Friday, January 30, 2015

Math Links for Week ending Jan 30th, 2015

Last year Mary at the Making Math Meaningful blog gave us a day by day glimpse of how she spiralled through the curriculum in her grade 10 applied class. This year she starts of giving her starter for her entire semester of classes. All 5 days for each of the 18 weeks. Check out the download on her site. Thanks Mary
Curriculum Tags: MFM2P

Andrew Stadel has maintained the Estimation 180 site to entertain a great discussion on what is essentially the idea of being numerate. Now he expands to a Twitter feed: @Estimation180. So a tweet a day to satisfy his daily estimation fix. Thanks to Mary Bourrassa for this one.
Curriculum Tags: Gr7, Gr8, MAT1L, MPM1D, MFM1P, MAT2L, MPM2D, MFM2P, MEL3E, MEL4E
It turns out there are some strategies for doing well at Monopoly. All it takes is some work with probabilities. Take a look here
Curriculum Tags: MBF3C, MDM4U

I really like these visualizations of the effectiveness of various medications. They really connect the idea of how visualizations can make a concept much more clear. For example, many people will tell you that someone who is at risk of a heart attack should take aspirin. But the data shows that if two thousand people did this, only one would avoid having a heart attack. Take a look for the dynamic versions on the site below.
Curriculum Tags: MDM4U

In measurement, precision and accuracy are often use synonymously but they are different. It is probably worth talking about this when doing anything to do with measurement. One of the more interesting bits is how some electronic conversion devices deal with ounces and grams.
Curriculum Tags: All

It turns out that we have been giving math problems with contrived contexts since at least the 12th century:
The Liber mahameleth, which has just been translated into English, was one of the largest books on mathematics written in the Middle Ages.
And some of the problems might look familiar: 
A messenger is sent to a town and advances daily by twenty miles. In how many days will another messenger, sent five days later and advancing daily by thirty miles, overtake him?
A good way to bring your students back to dark ages :-)
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MPM2D, MFM2P

 I have added a couple more Geometer's Sketchpad files to my Engaging Math blog. The first is a practice file for doing the Pythagorean Theorem. This will randomly generate right triangles with either the hypotenuse or a leg missing (you decide). You can then check the solution and try another. Although PT is in the grade 8 curriculum, this file is probably not appropriate for it since in grade 8 the focus is mainly about the geometric representation.
Curriculum Tags: MPM1D, MFM1P, MPM2D, MFM2P

The second one is for practicing determining the midpoint of a line segment. The first page lets you create your own problem then check the answer and the second will generate a random set of points for you to find the midpoint. Both of these files are intended for students to use directly and work really well on the free Sketchpad Explorer app on the iPad
Curriculum Tags: MPM2D

So it turns out the best visual effects laden movies require a lot of math to pull off. And those mathematicians who help? Well, they get Oscars.
Curriculum Tags: All

Visualizing data is always a good thing for humans. Here is a video that ties to visualize the different ways we can look at 200 calories by showing how much of different types of food equal that. It think it might have been based on this graphic that has been circulating around the web for some time.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

I am a sucker for these videos as I think they give a real world application for vector addition. Plus the fact that this is just at one airport. That is some crazy cross winds. Thanks to Mark Esping for this one.
Curriculum Tags: MCV4U

Some geometric fun from George Hart in honour of SuperBowl Sunday.
Curriculum Tags: All

And why not a bit more kinetic art that has mathematical precision.
Curriculum Tags: All

On a recent Mythbusters they did a whole show on Raiders of the Lost Arc. On one of the segments, they were simulating the part of the movie where Indie jumps over the chasm and they used quadratic modelling pretty explicitly to determine the distance. Too bad this is only an image of what was on my TV screen but hopefully you get the idea
Curriculum Tags: MPM2D, MFM2P, MBF3C, MCF3M, MCR3U

This is a cool exercise in proportional reasoning. In this infographic they take the size of the country and change it based on the population of the people in that country. It's also good for data management discussions about the validity or comparison of big numbers. Boooo, Canada almost disappears. Make sure you look at the original image in large format to get the whole picture
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MDM4U

Friday, January 23, 2015

Math Links for Week Ending Jan. 23rd, 2015

So Nix the Trix is an initiative born of Twitter. I mentioned it first way back here. The idea is that we need to abandon short cuts in math (eg cross multiplying) in favour of conceptual understanding instead. The new version can be downloaded as a pdf or ebook for free. It's a collaboration between a number of teachers from the Twitterverse (or more specifically the Math Twitter BlogoSphere #MTBoS).
Curriculum Tags: All

