## Friday, February 27, 2015

### Math Links for Week Ending Feb. 27th, 2015

Giving students feedback that is timely is important for helping them learn from their mistakes. Giving them enough assessments so that they can actually learn from those mistakes is also important. Another nice thing that can be done to help students is to help them to become more self aware of their problems.Doing all of these things on a frequent basis is tough. Part of the problem is that, often, when teachers give written feedback, students ignore it while focussing only on the mark. In fact, there are studies that suggest that if you really want students to gain from written feedback, then only give them written feedback. They found that when students were given a mark & feedback that was just as effective (ie not effective) as just giving them a mark only in improving student learning (students were often only interested in the mark and would just ignore the written stuff if there). That being said, Amy at the Square Root of Negative One blog seems to have a workflow that takes care of all of that. Assessments that students self grade, comment on and correct before the teacher even sees it. Check it out here
Curriculum Tags: All
http://squarerootofnegativeoneteachmath.blogspot.ca/2015/02/giving-immediate-feedback-without.html

I like graphic organizers. And although there isn't just one way to attain prime factorization, this graphic organizer can help when students do.
Curriculum Tags: Gr7, Gr8
http://mathfour.com/arithmetic/prime-factorization-graphic-organizer

I like this activity from SlamDunk Math. They spend a lot of time attacking the curriculum from many angles and repeatedly throughout the year (they call this spiralling through the curriculum). I used to do something just like it to talk about linear relations and modelling. And here is the results of their activity. In this activity the point is to try to determine how much rope is needed to tie a knot (or conversely how does the length of the rope change with every knot tied?). That is, as you continue to tie knots in a rope, that rope becomes shorter. So you collect data about the number of knots and the length of the rope. Then repeat with a different thickness of rope. Check out their data at their site. The last time I did this it was with my MAP4C class. You can see my data set here. Update March 6th. Jon Orr has put his spin on it. Check it out at this link here
Curriculum Tags: MPM1D, MFM1P, MFM2P, MAP4C, MDM4U
http://slamdunkmath.blogspot.ca/2015/02/ropes-of-different-thickness-and-equal.html

I was actually surprised a bit by this activity in that my first instinct was to say that the relationship would be non linear. Spoiler alert. It's linear (when I thought about it, it made sense). The relationship in question is the connection between the side length of of a square and it's diagonal. Check out the video and all handouts at the Tap Into Teen Minds blog.
Curriculum Tags: MPM1D, MFM1P, MFM2P, MAP4C, MDM4U
https://tapintoteenminds.com/2015/02/19/connecting-relationships-multiple-strands/

Animated Gifs are pretty popular on the web. And IFL Science had a post on some animated gifs relating to math. Some of them are good others, not. Some of them fit Ontario curriculum, others not. There are 21 all together. Check them out at this link but here are a couple to get you started.
Curriculum Tags: Gr8, MFM1D, MFM1P, MCR3U, MDM4U
http://www.iflscience.com/brain/math-gifs-will-help-you-understand-these-concepts-better-your-teacher-ever-did

## Friday, February 20, 2015

### Math Links for Week Ending Feb. 20, 2015

Lately I have been finding a lot of resources that resonate with the idea that just focusing on practicing questions in math class is not where our focus should be. That we have to incorporate more problem solving, inquiry and messiness into our math student's every day lives. Here is another reminder from Andrew Stadel and Steve Leinwand in what they call an "Elevator Pitch"
Curriculum Tags: All

I have been finding a lot of resources lately that are the result of two or more people collaborating via the Interwebs. Here is another one. Amy at the Square Root of Negative One blog started with an activity to teach properties of polynomials functions that just had cards with graphs. Then Julie at the I Teach Math blog tweaked it to include description cards so that they could be used as a card matching activity. One of the things I liked on Amy's original blog post (from 2013) was this statement:
"This used to take me 4 minutes. I would write four rules on the board and they would copy them down.Today it took 24. But it was fun. And later I saw somebody end-behavior dancing in the hallway.This approach is better than just telling them, right?"
That is, sure it's faster to just tell them, but they likely won't retain the info or enjoy it as much. Get all the cards from these two posts.
Curriculum Tags: MHF4U
http://ispeakmath.org/2015/02/16/polynomial-roots-and-end-behavior-card-sort/
http://squarerootofnegativeoneteachmath.blogspot.ca/2013/01/how-i-sextupled-time-it-takes-to-teach.html

Here's a great maximizing volume activity that can be done with grade 9 students for that part of the curriculum. Of course it could be a calculus activity too but the basic principle is "what is the largest open topped box you can make from a standard piece of paper. This is actually an old post from Fawn but was just mentioned by used by Julie at I Teach Math and updated from the original 2013 post with Desmos and Google forms.
Curriculum Tags: MPM1D, MFM1P, MCV4U
http://ispeakmath.org/2015/02/16/maximizing-box-volume-with-popcorn/
http://fawnnguyen.com/why-wait-for-calculus/

