## Friday, March 27, 2015

### Math Links for Week Ending March 27th, 2015

Another great product of the MTBoS (Math Twitter Blog-o-Sphere) has just launched via @marybourassa. Which One Doesn't Belong (wodb.ca) is a new website that houses a pile of these little square images. You can read about how Mary about how she uses these in her calculus class here (spoiler alert: she is having her students create these) and her grade 10 class with surface area and volume here, and the launch of the website here.
The premise is that we are given four images (numbers, shapes or graphs) and simply asked "Which One Doesn't Belong? Besides the obvious part that starts the conversation about math in your class, the very cool thing about these is that they are constructed so that there is a reason that could be used to suggest any one of the four doesn't belong. So for example looking at the calculus image in the middle (below) the top left doesn't have a max or min, the top right have an asymptote, the bottom left has two vertical asymptotes and the bottom right has an oblique asymptote. The other thing about that is that in those discussions you might find more than one reason for a particular thing to not belong. So for example in the number example below, the 43 doesn't belong because it's a prime number or because it's not a perfect square
Right now, there are three categories: Shapes, Graphs & Equations, and Numbers
Curriculum Tags: All
http://wodb.ca/
http://marybourassa.blogspot.ca/2015/03/announcing-which-one-doesnt-belong.html
http://marybourassa.blogspot.ca/2015/03/which-one-doesnt-belong-for-calculus.html

I like when Rhett Allain does his video analysis posts because we can usually bring those into math class. In this particular one the subject is jumping. Specifically jumping competitions. In this case, standing long jump and a height jump. So there is a link to great video that shows good quadratic motion and he does a lot of great analysis that goes way beyond just quadratics.
Curriculum Tags: MPM2D, MFM2P, MCR3U, MCF3M, MBF3C
http://www.wired.com/2015/02/physics-record-breaking-long-jump/

I saw this on Andrew Stadel's blog. He was doing a summary of the week and one part was about a version of War that his colleague made. Different representations of rational number on cards (print them out here). Kids decide which is bigger. You can take out the fraction cards and even do this in grade 8. Check out Andrew's instructions on his site
Curriculum Tags: Gr8, MPM1D, MFM1P

Pi Day leftovers. Wolfram Alpha created a neat little app (http://mypiday.com/) that takes your birthday and finds out where it appears in the first million digits of pi. Fun. Check out their blog post for their PiDay fun and try your birthday out in the PiDay app. Thanks to Sue Latour for pointing this one out.
Curriculum Tags: All
http://mypiday.com/
http://blog.wolframalpha.com/2015/03/12/pi-or-pie-celebrating-pi-day-of-the-century-and-how-to-get-your-very-own-piece-of-pi/

Hey, data is good. And if you can find data that might interest students, even better. So here is some data from the TV show Glee. It's just finishing right now but take a look at its viewership over the years. There are some interesting blips that could be easily discussed (like the spike when the episode followed the superbowl)
Curriculum Tags: MDM4U

More Piday remnants. This time its an interesting way to connect data to Pi. The question is, how many digits of pi do you have to memorize to be considered "Special". Almost 1000 people were surveyed and here are some results. This might be a neat thing to do in your classes.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U
http://fivethirtyeight.com/datalab/how-many-digits-of-pi-you-have-to-have-memorized-to-be-special/

When we introduce trig we are supposed to do it via investigation. And if you are going to use investigation, then it is pretty standard to start with similar triangles. Here is a post from Sam Shah that basically gives his whole process. All 135 pages of it. I love it when people share like this and one of the things I like are the 89 pages of right triangles one made with each degree from 1 to 89.
Take a look at the progression of the concepts.
Curriculum Tags: MPM2D, MFM2P
http://samjshah.com/2015/03/25/my-introduction-to-trigonometry-unit-for-geometry/

Nice to see there are some stereotypes that continue to be broken. This pro football player has just published a paper in a math journal.
http://its-interesting.com/2015/03/19/baltimore-ravens-offensive-lineman-john-urschel-publishes-paper-in-math-journal/
It's always good to have real examples of mathematical concepts. In this video they go over how you can use the 3-4-5 triangle to create a footprint for a construction project with square corners. Then at the end shows how to make sure a quadrilateral is a rectangle by measuring the diagonals. Thanks to Graham Gould for this one.
Curriculum Tags: Gr8, MPM1D, MFM1P, MPM2D, MFM2P

It's maybe not appropriate for math class (starting with 38 if you don't like guns and then of course .....69 dudes) but here are the first 200 numbers as images via Google image search. It's still pretty neat how some of the numbers are coopted.
Curriculum Tags: All

Vi Hart release another one of her anti Pi (pro Tau) videos on last weeks Pi Day. Always entertaining.
Curriculum Tags: All

What starts out as a talk about the connection between math and sex turns out to be a talk about patterning and modelling in mathematics.
Curriculum Tags: All

Add this one to your list of coupon images. Which one would you choose?
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P

