Math Links for Week Ending Mar. 21st, 2014

I have been teaching solving systems of equations for many years and I have found it to be really nice and challenging and rich for academic students. But for applied students it can be meaningless and very abstract. Here is the expectation from grade 10 applied: solve systems of two linear equations involving two variables with integral coefficients, using the algebraic method of substitution or elimination (Sample problem: Solve y = 2x + 1, 3x + 2y = 16 for x and y algebraically, and verify algebraically and graphically.) Do you see what I mean? Too abstract for applied students. Even within a context, the method of elimination or substitution is still abstract. However, if you can find a way to take away that abstraction of the solving process (at least for a minute) then you might actually get them to eventually buy into those methods. That being said I love this post from the Making Math Meaningful blog giving a problem that is manageable for applied students and then giving them manipulatives to create the solution. Take a look at the solution seen here to the problem "If 4 jujubes and 6 smarties costs 24 cents and 2 jujubes and 5 smarties cost 16 cents, then how much does 1 jujube costs and how much does 1 smartie cost? "
Curriculum Tags: MPM2D, MFM2P
http://marybourassa.blogspot.ca/2014/03/mfm2p-day-23.html

When not creating his own from scratch Kyle at the Tap Into Teen Minds blog is adapting found resources and turning them into 3Act Tasks. Some new ones include a probability task for MDM4U and a linear relations task for grade 9. And the other thing he does is matches them up to Ontario curriculum (by course and expectation), even Dan Meyer's. And then he does another solid and makes them searchable by grade, expectation and author. 
Curriculum Tags: MFM1P, MPM1D, MDM4U
http://tapintoteenminds.com/3act-math/darius-washington-free-throws-win/
http://tapintoteenminds.com/3act-math/crazy-taxi/


And why not some more basketball math. Warren Buffet has put up a Billion dollars for anyone who can pick every game in every bracket in this year's college basketball tourny. Scientific American has done the math on this and apparently only each American needs to enter 425 trials for someone to be likely to win. Here it is
Curriculum Tags: MDM4U
http://blogs.scientificamerican.com/roots-of-unity/2014/03/17/we-only-need-to-fill-out-425-brackets-each-to-win-buffets-billion/




Hey do you need some data on the frequency of rhyming words in pop songs? And as an extra bonus, it's dynamic. Click on the desired pair of rhyming words in the graph and the graph changes to give the historical frequency in pop music.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U, MAP4C
http://www.slate.com/articles/arts/culturebox/2014/02/justin_bieber_and_the_beatles_they_both_liked_to_rhyme_the_same_words.html

OK, so this I love. Its one of my favourite MDM4U problems. the ones that deal with false positives and their meaning. Take this example of a test for Alzheimer's that is supposed to be 90% accurate. However, when you actually do the math and incorporate that accuracy on two groups of people (those with and those without Alzheimer's) you actually see that the test isn't that accurate at all due to all the false positives. Check out the math and the nice visuals here. 
Curriculum Tags: MDM4U
http://ampp3d.mirror.co.uk/2014/03/11/how-a-90-accurate-alzheimers-test-can-be-wrong-92-of-the-time/

It seems that there still needs to be some work done in this area. Both genders think women are bad at math! That is not good. Read about it here.
Curriculum Tags: All
http://news.sciencemag.org/math/2014/03/both-genders-think-women-are-bad-basic-math

And to make things worse now it seems that genetics might predispose people to math anxiety. This doesn't bode well for the growth mind set. Read about it here.
Curriculum Tags: All
http://www.sciencedaily.com/releases/2014/03/140317095843.htm

Do you need some examples of scatter plots of real data? These aren't so good for line of best fit but they are pretty good for talking about the meaning of where points are on the graph. These graphs are about the connection between life expectancy and income. Go to the website for the details.
Curriculum Tags: MDM4U
http://www.nytimes.com/interactive/2014/03/15/business/higher-income-longer-lives.html

And finally this week, some mathematical poetry about parallel lines.
Curriculum Tags: All
https://twitter.com/SciencePorn/status/441748070133272577/photo/1

Math Links for Week Ending Mar. 7th, 2014

Seeing as Pi Day is in a week I thought I would put my annual Pi Day post up a bit early. This just comes from my Pinterest Pi Day Page. My favourite video is below. Enjoy. Keep in mind that next year's Pi Day will be even more special since it will be 3.14.15
Curriculum Tags: All
http://www.pinterest.com/davidpetro314/pi-day/

