Math Links for Week Ending Aug. 29, 2014

I really like this series of posts from Dan Meyer. The premiss is that we need to do a better job of developing what is going on in our math classes rather than just doling it out. And I don't think these are posts necessarily about Problem Based Learning (if that's your thang) but more about how (and why) you can tweak what you are doing so that it's a little more interactive for the kids
In my opinion though, I think one of the issues is that most of us got into teaching because we like to show people how to do stuff. So it's hard to switch gears and not be so explicit about everything (regardless of whether it's good for kids or not). Check out the series with the links below.
Curriculum Tags: All 

http://blog.mrmeyer.com/2014/developing-the-question-why-students-dont-like-math/

http://blog.mrmeyer.com/2014/developing-the-question-good-work/

http://blog.mrmeyer.com/2014/developing-the-question-needs-improvement/

http://blog.mrmeyer.com/2014/developing-the-question-ask-for-a-sketch-first/

http://blog.mrmeyer.com/2014/developing-the-question-ask-for-a-sketch-first-ctd/

http://blog.mrmeyer.com/2014/developing-the-question-bike-dots/

Note that there are a lot of links this week so I will probably be brief in my descriptions.

Which waffle is a better deal? This 3Acts combines rates, and area of a circle.
Curriculum Tags: Gr8, MPM1D, MFM1P
http://whenmathhappens.com/2014/08/10/waffles/

I like this 3Acts because I have tried to do this in my own home. The red light comes on in the fridge to say that the filter needs replacing but how it decides to come on is a mystery to me. Is it some sort of timing thing or is it actually measuring something in the filter to determine that the water isn't as clean. This 3 Acts uses extrapolation as the main tool but currently doesn't give a complete Act 3. We'll have to wait until he drinks more water.
Curriculum Tags: MPM1D, MFM1P, MDM4U, MAP4C
http://whenmathhappens.com/2014/07/29/water-filter/

Here is a nice little activity to help develop ideas of congruency. Students are given sets of shapes and asked whether they are the same or not the same (with explanation).
Curriculum Tags: Gr7, Gr8
http://function-of-time.blogspot.ca/2014/08/arguing-about-shapes.html?m=1

In this task students are asked whether a pattern is linear or not. As it is laid out there would be some graphing involved so it connects best with grade 9 applied or academic but could also be extended to grade 10 or simplified for grade 7 or 8.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MPM2P, MFM2D

http://function-of-time.blogspot.ca/2014/08/is-it-linear.html?m=1

Understanding the difference between zero slope and undefined slope is important when learning this concept. Here is an activity that tries to address this issue.
Curriculum Tags: MPM1D, MFM2P

http://function-of-time.blogspot.ca/2014/08/zero-and-undefined-slopes.html?m=1g

I like encouraging activities in the grade 11 university course. This one is dealing with recursive sequences and using Skittles to do so. Fun and Nutritious :-)
Curriculum Tags: MCR3U

http://ispeakmath.org/2014/08/25/recursively-defined-sequence-with-limits-investigation-skittles-activity/

I always had trouble with random variables. Here are a series of videos to help with this. Check out the website link as well for more information.
Curriculum Tags: MDM4U 

http://learnandteachstatistics.wordpress.com/2014/08/18/random-variables/

New research seems to show that we are born with an innate ability to understand simple probability. I wonder why that seems to change (ie why are lotteries so popular).