One of my favourite books about autism, math and dead dogs is now a Broadway play. The Curious Incident of the Dog in the Nighttime is a great little novel that has a compelling story as well as math interwoven through out (including chapters numbered only with prime numbers). Now it's a Broadway play. The actor who plays the lead is interviewed here on Science Friday
Curriculum Tags: All

I like this post from Dan Meyer where he highlight what has become to have the moniker "WTF problems". These are problems that, when given to students, cause them to pause and wonder what is going on. Although there are only a few examples, the ones give are pretty good. For example:
Here are some points in the plane:
(4, 1), (17, 27), (1, -5), (8, 9), (13, 19), (-2, -11), (20, 33), (7,7), (-5, -17), (10, 13)Choose any two of these points. Check with your neighbor to be sure that you didn’t both choose the same pair of points. Now find the rate of change between the first and the second point. Write it on the board. What do you notice?
I like the idea of giving students different things to do and having a surprising result. Hopefully there will be more to come or if you have your own then add it in Dan's comment section.
Curriculum Tags: MPM1D, MFM1P
I like this question posed by Patrick Honner: "To increase the volume of a cylinder, is it better to increase the radius or the height?" Sometimes it is just the question that you ask that makes a simple thing (in this case, calculating the volume of a cylinder) a little more engaging for students. 
Curriculum Tags: Gr8, MPM1D, MFM1P

A second post from Mr. Honner is a nice little talk he does about how technology can fail you. I really like how he takes the time to talk about what various technology does with things like holes and division by zero in functions. These are things that I have done (zooming into a hole) but I really like the ease and demeanour that he does it in such a nice and concise package. Take a look.
Curriculum Tags: MCR3U, MHF4U, MCV4U
Here is a nice video that could be used to talk about distance time graphs with non linear relations. I think you could use it in grade nine as a real example of both non linear relations and distance time graphs but could be used equally as well in advanced functions and calculus when talking about rates of change
Curriculum Tags: MFM1P, MPM1D, MHF4U, MCV4U

Some nice connections to Fibonacci numbers on these 3D printed sculptures.
Curriculum Tags: All

This may be quite the opposite of how I started this week's post with Nix the Trix but I still like this simple reminder of the properties of division by zero. Plus it comes with a printable template.
Curriculum Tags: All

Friday, January 16, 2015

Math Links for Week Ending Jan. 16th, 2015

I have mentioned Alex Bellos before (here) and talked about his books and his quest to find the worlds most favourite number. Here he is on Story Collider talking about how that quest started (and how he himself blew off the idea of having a favourite number in the first place). I think that it is important for students to get these parts of mathematics so that they don't just see the drudgery of just doing problem after problem. Things like this bring out the humanity in math.
Curriculum Tags: All

With all of the great and interesting ways to calculate or estimate the value of Pi, this is probably the most dangerous. It requires firing a pump action shot gun (and perhaps yelling "Get to the Choppah!!!")
Curriculum Tags: Gr8

If you need a good example of how probability works (or maybe doesn't work) check out this story about how a couple won on the slots on a machine that hasn't had a jackpot in over 20 years. That is certainly on the tail end of the probability distribution.
Curriculum Tags: Gr7, Gr8, MAT1L, MAT2L, MBF3C, MDM4U

OK this is not so much an article but a great article about how tough this old calculator is. I think I remember having one just like it and it probably met its demise through some catastrophic failure (eg crushed, dropped from a high height etc). Fun none the less
Curriculum Ties: All

We have these discussions in class about misleading statistics and statistical representations all the time and hopefully you have read "How to Lie with Statistics" to help hone your skills on giving examples to students. But as it turns out, How to Lie with Statistics might be used more nefariously by certain congressional departments. This is the first time that statistics has probably been discussed this way in a congressional hearing. See a couple videos of it here (especially if the embedded video doesn't work).
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U, MAP4C

Another example of a graph that misrepresents by chopping the scale off (as pointed out in How to Lie with Statistics). This time coming from a particular weather network. You would think that a network that uses science so much would be more careful about this.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

And lastly a probability question that may not have an answer. At the very least it should develop some interesting conversations.
Curriculum Tags: MDM4U

Friday, January 9, 2015

Math Links for Week Ending January 9th, 2015

We have been adding to our Engaging Math blog. This time it's one of the first activities we ever made for grade 9 applied. We started by modelling the board after Candyland and then generated questions dealing with determining angles. Kids really seem to enjoy doing math while playing this game. It is meant as a review of skills and works really well.
Curriculum Tags: MPM1D, MFM1P