Some big data on big data. You could easily find some connection to exponential growth here. Thanks to David Broad for this one
Curriculum Tags: MCR3U, MCF3M, MBF3C, MAP4C, MCT4C, MDM4U
http://www.bitrebels.com/technology/things-know-big-data-infographic/

## Friday, March 20, 2015

### Math Links for Week Ending March 20nd, 2015

Last week I pointed out a blog post from @d_martin5 about assessing without percents. This week it was pointed out that he was featured on CBC radio where he talks more specifically about this idea. Thanks to Michael Leiff for this one. Listen below
Curriculum Tags: All

I learned about a new blog Math = Love from a few different people this week. It's part of this NPR story that is part of their series on the best 50 teachers in the US. Listen at the link below. And you can see a sample of what she has on her blog with the following posts
Curriculum Tags: Gr7, Gr8, MPM1D, MFM2P
http://www.npr.org/blogs/ed/2015/03/09/376596585/the-teacher-who-believes-math-equals-love

The first one is an I Have, Who Has game that is dealing with concept of connecting words to expressions. If you don't know about these types of game, the premiss is that everyone has a card with a question and an answer. One student asks their question and the student who has the answer claims it and asks their question. This continues until you come back to the first person.
Curriculum Tags: Gr7, Gr8
http://mathequalslove.blogspot.ca/2015/03/trying-out-i-havewho-has-for-first-time.html

In this activity there is a nice mix of using dice, Desmos, foldables and portable whiteboards to look at properties of lines. This takes the tediousness out of just graphing lines.
Curriculum Tags: MPM1D, MFM2P
http://mathequalslove.blogspot.ca/2015/02/rolling-dice-for-point-slope-form-and.html

And finally an interactive notebook (INB) on slope.
Curriculum Tags: MPM1D, MFM2P
http://mathequalslove.blogspot.ca/2015/02/finding-and-interpreting-slope-inb-pages.html

A couple of of related activities from the Making Math Meaningful blog. Related in that they both use Smarties as the catalyst. The first takes the idea of ratios, rate and linear relations to predict the price of a large box of Smarties. The second one is trying to estimate the amount of air within a Smartie box.
Curriculum Tags: MPM1D, MFM1P
http://marybourassa.blogspot.ca/2015/02/smarties-part-i.html
http://marybourassa.blogspot.ca/2015/02/smarties-part-ii.html

A couple dealing with making algebra meaningful from Jon Orr. The first one does it by connecting the idea of adding and subtracting polynomials and multiplying polynomials.... with Dora! In this 3Act task we use Dora as a unit of measure to simulate a polynomial.
Curriculum Tags: MPM1D, MFM1P
http://mrorr-isageek.com/?p=3811

In grade 12 Data Management we have to talk about probability distributions and when we do that we talk about Bernoulli Trials. That is, given the probability of failure for any individual experiment, what is the probability of failure after n experiments. That being said, it is always good to have real examples to go with mathematical concepts so here is some data on hard and flash drive failures (something that many of us have experienced first hand).
2013 study by cloud storage company BackBlaze looked at 25 thousand drives and found that around 5 percent failed during the first year and a half, most likely due to manufacturing defects. They were then largely stable until the fourth year, when the failure rate rose to 11.8 percent. 74 percent of drives lasted beyond the fourth year.
Curriculum Tags: MDM4U
http://www.makeuseof.com/tag/hard-drives-ssds-flash-drives-how-long-will-your-storage-media-last/

There has been a lot in the media as of late about the song Blurred Lines being a rip off of a Marvin Gaye song. So that being said, from Wired Magazine comes the attempt at answering the question "How many songs are there?" That is, given the finite number of sounds that can be produced and the number of ways those sounds could be arranged, how many different ways could you do that. Combinatorics and Wired to the rescue. Take a look here
Curriculum Tags: MDM4U
http://www.wired.com/2015/03/many-different-songs-can/

I have shown links about the Monty Hall problem before. I like this one because it highlights how the female columnist that made it popular was correct in her analysis yet all the professors who attacked her were wrong.
Curriculum Tags: MDM4U
http://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/

The second one from Jon Orr is also about simplifying polynomials and it's based on this Mad TV skit. Totally great application of algebra (and a funny skit). Check out the entire activity here
Curriculum Tags: MPM1D, MFM1P
http://mrorr-isageek.com/?p=3790

You have all seen TED talks but you may not know there is also the TED Radio Hour. This is a radio show that picks a theme and then highlights several TED talks on that theme with interviews with the TED speakers. Recently they had a radio hour on math called Solve for X. In it they covered topics as diverse as why we use x as our main variable in algebra to the mathematics of drumming and love. See the full video of the mathematics of love below and click on the link to hear the entire radio show
Curriculum Tags: All

These things show up on my Facebook Feed. I like them because they take patterning and put it in a friendly palatable format that most people are willing to try out
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P

