Though I don't agree with the use of "controversial" in this article (I would use the word surprising instead), there are some nice summaries of some classic math problems. From infinity, to Benford's law, to the birthday problem, to Pi to the Monty Hall Problem, there is something for everyone here. Thanks to @mathletepearce for this one.
Curriculum Tags: Gr8, MCR3U, MDM4U, MHF4U http://www.businessinsider.com/the-most-controversial-math-problems-2013-3?op=1
I have been known to say that we humans are bad at understanding probability. And it may also be true that maybe we don't take it seriously enough when we teach it. If you believe Arthur Benjamin then its way more important than calculus and I think I agree. Well NPR's All Things Considered have a special series called Risk and Reason about how we deal with probability in the news. For example, if the forecast calls for a 20% chance of rain, what does that mean? You can get them all at the link below.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U http://www.npr.org/series/333708682/risk-and-reason
The first video from Numberphile this week is on Friedman Numbers. These are numbers that can be made up by taking their digits and creating a math problem with them (eg 25 = 52). And as these numbers get bigger the expressions get more complex. Seems like a perfect opportunity to talk about order of operations.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P https://www.youtube.com/watch?v=I7v2wAXFQpc
The second is about a great geometry problem with 54 solutions. See one of them here that fits well with properties of angles. Its a very cool and elegant solution.
Curriculum Tags: Gr8, MPM1D, MFM1P https://www.youtube.com/watch?v=m5evLoL0xwg
This is a neat problem that you could have grade 7 or 8 students work on that fits really nicely into the geometry strand. The premiss is you have 5 points then there is always a way to create a convex quadrilateral and then extends from there.
Curriculum Tags: Gr7, Gr8 https://www.youtube.com/watch?v=xPk3SZiFEvQ
If you have students who are Dr. Who fans then maybe you can use some of this data to deal with data management.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U https://www.youtube.com/watch?v=FLH6GprKhsc
If you are a fan of Archie (yes, the Archie of Archie comics) then you may be sad that (spoiler alert) he will be taking a bullet and dying in the latest issue (it's been a while since I looked an Archie Comic and it looks like things have been getting a bit darker). None the less, according to 538, Archie has been dying for years and here is the data to prove it.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U http://fivethirtyeight.com/datalab/archie-death-comic-sales/
I really like Arthur Benjamin. Not just because he was a featured speaker at OAME 2011 (of which I was the Co Chair), but also because he is pretty good at mental computation and also thinks that knowing probability & statistics is more important than knowing calculus. And now he has done his third TED talk, this time on Fibonacci. And I know there are all kinds of videos on Fibonacci out there but I really like the way he connects the geometric to the numeric. A good video for anyone teaching about sequences or patterns.
Curriculum Tags: Gr7, Gr8, MCR3U, MCF3M http://www.youtube.com/watch?v=SjSHVDfXHQ4
You can never have too much data or too many good representations of data. Here you can find a collection of some of the best graphs dealing with behavioural science. And although its not new, probably my favourite is the one on water consumption in Edmonton during the 2010 Olympic gold medal game. This is certainly good for any classes looking at interpreting graphs.
Curriculum Tags: Gr7, Gr8, MCF3M, MDM4U, MAP4C http://economicspsychologypolicy.blogspot.ie/2013/12/the-15-best-behavioural-science-graphs.html
Need some data on linear relations? Want to use technology in your classrooms? Have a video camera of some sort? Been to an airport? If you have answered yes to any of these questions then take a look at this link where someone was bored at the airport and collected some simple linear data. This data exists all over (not just airports) and this post shows how you can use the Tracker software to analyze any motion.
Curriculum Tags: MFM1P, MPM1D http://www.wired.com/wiredscience/2013/12/video-analysis-at-an-airport/
In grade 9 we have to connect the algebraic form of Pythagorean Theorem to the geometric. This video tries to do just that. Thanks to Corrie Silva for this one
Curriculum Tags: MPM1D, MFM1P http://www.youtube.com/watch?v=uaj0XcLtN5c
A relatively new video from Vi Hart on logarithms. I totally love the way she starts with simple addition and works her way to logarithms. At first you don't see the connection but I think the payoff at the end is worth it.
Curriculum Tags: MHF4U http://www.youtube.com/watch?v=N-7tcTIrers
I have spoken a few times over the last few weeks about Simon Singh and his new book about math and the Simpsons. Here he is on Numberphile to talk about it (and Futurama)
Curriculum Tags: All http://www.youtube.com/watch?v=bJDiZi9dqOg
"Mathematics is really about discovering patterns...." I love this video about the limitations of computers in math. Thanks to Dan Meyer for this one. http://www.youtube.com/watch?v=piyGXW_gMbc
Curriculum Tags: All
I really like this video with Simon Singh where he talks about the near proofs of Fermat's Last Theorem that occur not once but twice in The Simpsons. I have always liked Fermat's Last Theorem because it is something that kids of many ages can try out. The other thing I like about this is it shows the limitation of the calculator when doing proofs. Plus its a great preview of his new book "The Simpsons and their Mathematical Secrets".
Curriculum Tags: All http://www.youtube.com/watch?v=ReOQ300AcSU
Just one more about sampling. This time the classic story of sampling bias in the 1936 election where it shows that just because you have a large sample size (2.4 million!!), doesn't mean you have a good sample.
Curriculum Tags: MDM4U http://www.math.upenn.edu/~deturck/m170/wk4/lecture/case1.html
This is an interesting post about research based ideas on how to help students with simplifying equations. Some of them seem counter intuitive to me but I am intrigued. For example, don't use the first letter of the object as the variable name. Thanks to Dan Meyer for this one.
I like this 3 act task because it nicely combines both the measurement strand and the proportional reasoning strand (number sense) so it could be used as part of a summative assessment too.
I love this calculator "unboxing" video from Numberphile. If you have never seen an unboxing video then just search for them on YouTube and you will find so many of people opening up their favourite things for the first time. It's a weird meme, I know. I love the commentary on the calculators here "its got 0 and 00 so if you want to have a number really close to zero then you are all set". All fun aside, I do like the tests he goes through to detect the accuracy of each calculator http://www.youtube.com/watch?v=eaJtjJNrWf0#t=547
Curriculum Tags: All
Area Paradox done in chocolate. Perfect if you want to talk about slope. Personally I think that is the best way to show why it happens but that is just me. http://www.youtube.com/watch?v=Y13tSEyOqGs
Curriculum Tags: MPM1D, MFM2P
Though I don't agree with the use of "controversial" in this article (I would use the word surprising instead), there are some nice summaries of some classic math problems. From infinity, to Benford's law, to the birthday problem, to Pi to the Monty Hall Problem, there is something for everyone here. Thanks to @mathletepearce for this one.
I have been known to say that we humans are bad at understanding probability. And it may also be true that maybe we don't take it seriously enough when we teach it. If you believe Arthur Benjamin then its way more important than calculus and I think I agree. Well NPR's All Things Considered have a special series called Risk and Reason about how we deal with probability in the news. For example, if the forecast calls for a 20% chance of rain, what does that mean? You can get them all at the link below.
