Friday, June 24, 2016

Math Links for Week Ending June 24th, 2016

I finally put this post together after literally months of tweaking. I even found some stuff out as I was shooting the demo video that was a revelation. The premiss is that we have to investigate the nature of the power rule for derivatives in Calculus. So this does it two ways. First students do so with paper & pencil to build the derivatives from the slopes of tangents and then they take it to the next level with a Desmos activity that extends to cubic functions.
Curriculum Tags: MCV4U

There is no secret that I have fell back in love with coding and love that many teachers have shared what they are doing with coding and math. Check out these videos from @MrAspinal where he shows how he uses coding with math in his class. Thanks to @Ecokrisb for this one
Curriculum Tags: Gr7, Gr8

I came across this new Twitter feed this week. Sounds like fun. If you are an Ontario Math teacher (or any math teacher) you might be interested in participating in a bi-weekly chat on Twitter. The next one is Tuesday June 28th from 8-9PM EST.
Curriculum Tags: All

In a conversation with @mathgarden this week I was introduced to The Global Math Project. He's an ambassador for the project which hopes "... to thrill 1 million students, teachers, and adults with an engaging piece of mathematics during one special week in 2017". Go do the site to see how you can participate (and even become an ambassador). And if you want a taste, see the series of videos below from @jamestanton to see what exploding dots are all about.
Curriculum Tags: All

Global Math Week 2017 Preview from The Global Math Project on Vimeo.

Although this is old (check out the computers in the video), I love anything about weird probability calculations. In this case it's a company that specializes in underwriting contests like "hole in one" or "free throw" or "field goal" competitions where the winner might win a large sum of money. In those cases, the people rarely has the money to pay the winners but instead pay a smaller fee to an insurance company who would pay the big prize if someone wins. Like when Brian Diesbourg missed at the 20, 30 & 40 yard lines and then nailed the 50 yard shot to win a million dollars. So here is a short video of what is involved in doing that sort of probability calculation. And even though this is older too, here is the audio of a talk from a similar insurance adjuster (Risky Business). It's a little dry but I find it fascinating. Thanks to Joseph Bengiovanni for this one
Curriculum Tags: MDM4U

I am a big fan of dynamic math software. There are a lot of choices out there. My two faves are Geometer's Sketchpad and Desmos (with Geogebra not far behind). So I am always looking for something new. This week @MaryBourassa tweeted out about DudaMath. This is a free, multi-platform dynamic math package that does, calculations, algebra, patterning, geometry, statistics and more. This week it looks like they added a package to do distance time graphs. I think there is a lot more to test out here and with each tool there is a helpful step by step video so don't be shy, give it a try. One thing I do like is the fact that you can draw stuff on the screen free hand and it turns it into objects (lines, angles). It makes the interface nice on the iPad
Curriculum Tags: All

I love articles about real mathematicians and this one interviewing @FryRsquared. And don't forget her TED talk (and book) on the Mathematics of Love. Thanks to @mrhonner for this one
Curriculum Tags: All

Though I had kind of seen this before, it wasn't until @mathgarden pointed out that Exploding dots would be used for the Global Math Project and then went on to explain how they can be used all the way up to dividing polynomials. I was intrigued and spent about 30 min going through some of @jamestanton's course on exploding dots and fine it quite cool. And I am happy to say that I was able to figure out the method that he teased at the end of the first polynomial division page (without watching the next video). Take the time to watch these three which is all I needed to get me to polynomical division (I don't think you will be disappointed) and then maybe check out his other courses on things as diverse as fractions and combinatorics.
Curriculum Tags: MHF4U, All

Do you want a video that you can used to talk about how transformations are used? Or how about a practical use for complex numbers. If so then watch this @standupmaths (with @henryseg) video on the mathematics of spherical videos (I love the part with the point source of light in the 3D printed sphere). If you are not sure what they are then you might want to look at my blog post on Google Cardboard.
Curriculum Tags: Gr7, Gr8, MCR3U

Thanks to @MrOrr_Geek's tweet and @ddmeyer's response about the worlds largest nerf gun, I now know there is a twitter hashtag for #mathphotos16. So many good pictures.
Curriculum Tags: All

I could see using this in a grade 8 class or having grade 11s prove it algebraically
Curriculum Tags: Gr8, MCR3U,