A nice proportion activity is to take a standard Barbie and scale her up to what human size would be. Kids are typically shocked at how unrealistic she is. And here are three takes from three different people on how that goes in class
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
http://ispeakmath.org/2015/02/19/barbie-proportions-geometry/
http://fawnnguyen.com/playing-barbies-2/
http://iisanumber.blogspot.ca/2013/01/if-barbie-were-as-tall-as-me-lesson-in.html

Mary at the Making Math Meaningful blog has an activity that reminds me of our own squaring activity for discovering Pythagorean Theorem in grade 8. It's one of the activities she is using to spiral through the curriculum in grade 10 applied. As she did last year, this year she is blogging about each class. If you teach grade 10 applied and are into something a bit more progressive, then check out her blog
Curriculum Tags: Gr8, MPM1D, MFM1P, MFM2P
http://marybourassa.blogspot.ca/2015/02/mfm2p-day-13-triangles.html

I know it's late but the Valentine's Desmos app was a fun way to say you love someone - with math. You can still send them a Math-o-gram
Curriculum Tags: All
http://mathogram.desmos.com/

## Friday, February 13, 2015

### Math Links for Week Ending Feb 13th, 2015

On the Math with Bad Drawings blog there has been a series of posts on over reliance on using algorithms in place of conceptual understanding. The series was called How to Avoid Thinking in Math Class. We have had conversations similar to this at our end. The way that I have always framed it is that "we can teach monkeys to use the quadratic formula (but they won't understand what they are doing)". The last of the six posts is titled The Church of the Right Answer. And starts with an interesting thing a student said:
So, like, I don’t really understand anything you’re saying, but I can still get the right answer. Oh, you were talking about this extra stuff, like the ideas behind it and everything. I don’t… you know… do that. So is that okay? I mean, as long as I can get the right answer? - A. Student
The whole thing reminds me of the Phil Daro video I posted last year where he talks about our penchant in North America for "Answer Getting" (if you haven't seen this video then I strongly suggest you take the time to watch it). I think these are very good discussions to have and if you want to start then I suggest starting with this series of posts.
Curriculum Tags: All
Post 1, Post 2, Post 3, Post 4, Post 5, Post 6

I have mentioned before that I like performance tasks. I also like when teachers collaborate with each other via the Interwebs. Last year I mentioned Alex Overwijk's grade 10 performance task and this year Amy Lin used it as a model to create a performance task for her grade 9 and 10 applied students. She has posted the results (and the task) online on her blog. See the link below for the full report.
Curriculum Tags: MFM1P, MFM2P

Here's a nice 3Act task from Jon Orr. Watch the video below of Act 1 to see that the general purpose of the task is to figure out the model for how points are given out based on where Mario lands on the pole. You can make connections to all kids of functions including quadratic and exponential. He uses PearDeck as his technology of choice which has the nice feature of allowing students to drag points to secure their guesses for things. Depending on which course you are using this in will probably require some adjustment of the task but still it has a lot of places that it could be used.
Curriculum Tags: MBF3C, MCF3M, MCR3U, MHF4U, MAP4C
http://mrorr-isageek.com/?p=3704

I like this simple investigation of sine law on Dave Lenovaz's Sine of the Times blog. It uses a Geogebra plugin that students interact with to complete the investigation. This would really save the time of actually having to measure all the angles and side lengths to let you get to the theory relatively quickly. Students get  the worksheet which has direct link to the Geogebra Sketch.
Curriculum Tags: MPM2D, MBF3C
http://sine-of-the-times.blogspot.ca/2015/02/sine-law.html

I love kinetic sculptures. Especially ones that help me teach math. In this one there is all kinds of math going on. From the 3D graphing that could be linked to vectors to the moving functions that could be linked to advanced functions.
Curriculum Tags: MCV4U, MHF4U

And this one is a bit older but follows the same principles.
Curriculum Tags: MCV4U, MHF4U

Keeping in line with the featured link above, this video might give some insight as to what an extreme version of just applying an algorithm to get an answer might look like to someone who doesn't get it. This is from a British comedy show and it is a skit of a fictitious game show called Numberwang where the rules are nonsensical. Like having a function machine with no discernible pattern.
Curriculum Tags: All
https://mythagon.wordpress.com/2015/02/08/in-which-british-comedy-is-investigated/

I saw this at a workshop I was at yesterday. Surely there is some math that could be done here on patterning or series and sequence.
Curriculum Tags: Gr7, Gr8, MCR3U

