. I feel that technology makes these questions manageable from a busy teacher perspective, but also makes these questions essential as they can't be Googled. I also feel that I am not limiting any of my students (some go way above and beyond my expectations, which is really cool), nor am I making it such that a student doesn't have an entry point.

Wednesday, 7 January 2015

The Ambiguous Case

This song came on the radio this morning, which naturally made me think of trig (less the song, more the band - sorry if I was ambiguous). I thought that if I was teaching the ambiguous case I would start with an activity like this.

Student would be paired up and one of each pair (let's call this student A) would receive an envelope. Their job would be to describe the contents of the envelope to student B so that student B could replicate it. Student B could not ask any questions, nor could they show their work until they finished. Then the two students would compare triangles.

Inside the envelope would be something like this:


I would be curious to see how many students would create a triangle that matched.

The irony here is that I don't teach the ambiguous case. I teach trig before it and trig after it, but not that part!

Tuesday, 6 January 2015

One Sad Thing, One Good Thing

I have always been a dog person. Yesterday, our family lost Théa, one of our Bernese Mountain Dogs. We are all incredibly sad. She gave us so much and I am thankful that she let us be part of her life.



Hard as it is, life goes on. One good thing today happened with my grade 10 academic class. They were preparing for tomorrow's test on quadratics. One (fake-world) question was about someone making something and the equation modelling profit was quadratic. Several students couldn't understand why profit would go up, then go back down. When I explained it to them, they thanked me and seemed to be genuinely expressing gratitude to have understood something new that was somewhat connected to real life. They made me feel valued.