Friday, June 17, 2016

Math Links for Week Ending June 17th, 2016

In Ontario, when we introduce Pythagorean Theorem, we are supposed to do so by considering the Pythagorean Relationship instead. That is, the fact the the area of the square on the hypotenuse equals the sum of the two squares on the sides of the legs. This is the geometric version of PT. And as it turns out it doesn't have to be a square on each side. As it turns out it can be any shape as long as the size of shape is scaleable based on the sides of the right triangle. You can test that out in this simple multipage WebSketch that shows the relationship works for many different regular shapes and finishes showing that it works for any irregular shape too.
Curriculum Tags: Gr8, MFM1P, MPM1D

I was skeptical at first when I saw the blog title "Worst Problem Ever" from @MarkChubb3 but like any good title, it gets you in the door. He talks about giving a simple surface area of a rectangular prism problem where it happened to work out the that both the surface area and volume worked out to the same number (with dimensions 5x5x10) - obviously not the same units. But the cool thing was the opportunity for learning that he took at that time. He challenged his students to find other rectangular prisms that had the same property. Those kids probably will never ever get the volume or surface area wrong because of this because they had a purpose for doing both and they were engaged to do it.
Curriculum Tags: Gr7

I love this site from @c0mplexnumber on the cross between Art and Math. gives us man different ideas of how art and math mix. There are a lot of ideas here that fit many different grade levels. Thanks to @MathGarden for pointing this one out.
Curriculum Tags: All

I totally love this use of Desmos Activity builder by @ddmeyer. It's a great example of having kids discover something rather than just giving it to them. In this case it's the fact that if you take the diameter of any circle and create a triangle using it and any point on the triangle, it creates a right triangle. This way it is hidden until you use the overlay feature in the activity. The result is magical. The result would be a cool way to do analytic geometry.
Curriculum Tags: MPM2D

A great little @ddmeyer video that make students think about linear relations where there is an initial value (partial variation). Very simple yet the video makes it just that tiny bit more engaging
Curriculum Tags: MPM1D, MFM1P

I though this was a totally interesting way to consider how a function works. A bit of warning though, it might not be for sensitive students (and probably not vegans). Thanks to @GrayKimBKim for pointing this one out.
Curriculum Tags: MCR3U, MCF3M

This is a really great problem that, when I heard it, wasn't sure it was true. Consider two people, one who invests $2000 for 8 years starting when he was 19 and then stops but lets that collect interest for another 27 years. Another starts investing $2000 each year at 27 and does so for 39 years. Who will have the most money in the end. The answer will suprise you. Even if you can't get the artificially high interest rate used (12%) it does show the power of compound interest. Thanks to Giovanni Spadafora for this one
Curriculum Tags: MCR3U, MCF3M, MBF3C

Wow, someone at 538 sure did the research on Dwayne "The Rock" Johnson. This is a great reminder that data is everywhere and it doesn't take much to find stuff that students might be interested. In this case there is a lot of info on The Rock and his movies and two different graphs that would appeal to two different types of analysis. First you have the simple bar graph categorizing his movies and the other is a scatter plot comparing the Box office take to its movie rating. The second graph I like because the analysis is not your typical scatterplot type. That is, no line of best fit - you have to really make some inferences in other ways of grouping.
Curriculum Tags: Gr7, Gr8, MBF3C, MAP4C, MDM4U

Saturday, June 11, 2016

Math Links for Week Ending June 10th, 2016

I have started to put some of my calculus activities online. The first one is a card matching activity where students are given a set of cards with linear, quadratic or cubic functions on them and they are to match them in pairs (functions and their derivatives). A relatively simplistic activity that reinforces how functions and their derivatives are connected.
Curriculum Tags: MCV4U

Another calculus activity that I finally completed has students graphically develop the derivative of quadratic and cubic functions by guessing at the slopes of the tangents. If they get those tangents correct then the derivative will appear. It's a great activity for students just as you are introducing the idea of what a derivative is. Eventually I will have a low tech version of this posted but for now, the tech version. Click on the link below to make your own copy.
Curriculum Tags: MCV4U