Curriculum Tags: All
http://www.sciencedaily.com/releases/2014/08/

Kyle at the Tap Into Teen Minds blog took the Ice Bucket Challenge and turned it into a 3Act task dealing with scatter plots and extrapolation. Check out the link below for all the videos in their individual form.
Curriculum Tags: MFM1P, MPM1D, MDM4U, MAP4C

http://tapintoteenminds.com/3act-math/ice-buckets/

With all of the hoopla about the ALS Ice Bucket Challenge (here's my attempt if you are interested) there have been a lot of people saying this or that about it and it's effectiveness. There is no denying that it has spiked donations to ALS but this infographic compares money raised with deaths by disease. Thanks to Michael Lieff for this one.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U
http://www.vox.com/2014/8/20/6040435/als-ice-bucket-challenge-and-why-we-give-to-charity-donate

Math Links for Week Ending July 25th, 2014

I am a sucker for any resources on the nature of randomness. We really have a hard time understanding what random really is. In this interview from Science Friday, they talk to William Poundstone, author of “Rock Breaks Scissors: A Practical Guide to Outguessing and Outwitting Almost Everybody”. In it he talks about how knowing how random truly works can be an advantage that you can exploit. This is a good topic of conversation for any students talking about probability. Listen to the full interview below.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U
http://sciencefriday.com/segment/07/11/2014/the-surprisingly-predictable-patterns-of-random-choice.html

There are a lot of people blogging about teaching math these days and someone has been trying to catalogue the efforts. This blog is even on the list that you can find here:
Curriculum Tags: All
http://mathtwitterblogosphere.weebly.com/list-of-tweeps-and-blogs-by-category.html

At first I thought this problem might be a little trivial. But this 3Acts from Dan Meyer is actually nicely done and works well with both addition of fractions or division of fractions as well as proportional reasoning. Get the full task at the link below
Curriculum Tags: Gr7, Gr8
http://www.101qs.com/3043-nanas-lemon-water

This 3Act from When Math Happens is a nice problem that brings expectations from multiple strands in. It includes volume of cylinders and then potentially proportional reasoning and data management (depending on how far you want to take it). Plus it might get you all fired up since someone will have to drink all of those energy drinks. Since I am writing this for Ontario curriculum, keep in mind that the measurements are in inches and ounces so you may want to redo this in metric (or not). Get the full task at the link below

Curriculum Tags: Gr8, MPM1D, MFM1P

http://whenmathhappens.com/2014/07/16/energy-drinks/

In general, I like the idea of problem based learning but sometimes getting good problems is an issue. A good stepping stone to those types questions are what Jo Boaler calls "low floor, high ceiling" questions. That is, easy for students to start but can become more complex and deep as well. She has started to compile a list of these that you can try out on her youcubed.org site. In the coming weeks I will try to highlight some of these individually but for now take a look for yourself.
Curriculum Tags: All
http://youcubed.org/teachers/category/low-floor-high-ceiling/

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 Feb. 14th, 2014

It's Valentine's Day today so why not have a post with carderoids in them. Thanks Desmos.

Curriculum Tags: All

https://www.desmos.com/calculator/4dqgvrtdze

Trig identities a can be and issue as their abstractness can be a hurdle for many kids. Don't get me wrong, I think it's important for our kids to be able to work in abstractions but if there are ways to make topics less abstract than they need to be, then I think that's a good thing. That is why I like this post about a graphical way to get to the Pythagorean trig identities. Well done.
Curriculum Tags: MCR3U
http://samjshah.com/2014/02/10/trigonometric-pythagorean-identities/

I love learning stuff about things I like. For example, to day I learned you can import pictures into Desmos from Mary at the M^3 blog. I love doing this with Geometer's Sketchpad (my premade sketch is here) but now that I know Desmos does it that gives a nice alternative. Although I do like my sketch because it has a feature to scale the axes so that the equation actually has a connection to real measurements. So take a look at this blog post and if you want some more images to use, you can look at some I have collected here.
Curriculum Tags: MFM2P, MPM2D, MCR3U, MCF3M, MBF3C
http://marybourassa.blogspot.ca/2014/02/mfm2p-day-6.html

