Friday, March 28, 2014

Math Links for Week Ending March 28th, 2014

OK so this is not necessarily about grade 7-12 math but it has been making the rounds on the Facebook and Twittersphere. It's more about the fight between the "back to basics" and the "problem solving" camps. The premiss is that this incremental step approach to subtraction is outlandishly complex compared to the traditional algorithm. And yes the traditional method is definitely more efficient but there are two main issues as far as I am concerned:

  1. the examples they show are really simple so the complexity of this alternate method seems even more ridiculous
  2. both examples require no carrying. It is when carrying is involved that those kids with difficulty fall apart. 

There were several nice responses to this. Mathy Cathy was the first one that I saw and she pointed out two others. One from Jusin Alon had a nice summary of what Common Core is. I especially liked the example of 1001 - 999 where carrying is crazy if you do it the traditional method. Christopher Danielson took it two steps further and actually answered the question posed in the 2nd example but also showed a great video of a student solving 1001 - 999 using a step method and getting the answer with no problem but completely falling apart when forced to do it the traditional method.

I guess my best analogy of why this sort of thing is important is about this fictitious example. Imagine there was an expectation that required a student to lift a pile of 10 books from the floor to a desk. Some kids might be able to lift all the books at once while others can only do it one at a time. But if they all get the books up their then that's all that should matter.
Curriculum Tags: All

I love this challenge:
Your challenge is to design a game, using only a fair coin, that you have a 1/3 chance of winning
I think it could be done in a grade 7 or 8 class with a little bit of scaffolding but for sure in a grade 11 college or Data Management class.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

Triangle congruence used to play a much bigger role but it still exists in our grade 7 curriculum. Here is a nice discovery activity for investigating the idea of congruence. I like all the handouts and templates available.
Curriculum Tags: Gr7

I really like this investigative approach to introducing permutations and factorials. I have done something similar to parts of this but this is far more extensive. I love the detail here.
Curriculum Tags: MDM4U

As I said, I like actually doing experiments to collect data. This one using paper airplanes is good for central tendency and single variable data with dot plots.
Curriculum Tags: Gr7, MBF3C, MDM4U

It seems like we have no shortage of data collection here. I like this experiment to get some "dirty" linear data with nothing more than some dry spaghetti, paper cups and pennies (you gotta do something with them).
Curriculum Tags: MPM1D, MFM1P, MFM2P

Powers of 2. They have a hold on me. That is, the game 2048 does. I don't usually play games on my phone but I like this one. And its pretty cool that it was developed by a 19 year old.
Curriculum Tags: Gr7, Gr8

I have always been a fan of collecting real data and fitting it to a mathematical model. Science has a lot to offer us in this area and Boyle's Law is one of those relationships. The nice thing is that this experiment is really easy to pull off. So if you need an experiment for MCR3U regarding inverse functions, then this is the experiment for you.
Curriculum Tags: MCR3U

Friday, March 21, 2014

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

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

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

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

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

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

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

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

And finally this week, some mathematical poetry about parallel lines.
Curriculum Tags: All

Friday, March 14, 2014

Math Links for Week Ending Mar. 14th, 2014

Even though I posted a Pi Day link last week (to my Pinterest Page), most of the links this week will relate to Pi since today is actually Pi Day. There have been new finds this week including this page of 10 Pi Day lessons, Buffon's needle and these two videos (posted today). One from Numberphile (one of my favourite Pi properties) and the other from Vi Hart (another in her anti Pi Day series).
Curriculum Tags: All

Key Curriculum, the maker's of Sketchpad, have really started to include a lot of web based sketches (ie no Sketchpad needed) in this one they have several different derivations of Pi using geometric and dynamic means.
Curriculum Tags: Gr8

The Language of Functions and Graphs is a resource that might be old but there are a lot of great problems here for the picking. This used to be a paid resource but now its available for free in PDF form, both the black line masters and the teacher resource. Thanks to Michael Pershan and Dan Meyer for this one.
Curriculum Tags: MPM1D, MPM2D, MCR3U

Keith Devlin has written a lot about Fibonacci and he has now put out a new video debunking a lot of the myths about the Golden Ratio and Fibonacci.
Curriculum Tags: All

Why not at least one image for Pi Day
Curriculum Tags: All

Here is a neat little poster that talks about different types of numbers. It could be good to start some discussions on what characterizes a number. Thanks to Edudemic for this one.
Curriculum Tags: All

Friday, March 7, 2014

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

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
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

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

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

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

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

I guess showing your work can be different now. Thanks to @thescamdog for this one too.
Curriculum Tags: All

I thought this one from XKCD was a great example of a cool area plot
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

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