## Friday, March 13, 2015

### Math Links for Week Ending March 13th, 2015

I have always liked the idea of a "foldable". I think they were popularized in Dinah Zike's book Teaching Math with Foldables. Well there are some that have used these to have their students make "interactive notebooks" (INBs). One who is quite prolific is Elissa Miller (Miss Calcul8). Very recently she has shared quite a few examples of her INBs on her blog. Check them out below, including all the downloadable templates in Word and PDF format. There is stuff that ranges from grade 7 geometry all the way to grade 12 Advanced functions:
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MPM2D, MFM2P, MBF3C, MCF3M, MCR3U, MHF4U
Characteristics of Functions
Solving Quadratics with Square roots (with a Row Game)
Properties of Triangles and Angles
Angles and Lines
Transformations
The Unit Circle
Trig Basics (with Radians)

We are a little behind on our resource blog but here is a new post. This one is an activity dealing with multiple representations of quadratics to put kids into groups of three. Each student gets one card and they have to find the two other students that have different representations of the same relationship. Get all the downloads here.
Curriculum Tags: MPM2D, MBF3C, MCF3M, MCR3U
http://engaging-math.blogspot.ca/2015/03/sort-students-into-groups-using.html

Calculating the probability from a normal distribution can be a bit tedious (using a z score table). So it is probably a good idea to have a probability calculator. Here is a good one. You enter the mean, standard deviation and the range you wish to calculate from and it uses the integral of the normal curve to calculate the area under the curve to get the probability. And as an added bonus, you get a diagram of the area. One note: if you use this calculator (or a TI-84) you will get a different answer than if you used a z-score table. This is because the z-score table is only accurate to 2 decimals, whereas this calculator or the TI-84 would be far more accurate due to the calculation method. Thanks to Mark Esping for this one.
Curriculum Tags: MDM4U
http://onlinestatbook.com/2/calculators/normal_dist.html

I always like interesting ways to talk about combinatorics. There are some interesting apps that help out in this area. The first one is a music app. Music is always a great way to talk about combinatorics. In this case the app lets you take samples and add them together to make a song. The specific thing about this one is that all the sounds are created by the same person via their vocals (kinda like Bobby McFarren). So the combinatoric question would be about how many possible songs you could make. Just drag the symbols up to the avatars to start creating your songs.
Curriculum Tags: MDM4U
http://www.incredibox.com/

Another fun one is more than a few years old but it is still super fun. On this one you get to choose how the character gets to dance. You make two choices, one about how the arms move and the other for the legs. You won't be able to stop playing with this. Just try to stop long enough for your students to calculate the total number of dances. The site is Swedish so that accounts for the non english words and if you are really looking for a good time you can upload a picture of your own face on it.
Curriculum Tags: MDM4U
http://fuldans.se/

I have had a few posts about assessment recently. And one of the flavours of the day is the idea of not assigning grades but just feedback. This really intrigues me. And if you are like me you might like this post from @D_martin05 on how grades aren't used at all. Some interesting stuff here. And if you saw my earlier posts then you might be interested in some more clarification @MathletePearce has made on his assessment method developed with @Mr_OrrGeek . Take a look at the link below to see his workflow with Google Docs.
Curriculum Tags: All
http://realteachingmeansreallearning.blogspot.ca/2015/03/no-percentages-in-math.html

And speaking of Kyle Pearce, here he tweaks Dan Meyer's Superbear task to spread over more expectations beyond just proportional reasoning. Take a look here.
Curriculum Tags: MAT1L, MAT2L, MFM1P, MPM1D, MFM2P
https://tapintoteenminds.com/3act-math/super-bear/

Are you looking for something semi interesting to do with factors of numbers? How about the number 3608528850368400786036725 which has the property that each number formed by the first n digits is divisible by n. So if n = 5 then the first 5 digits make the number 36085 is divisible by 5. Have your students work on checking that and look for some more high end stuff at this post.
Curriculum Tags: Gr7
http://www.blog.republicofmath.com/the-number-3608528850368400786036725/

I like this use of Desmos as I used to do this a lot with Geometer's Sketchpad. That is, showing that two (or more) representations may look different but have the same graphs. A great exercise to verify simplified forms.
Curriculum Tags: All
http://teachhighschoolmath.blogspot.ca/2015/02/sometimes-un-simplified-is-better.html

Hey, I almost forgot, it's epic PiDay this week. So here is my favourite expansion of Pi. Super fun. And if you want here is my Pinterest page and my full set of Pi Links on my Delicious page.
Curriculum Tags: All
http://devlinsangle.blogspot.ca/2015/03/pi-day-cyclical-motion-and-great-video.html

As it turns out being a mathematician can be quite dangerous. Find out here just how many of them have reached untimely deaths.
Curriculum Tags: All
http://www.usatoday.com/story/tech/2015/03/08/mathematician-deaths/24605901/

Patrick Honner writes for the NY Times Learning network. In this article he discusses the benefits of compound interest. Take a look
Curriculum Tags: MBF3C, MCF3M, MCR3U
http://learning.blogs.nytimes.com/2015/02/11/the-power-of-saving-exploring-the-mathematics-of-compound-interest/?_r=0

Hey, one last PiDay link. It's the mug I got for Christmas. It's heat sensitive.
Curriculum Tags: All