There is nothing like a real contextual problem to expose the problem people have with probability (a lot of "prob's" in that sentance). Here is the context. You are taking a medical test that is 95% accurate when people have the disease (in this case cancer). So this means there are 5% false positives. If your results come back positive, should you be concerned? The counter intuitive result is "no". John Allen Paolos wrote about this 4 years ago (and just retweeted it now) in the context of mammograms. So here's the scenario: 95% accurate when people have cancer, 99% accurate when people don't have cancer and assume that 0.5% of the 100,000 person population actually have cancer. I will leave it up to you to do the math or you can just click on the link below.
Curriculum Tags: MDM4U
http://www.nytimes.com/2009/12/13/magazine/13Fob-wwln-t.html?_r=3&emc=tnt&tntemail1=y&

I think one of the best things you can do for students is not give them the answers. To take Dan Meyer's tag line "less helpful". I realize that this is totally counter intuitive to teachers. Most of us got into teaching because we like telling people how to do stuff. So when a kid asks a question (or gives an answer that is wrong), it is a natural reaction to just give them the answer (or just say 'nope'). But why not, instead, lead them to the answer or at least have them reveal their thinking (even when they are correct). That is why I like this post from Andrew Stadel so much. It gives tips on how to approach those situations in ways that will best benefit the student.
Curriculum Tags: All
http://mr-stadel.blogspot.ca/2014/02/explain-that-please.html

For any of you teaching conversion from metric to imperial (and vise versa), this video from Matt Parker gives a nice overview of the logic behind the imperial system.
Curriculum Tags: MFM2P, MBF3C, MAP4C
https://www.youtube.com/watch?v=r7x-RGfd0Yk

Math Links for Week Ending Sept. 27th, 2013

I am not sure of exactly what applications this might have in the classroom and it does have some limitations but I think the interface is really smooth and nice.
Curriculum Tags: All
https://itunes.apple.com/us/app/myscript-calculator/id578979413?mt=8

I was watching the show Tanked (they make custom aquariums) and they did this neat thing where they had to make a martini glass so they cut a flat piece of plastic and then placed it on a form and baked it so that the plastic bent around the form to make the cone. It was very impressive. I tried to find the video but couldn't. I did, however, find a real company that makes these cones and they had a page on how they make them (including an Excel spreadsheet)
Curriculum Tags: MPM1D, MFM2P
http://www.polyfab.biz/plastic_cones_fabricate.htm

I think that the concept of functions might be one of those things that sometimes doesn't get the treatment that it should. Here is an interesting treatment that uses the analogy of using a vending machine. Take a look.
Curriculum Tags: MCF3M, MCR3U
http://christopherdanielson.wordpress.com/2013/09/15/sameness-in-college-algebra/



Here is a nice progression from similar lines to similar shapes.
Curriculum Tags: Gr7, Gr8, MPM2D, MFM2P
http://feedproxy.google.com/~r/ratexp/~3/PxATwiz5mTU/are-these-figures-same-shape.html

As far as I am concerned, you can't have enough activities that show how improbable it is for someone to win the lottery. As it is with other Yummy Math activities, you have to be a member to get the solutions and an editable version of the activity. I particularly like the link to the app to simulate the powerball lottery.
Curriculum Tags: MDM4U
Probability http://www.yummymath.com/2013/powerball/


I like this update of an older Dan Meyer activity dealing with the relationship between ticket cost and distance travelled/time taken for flights. A nice scatterplot/line of best fit activity. The main part of the update that I like is the use of Google docs.
Curriculum Tags: MPM1D, MFM1P, MDM4U, MAP4C
http://thefischbowl.blogspot.com/2013/09/air-travel-google-apps-style.html


Whenever I can introduce an algebraic concept by first using a numerical method I am happy. Apparently I am not the only one. Here is one dealing with the distributive property. Thanks to Dan Meyer for this one.
Curriculum Tags: MPM1D, MFM1P, MFM2P
http://www.mathycathy.com/blog/2013/08/simplest-inquiry-strategy-ever-discovered-completely-by-accident/