I like this recent post from the Tap Into Teen Minds blog on the importance of conceptual understanding (not just memorization) there has been a lot of discussion of this in recent months so it is quite topical. I especially like the nod to algebra tiles.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MPM2D, MFM2P
http://tapintoteenminds.com/2014/03/02/striving-for-deeper-understanding-and-retention-in-math-class/

Combinations with a connection to data management in one of the latests posts from Yummy Math. First determine the number of different types of hot chocolate you can make then see which one is the "healthiest"
Curriculum Tags: MDM4U
http://www.yummymath.com/2014/too-early-in-the-day-for-so-many-choices/

Five year olds can learn to do Calculus. It sounds outrageous but if you are talking about the fundamentals of what calculus is, pattern recognition, then absolutely. Recently I posted an article stating that you never learned math in high school, this article seems to suggest that the opposite can happen.
I think my favourite quote from this article is

The one side says, “drill and kill.” The other says “drill for skill.” Basically, though, just about every mathematician and math education researcher who was interviewed for this story agrees that the perfect math class should have a mix of skills and problem solving. They just can’t agree on the amounts of each, when to add them, and what to skip.

Curriculum Tags: All
http://www.theatlantic.com/education/archive/2014/03/5-year-olds-can-learn-calculus/284124/

Probably the most well researched and balanced articles in the "math wars" lately came from the Globe and Mail this week. Definitely well worth the read. There are two quotes I liked the most in this, both from Marian Small. The first one refers to the idea that often teachers teach the most efficient method for doing a problem but what is efficient for them may not be the most efficient for all students:

Dr. Small is showing a third option for two-number multiplication when a father raises his hand and asks: “But what’s the most efficient way?” “What’s your definition of efficient?” Dr. Small responds. “I think it’s probably the calculator.” When a few parents chuckle, she clarifies, “that was only half a joke.”

And I also liked the quote about claiming to not like math or not be good at math. It is a problem that we have with parents.

If you don’t like math, keep it to yourself.” Don’t tell your kids, you were bad at algebra or hated fractions, she explains, cause you’re giving them permission to be the same way.

Curriculum Tags: All
http://www.theglobeandmail.com/news/national/education/why-the-war-over-math-is-distracting-and-futile/article17178295/

On Mike's Math Page, he wrote about a recent Ed Frenkel's Op Ed which was basically the same as his Numberphile video on why people hate math. You can follow all of those links to refresh your mind if you wish. But the thing that Mike reminded me of is this great Richard Feynmen segment where he talks about the problem with math (specifically about algebra)
Curriculum Tags: All
https://www.youtube.com/watch?v=VW6LYuli7VU

I thought this was a great image of one of the early MacDonald's menus. Not sure from what year but It think you could use it to see if the prices have all proportionally increased since then. Thanks to @thescamdog for this one.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
https://twitter.com/thescamdog/status/439551795388379136/photo/1

I guess showing your work can be different now. Thanks to @thescamdog for this one too.
Curriculum Tags: All
https://twitter.com/thescamdog/status/440944315154452480/photo/1

I thought this one from XKCD was a great example of a cool area plot
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U
http://xkcd.com/1338/

I was in Toronto this week and saw this and thought there must be some way to relate this to parallel lines or angles.
Curriculum Tags: Gr8, MPM1D, MFM1P
https://twitter.com/davidpetro314/status/441991510222200832/photo/1

Math Links for Week Ending Jan. 17, 2014

Just announced this morning is the newly designed Math Gains Site (actually all of Edugains has been redesigned). Among the changes are

• 'Links' connects the user to a number of ministry and educational partners' websites (e.g., subject/division associations, Ontario Educational Resource Bank (OERB), Ontario Software Acquisition Program Advisory Committee (OSAPAC), Publications Ontario, Ministry of Education) to provide a greater number of educational learning resources. 
• 'Social Media' icons provide the user with the opportunity to share content with colleagues via Facebook, Twitter, Pinterest and/or Google+. 
• 'Survey' links allow the user to provide input that informs the evolution of EduGAINS, so that the website can be responsive to the learning and teaching needs of Ontario's educators.