Apparently I had some time this week because my third post was a set of Canadian data (specifically, Ontario) about rebates on electric cars. The premiss of the article is that luxury electrical car owners are getting undeserved rebates. But there is lots of data to be had for single and double variable analysis.
Curriculum Tags: MBF3C, MDM4U
Some cool stuff from the Friday five from @Desmos. I love the Sketchy Parabolas as it's a great way to ease into quadratics without getting too technical. Then once students grasp their parabolic knowledge they can try the quadratic Des-Draw and then end up doing some Calculus and learning about Turning points. Plus a couple more.
Curriculum Tags: MPM2P, MPM2D, MCV4U

I typically don't focus much on these MindShift posts but this one resonated with me. The idea that we shouldn't be giving students all the information but let them discover on their own. And a strategy to get deep discussion in your math classes. Thanks to @KMarkPet for this one
Curriculum Tags: All

Here is a fun little video from @StandupMaths on whether any of the town squares in New York City are actually squares. Along the way he helps define what a sqaure is and looks at the properties of them as well as triangles.
Curriculum Tags: Gr8

This week I was in a virtual learning session that had a great problem that could span several grades. The premiss was that we were given the picture below and asked to show how it proves the equation shown. We had some good solutions but the most interesting stuff was when we got to see some of the solutions from students from different grade levels give their solutions (from grade 2 all the way to the gr9) . See them here and some of our solutions here. My favroute was the Math vine below
Curriculum Tags: All

Friday, June 3, 2016

Math Links for Week Ending June 3rd, 2016

I really love this activity from @alexoverwijk. And beyond the activity, I love all the detail that he includes as the history of the lesson study that went with the activity (the blog post is loooong but great). The activity has students put into groups and each given an x value. Then each group calculates a y value for a series of functions using that x value. All of those y values are plotted on a number line strip and then all the strips are placed on the wall ordered by x value. What results are the graphs of all of the functions. So good. There are some great suggestions for extensions to later grades and I love that he included all the comments from the teachers as they did the lesson study.
Curriculum Tags: MFM2P, MPM2D

I have started to put my GSP sketches online (here) but I just found this site that has all kinds of online GSP sketches. So far my favourite one is this one for investigating quadrilaterals. Besides the measuring tools I love that as you drag the vertices, the labels of the types of quadrilaterals change as required. But check out all the other sketches too
Curriculum Tags: Gr8, All

A couple of posts from Better Qs. This one from @MrJohnRowe is a little tweak on a classic trig question. I like how several answers are given and students are asked to determine what question is being asked to get each answer. Download the worksheet at the link below
Curriculum Tags: MCR3U, MCF3M

And the second from @srcav is a nice trig simplification equation. It looks complex but then wait to see what it simplifies to.
Curriculum Tags: MCR3U
Some Desmos Friday fives to get caught up on. This time with an neat activity with families of polynomial functions, roots of polynomial functions, neat data set about marathon times, and there is a new Activity Builder feature that allows students to draw lines right on the graphs (sketch). Some of those cover linear equations, another marathon activity, a neat data activity for predicting homerun records, and more
Curriculum Tags: MHF4U, MDM4U

Though it kind of bugs me that this is only available for teachers in the US, I thought I would mention it anyway. Are you a creator of Desmos activities? If so, maybe you want to apply get a Desmos Teaching Fellowship. See the link below for details
Curriculum Tags: All

I like this Keynote that @paul_math did for the Ontario College Math Association with the title "The Evolving Thinking Problem-Solving Classroom". You can see the whole keynote here but I think he summed up the way I have been thinking with this self quote "They are inflexible in their thinking because we made them rigid in their learning".
Curriculum Tags: All

I thought this kind of summed up how I used to teach years ago, I think it's a good reminder that sometimes we can focus too much on procedure. It kind of juxtaposes well with the post directly above.
Curriculum Tags: All

I seem to be talking more and more with people who are experimenting with going gradeless. Here's a post from @HTheijsmeijer talks about her journey towards that goal.
Curriculum Tags: All

This is older but I was reminded of it recently. It's @stephenStrogatz talking about parabolas and pendulums on Radiolab
Curriculum Tags: MPM2D, MFM2P, MCF3M, MBF3C, MCR3U

Who needs to read the whole article when you can look at @wheeler_laura's Sketchnote?
Curriculum Tags: All
Some good trignonometric humor
Curriculum Tags: MHF4U
Collect some data on Doritos Roulette and maybe Doritos will contact you
Curriculum tags: Gr7, Gr8, MBF3C, MDM4U