I love this interactive infographic about how accurate the predictions of ground hogs are on Groundhog Day. For what ever reason our society has put the start of spring in the hands of small rodents. This data set is from 30 years of predictions of all the ground hogs in the US and whether they predicted when the weather would shift. When you look at the data you really get a sense that it is as accurate as flipping a coin. So that is why I think, beyond the data, this is a great example of probability in real life.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U
http://www.washingtonpost.com/blogs/wonkblog/wp/2015/01/31/40-years-of-groundhog-forecasts-mapped/

Taking pictures of real things and then bringing them into the classroom is a nice way to make something abstract seem real. In this case it is the idea of "what is the angle for any vertex of a regular heptagon". Fairly abstract question until you come upon this park bench. Check the site out for more images and the connection that in real life things don't always turn out as expected.
Curriculum Tags: MFM1P, MPM1D

## Friday, February 6, 2015

### Math Links for Week Ending Feb. 6th, 2015

Have you heard of the Internet? How about blogs? Well if you answered yes to those two questions then you know how often one teacher will post something and then another will see it and then make it better or customize it in a different way. Some of this good collaboration has led to some really good ground work on using gamification and badges to measure assessment in math class. Jon Orr started the process and Kyle Pearce did some modifications and they look like they have a system that works really well. They are basically abandoning traditional tests for ongoing assessment of learning goals directly. But not only assessment but mastery. Then they take it all and cram it into a Google Sheets document with a page that each student has access to that has their entire practice. And then Jim Pai puts his spin on it. There is no way I can summarize it all here. Seriously, take a look at their posts to get the 411. Way to go team.
Curriculum Tags: All
http://mrorr-isageek.com/?p=3629

I think sorting activities are a nice way to have students do work in a very painless (to them) way. But the painful part is often for us teachers who have to actually spend the time to create them. This is especially since the time that it takes to make the activity is often longer than it actually takes for the kids to do the activity. So I am always happy when teachers share their activities. In this one, from Miss Calculate, the sorting is about recognizing the different types of quadratic factoring. As it is right now it would be only appropriate for grade 10 academic, grade 11 university and university/college and grade 12 college. However it could be modified for other courses or be used for review in some of the grade 12 university courses.
Curriculum Tags: MPM2P, MFM2D, MCR3U, MCF3M, MBF3C, MAP4C, MHF4U
http://misscalculate.blogspot.ca/2015/01/factor-sort-review.html

I like visualizations that make people think differently about everyday items. In this set of slideshows we get a sense of how portion sizes have changed over the years. Not only would this create a good discussion about health but also a great way to talk about proportions.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MAT1L, MAT 2L
http://www.nhlbi.nih.gov/health/educational/wecan/eat-right/portion-distortion.htm

Here is a really neat way to talk about unit rate. Have students answer the question: "Would you rather have a penny or a potato chip?". That is, how much does one potato chip cost?
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MAT1L, MAT 2L
http://www.wired.com/2015/01/rather-potato-chip-penny/

We have all seen the Ferris wheel type problems. This isn't much different than what you may have seen but I like the added feature of actually creating minature Ferris wheels from pipe cleaners. Now if you use something like this in grade 11 then it will probably be more along the lines as an introduction to trig functions where as in grade 12 you can go deeper since you have the use of radians.
Curriculum Tags: MCR3U, MHF4U
http://teachhighschoolmath.blogspot.ca/2015/01/math-is-lways-better-when-you-do-more.html

It's such a good tool that Desmos should be a staple in every math class. And so Mary at the Making Math Meaningful blog shows us a simple way to both introduce Desmos to her Calculus kids and start the course off with some discovery.
Curriculum Tags: MCV4U
http://marybourassa.blogspot.ca/2015/01/calculus-day-1.html

And some more collaboration. This set of mini challenges from Michael Fenton is a great way to use Desmos to promote thinking and learning with linear equations and also parabolas. So much better then a bunch of worksheets. But then Mathy Cathy gets ahold of it and creates some lovely Thinglink online worksheets that compiles them all. Again, well done team
Curriculum Tags: MPM1D, MFM2P
http://reasonandwonder.com/match-my-graph-linear-functions/
http://reasonandwonder.com/match-my-parabola/

More info on gap closing with boys. In this case a "tutoring program on steroids"
Curriculum Tags: All

To me this is a no brainer. If all you do is "Drill and Kill", that's not very effective.
Curriculum Tags: All

When talking about probability we often use games as examples. Rock, Paper, Scissors is a game you might consider. Especially since we often talk about "Fair" games. However, when you incorporate the element of psychology then maybe it isn't fair. And if it isn't fair, then if you know why and your opponent doesn't then that gives you an advantage. So with that, Numberphile is gonna tell us how to win.
Curriculum Tags: MDM4U