Curriculum Tags: All
http://www.edugains.ca/newsite/math/index.html

There is a just launched YouTube channel associated with The Nerdist called Math Bites. It's hosted by Danika McKellar, who is the author of books like Math Doesn't Suck, Kiss My Math, Hot X: Algebra Exposed & Girls Get Curves: Geometry Takes Shape (due out this August). You might also know her from the TV shows The West Wing and The Wonder Years. As Danica puts it Math Bites

"are little bites of mathy goodness - you'll learn a little something, but mostly you'll be entertained by the likes of yours truly, Felicia Day, Chris Hardwick, Jim O'Heir, Jonathan Bennett, Dustin Milligan, Amanda Crew, Matt Mira, Jonah Ray, Matt Kawcynzski, and more! "

Currently the first two episodes are out and can be seen here on the YouTube Playlist:
Curriculum Tags: All
https://www.youtube.com/playlist?list=PLl4T6p7km9dbGCsAooT8-ujI9xAQnjsfJ

Against All Odds appears to be a really great resource on statistics and probability created by Annenberg Learner. It comes in the form of 32 well produced videos on all manor of statistical topics. Real life examples of where statistics are used and resources to go along with the videos. Check out the sample video below.
Curriculum Tags: MBF3C, MAP4C, MDM4U
http://www.learner.org/courses/againstallodds/unitpages/index.html

OK so maybe these all aren't the best math jokes but any article that has the phrase "This is another hilarious reference to an infinite series" is worth a look (and there are explanations for those that are more difficult).
Curriculum Tags: All
http://www.businessinsider.com/13-math-jokes-that-every-mathematician-finds-absolutely-hilarious-2013-5

I can't help putting these up when ever someone creates a fun graph on Desmos. Of course these graphs aren't unique to Desmos but the Desmos crew do a great job of making their graphing program look fun (even though creating these graphs must be difficult). Anyway, this sort of thing fits very well in any discussion of domain and range:
Curriculum Tags: MCF3M, MCR3U, MHF4U
https://www.desmos.com/calculator/gafbe0otjh

Some more evidence that lotteries/gambling is a tax on stupidity. That being said, you can't win the lottery without actually buying a ticket.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U
http://www.theguardian.com/commentisfree/2014/jan/06/betting-shop-machines-predatory-capitalism

Math and Art collide when George Hart is put in charge. See how he creates this beautiful spherical sculpture using geometry and deft carpentry skills. Oh, yeah and he is Vi Hart's dad. Go figure.
Curriculum Tags: All
https://www.youtube.com/watch?v=DZN4vmQ93eQ

I love this video from Johnny Ball about how the capture-recapture method works. In it he shows how it works for ping pong balls and then he uses the method in a live experiment to estimate the number of black cabs in London (I won't tell you how it ends). I found out about this video from the I Speak Math blog where she has an entire lesson that uses this video as a starter when talking about proportionality. Then does a hands on activity to simulate it using Goldfish crackers. Fun stuff, check that out here. So that makes the video good for any lesson on sampling as well as any lesson on proportionality.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U
https://www.youtube.com/watch?v=tyX79mPm2xY

Numberphile demonstrates the craziness of infinity with this one: 1 + 2 + 3 + .... infinity = -1/12 . Even for students that don't understand series this is enough for them to say "Wah?". This is perfect for any high level discussion of infinite series with MCR3U or MHF4U students. Thanks to Mark Esping for this one

Curriculum Tags: MCR3U, MHF4U

http://www.youtube.com/watch?v=w-I6XTVZXww

Its always good to have real data. So if you are in need of a bar graph for a question, here is one that represents the total square footage of LCD screens made by Corning Glass over the years. Thanks to Mark Esping for this one.
Curriculum Tags: Gr7, Gr8
http://seekingalpha.com/article/1927231-the-spread-of-glass

From Twitter and perfect for any discussion of average (though probably a little subtle for anyone but MDM4U kids)
Curriculum Tags: MDM4U

There's a Mean Value Theorem problem lurking in here somewhere. pic.twitter.com/umvYdVcPgh
— Darren Glass (@darrenglass) January 12, 2014

Math Links for Week Ending Dec. 6, 2013

OK, so I am not going to say much about the features of Math Disk except to say watch the video below and try not to be impressed with all it does. Ok, so maybe I will mention some of the features. Algebraic and numerical calculations, function and statistical plots, probability, dynamic geometry and 3D vector plots (amazing stuff ripe for MCV4U) and even physics simulations (you can actually play angry birds). There is an iPad version as well. Though it doesn't have all the functionality, by creating an account on your computer, you can open and manipulate any files on the iPad. That being said, because it does so much, there will be a bit of a learning curve to figure out how to use it. There are a number of support articles and of course there are a pile of how to videos. My only complaint about these is that there doesn't seem to be any verbal instructions. They just show you how to do things. So when I was trying to make a dynamic plot, I found it hard to just watch what they were doing and mimic it on my screen without watching a few times. But once I got the gist of what to do the graphs and sketches started to flow. And its totally free. Go ahead, try to not be impressed by this. Thanks to Free Technology for Teachers for pointing this out.
Curriculum Tags: All
https://www.mathdisk.com/