I really like this nice collection of Number Sense videos. Nine videos in all. Take a look at one of them below and the rest of them here
Curriculum Tags: All

http://mrpiccmath.weebly.com/1/post/2013/09/number-sense-videos.html

A nice little tidbit of data
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

https://i.chzbgr.com/maxW500/7803799296/h7250D4D0/

Need some data about TV watching. Maybe after you see your favourite show

Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

https://i.chzbgr.com/maxW500/7807779584/hDB852DF8/

Math Links for Week Ending Aug. 23, 2013

One of the things that Dan Meyer did this summer is called "Makeover Monday"
where he and his readers take various bits of textbook work and retool them. Here are the results:
Bedroom Area (Area, Rates) http://blog.mrmeyer.com/?p=17230
Checkerboard Boarder (Quadratics, Patterning) http://blog.mrmeyer.com/?p=17257

Bedroom Carpet (Composite Area, Rates) http://blog.mrmeyer.com/?p=17348
Internet Plans (Systems of Equations) http://blog.mrmeyer.com/?p=17391
Meatballs (Composite Volume) http://blog.mrmeyer.com/?p=17442
Tire Marks (Root Functions) http://blog.mrmeyer.com/?p=17499
Postage Rates (Piecewise Graphs) http://blog.mrmeyer.com/?p=17502
Ferris Wheel (Periodic Functions) http://blog.mrmeyer.com/?p=17501
Shipping Routes (Systems of Equations, Patterning) http://blog.mrmeyer.com/?p=17500
Boat Race (Vectors, Geometry) http://blog.mrmeyer.com/?p=17503
Penny Circle (Quadratics) http://blog.mrmeyer.com/?p=17153

Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MPM2D, MFM2P, MCR3U, MCV4U

Here is a neat activity that links equilateral triangles and quadratics (or root functions)

http://www.cut-the-knot.org/arithmetic/algebra/ParabolaAndEquilateralTriangles.shtml

Curriculum Tags: MCF3M, MCR3U

One dot, one person. That is, over 300 million dots representing each person in the US. All plotted out and colour coded by race. Neat visualization. Here is the link to the large zoomable map.
http://www.coopercenter.org/demographics/Racial-Dot-Map
Curriculum Tags: MDM4U

I must be fascinated by these things because I know I have pointed them out before. These pictures made of curves are neat. But unrelated to this is a new feature of Wolfram Alpha to "Analyze My Facebook Data". To do this you have to give Wolfram Access to your Facebook page but then it does its magic. Give it a try. 

http://blog.wolframalpha.com/2013/08/12/set-the-curve-with-wolframalpha/

Curriclum Tags: MDM4U, MCR3U

From Edudemic, a nod to McGraw Hill's Eglossary of math
http://www.freetech4teachers.com/2013/08/eglossary-math-glossary-for-middle-high.html

Curriculum Tags: All

A whole pile of I Have, Who Has cards already premade for math.
http://www.mathwire.com/whohas/whohas.html
Curriculum Tags: Gr7, Gr8

Here is a really cool algebra puzzle that requires only generating and solving linear equations. Take a look here
http://letsplaymath.net/2013/08/22/puzzle-algebra-on-rectangles/
Curriculum Tags: MFM1P, MPM1D

In this video the boys from Top Gear (UK) take a look at how models scale down in size but actually scale up in durability
http://www.youtube.com/watch?v=ioYE_6Lx_hA
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P

The Big Bang Theory has no shortage of math references. Here's one that could be used as a Minds On for solving linear equations or speed
Curriculum Tags: Gr8, MPM1D, MFM1P
http://www.youtube.com/watch?v=9s9td5kvK5c

I still don't know what the 2nd guy says but this is still kinda funny "street math"
http://www.youtube.com/watch?v=stXG3np-BWE
Curriculum Tags: All

I love this one from XKCD dealing with the idea of small probabilities and statements that sound sensational but really aren't 

http://xkcd.com/1252/
Curriculum Tags: MDM4U