The Dot Physics blog continues to milk the latest Star Wars trailer for physics data. And here is more analysis on figuring out the speed of things using tools that would fit into Advanced Functions. Have fun.
Curriculum Tags:MHF4U

Another one from our Engaging Math blog was one that I actually had sitting around for years but then was reminded of it last week when I saw this post from Mike's Math Page. It wasn't specifically about volume of a pyramid but that is where it started.  So I tweaked mine a bit and made it more formal. You can download all the templates here (or just watch the videos).
Curriculum Tags: MPM1D, MFM1P

I have always liked the ambiguous case in Trig. And I really like the way that Mary from the M3 blog handles it. Letting students discover something is up. She pairs them up to draw triangles given information and then wait and see if some get the two related triangles. Take a look
Curriculum Tags: MCR3U, MCT4C

Nice video from Veritasium about the psychology of expected value. It would be a nice little experiment to do with students to give them an idea of what it means. I like the part were he talks about the difference of doing the experiment one time versus doing it one hundred times.
Curriculum Tags: MDM4U

It is old but who can resist a good Calculus parody video.
Curriculum Tags: MCV4U

I made a couple of videos on how to construct a circle. In grade 8, students are supposed to construct in three ways: 1) by centre and radius, 2) by centre and point and 3) by three points. The first two are relatively easy but the third one comes from the property that the perpendicular bisectors of any two chords of a circle will intersect at the centre. One of the videos is a manual construction and the other is via GSP. 
Curriculum Tags: Gr8

Some data to start the new year. Data about new year's resolutions that is. Sure there is a nice bar graph about the most common new year's resolutions but the one I like is the one that uses Google Trends to show how the words "diet" and "gym" are cycled throughout the year. This is a pretty cool tool where you can search the frequency of any search term or phrase you can think of.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

It's always good to find data that kids might be interested in. Why not help them win Wheel of Fortune then.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

My favourite Equation.
Curriculum Tags: MPM2D, MCF3M, MBF3C, MCR3U

Friday, January 2, 2015

Math Links for Week Ending Jan 2nd, 2015

Any time there are resources about assessment then I'm happy. This isn't specifically a resource about assessment but there are bits at the end that relate. It's a talk from Dan Meyer about making math more like video games. My favourite part is talking about the craziness of just adding math problems to an existing game and thinking that kids will dig it. But the main points are below and expanded upon in the talk. Take a look.
Curriculum Tags: All

Why not continue with Dan Meyer. This one where he points out a great real world opportunity to connect to systems of equations. This time dealing with the controversial movie The Interview and purchase and rental sales.
Curriculum Tags: MPM2D, MFM2P

Many of you may have played War as a kid (with cards, that is). Here is a version that could be used as a review for trig and logs in Advanced Functions. Already made, ready to go.
Curriculum Tags: MHF4U

Growth mindset is the big idea in education lately and here is a teacher resource that will help students along with realizing how a growth mindset can be beneficial to them. It uses a combination of online and paper & pencil forms. Take a look
Curriculum Tags: All

A couple from Mike's Math Page. And if you are not familiar with it then the short version is Mike working out math problems with his kids (and they do some pretty high end stuff). This first one is a neat problem that asks what is the area of the shaded area which you could probably hammer out using Pythagorean theorem but he does some neat things with some 3D printed pieces to find a more elegant solution. Take a look
Curriculum Tags: MPM1D, MFM1P

I like using geoboards when talking about similarity. So it is no surprise to me that I like this little activity.
Curriculum Tags: Gr7, MPM2P, MFM2D
Here is a good video that could be used when talking about vectors if you want to relate to the whole swimming upstream/downstream situation. Plus it's a good time to remind you of the site 101 Questions. Go the link below to ask your own question and see what questions others have asked about this same video.
Curriculum Tags: MCV4U

A second one from Mike's Math Page originates with this video but his treatment could dealing with the sum of squares could be used when talking about series calculations. Of course if you just use this video then you can talk about the proof of why a pyramid's volume is one third of that of the prism of the same base and height.
Curriculum Tags: MPM1D, MFM1P, MCR3U

Matt Parker makes part of his living as a standup mathematician and can be seen in some of the Numberphile videos. He has just published a new book: Things to Make and Do in the Fourth Dimension. Here he does a talk with some of his favourite bits from the book. I like the part about the adding machine made of dominoes or how check sums and bar code scanners relate to Sodoku puzzles. And he starts by having the audience cubing two digit numbers and correctly guessing the cube root based on their result (a pretty simple trick if you want to impress your students)
Curriculum Tags: All

Outlier humour. Awesome
Curriculum Tags: MDM4U, MAP4C