The second of two graphing applets today is called Plotly. Now I know in Ontario we have both Fathom and Tinkerplots to use freely at home or school and many of us also have Excel and possibly Google Docs now but this package does just about every type of graph relatively easily. That is something that none of the above mentioned can do. Excel is pretty good at making line, bar and circle graphs (same with Google Docs) and Fathom and Tinker plots are great for graphing microdata (scatter plots, histograms, box plots and dot plots). But Plotly does them all. Histograms, box plots, bar graphs, line graphs and my new favourite: heat maps among others. I do find it interesting that circle plots are curiously omitted (probably a nod to those statistics folks who think they are among the most misused and awful types of graphs). All of the graphs have mouse over features and can be customized. As an added bonus it seems to work fine on an iPad (sans mouse over features) and you can even import your data from Dropbox or Google Drive. I suggest looking gallery to see the scope of what can be done and at the tutorials to master any of the idiosyncratic features of making these graphs. And of course, don't forget to create an account to save all of your graphs.
Curriculum Tags: MDM4U
https://plot.ly/

Depending on how anal you are about pseudo random generators (purists among you will no doubt harp that any electronic random generator is not, in fact, random - and you would probably be right), you may think this is cool or useless. Flip a day has one purpose. To flip a real coin once per day and post the result. That's it. As of today they are at 220 flips. You can follow them on Twitter and download the csv file as well.
Curriculum Tags: MDM4U
http://flipaday.co/

If you haven't used Dragon Box, I think you are missing out. I truly believe it is one of the best games out there that actually teaches a math concept. It runs on multi platforms and isn't that expensive. But how would you actually use it in a classroom to teach solving equations? Thanks to Tap into Teen Minds you are one step closer to figuring that out. Thanks Kyle
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MPM2D, MFM2P
http://tapintoteenminds.com/2013/11/24/how-to-effectively-use-dragonbox-in-your-solving-equations-lesson/


Do you need an example of something big to give some meaning to number sense calculations? Well how about info around the largest container ship ever built? Here are some stats over 1600ft long (longer than the Empire State Building is tall), 600 000 tonnes. It is basically a floating liquifying natural gas (FLNG) facility that mines, processes and can store up to 3.9 million tonnes of liquid natural gas each year. To get a sense of how much use out of that gas consider that the average family might use about 2000-3000 cubic metres of natural gas during the year (in gaseous form - click here to help convert that)
Curriculum Tags: Gr7, Gr8
http://www.wired.com/autopia/2013/12/worlds-largest-ship/

I love this "proof without words" of the area of the circle and how it can be connected to the area of a triangle. You probably could even get into some calculus talk in terms of infinitesimal slices of a circle to I guess
Curriculum Tags: Gr8, MPM1D, MFM1P
https://www.youtube.com/watch?v=whYqhpc6S6g

Math Links for Week Ending Oct. 11th, 2013

"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

Need an example of where sample size comes into play. How about this poll about whether Montreal should have another MLB team. Thanks to Mike Lieff for this one.
Curriculum Tags: MDM4U
http://www.nationalpost.com/m/wp/sports/mlb/blog.html?b=sports.nationalpost.com/2013/09/24/more-than-two-thirds-of-quebecers-want-major-league-baseball-back-in-montreal-according-to-poll


I have had sampling on the mind. Here is a nice simple sample size and confidence interval calculator
Curriculum Tags: MDM4U
http://www.surveysystem.com/sscalc.htm#two

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.

http://nicoraplaca.com/5-ways-make-simplifying-expressions-make-sense/

Curriculum Tags: Gr7, Gr8, MFM1P, MPM1D, MFM2P, MPM2D

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.

Curriculum Tags: Gr8, MFM1P, MPM1D
http://tapintoteenminds.com/2013/09/28/mustard-mayhem/

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

Using interpretive dance to describe concepts in statistics. Here are four videos that do just that. Seriously.
Curriculum Tags: MDM4U
http://www.youtube.com/watch?v=5fGu8hvdZ6s&list=PLCkLQOAPOtT2H1hJRUxUYOxThRwfVI9jI

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

Its funny because it's true

Curriculum Tags: MDM4U

http://xkcd.com/1273/