## Saturday, February 27, 2016

### Math Links for Week Ending Feb. 26th, 2016

As @MaryBourassa recently pointed out, there has been a lot of activities being posted using clotheslines (see her post below). I have mentioned before that I love the concept of using clotheslines and thanks to Mary, now I know about ClotheslineMath.com. Basically this is a primer on how you can use clotheslines in your math class. From the obvious topic of numbers to, algebra, functions, geometry and statistics there are all kinds of ideas on how you can use a clothesline in math class.
Curriculum Tags: All
http://clotheslinemath.com/

As mentioned @MaryBourassa has been experimenting with clotheslines and in these two posts, doing so with logs. Really, anything that you can calculate, get a numerical value and then order, can then be put on a number line. In her first post she outlines the idea for using logs and has all of the downloads and in the second post it is after she ran the activity and gives the pros, cons and changes.
Curriculum Tags: MHF4U, MCV4U
http://marybourassa.blogspot.ca/2016/02/log-clothesline.html
http://marybourassa.blogspot.ca/2016/02/log-clothesline-my-post-activity-post.html

I love this game. Many kids (and humans in general) can't "eyeball" correlation. In this game, created by @omarwagih, (which has a great Atari 2600 feel) you are given a scatterplot and asked to estimate the correlation and then you are given points on how close you are to the actual correlation. It is surprisingly addictive. Don't blame me if you can't stop.
thanks to Michael Lieff for this one
http://guessthecorrelation.com/

I love when teachers do a good job with Desmos activities. Often I am guilty of just building stuff that is functional and ignores aesthetics but this activity from @MrOrr_Geek doesn't. It's an activity that covers expectations about rates of change as well as describing the contextual meaning of points by using sugary cereal.
Curriculum Tags: MPM1D, MFM1P
https://teacher.desmos.com/activitybuilder/custom/56c305acfcfd640056b23805

Do you want to get your kids interested in data management? Then you should tell them how much money they might be able to make as a data scientist. I think in past years we might have called it being a statistician but apparently now data scientists are considered "sexy" jobs. And sexy jobs that have salaries that start north of \$100K and are at some of the coolest places to work (Apple, Airbnb, Twitter etc). This of course would be no surprise to @HansRosling who sent the following Tweet out in 2011. Thanks to @Mark_Esping for this one.
Curriculum Tags:All
https://ca.finance.yahoo.com/news/heres-much-money-sexiest-job-195900295.html

This would have been more appropriate during the Christmas Holidays but, hey I just saw this video from @MathyCathy on how to create a fractal based card. I made one and it turns out that it's pretty easy. If you want more ideas you can go to
Curriculum Tags: All

A nice graphic highlighting all of the NHL Stanley Cup winners. Perfect for some data management inferencing (eg "I infer that the Maple Leafs used to be a really good team - until I was born :-)  ). Thanks to @mathletepearce for this one
Curriculum Tags: Gr7, Gr8, MDM4U
https://scontent-yyz1-1.xx.fbcdn.net/hphotos-xlp1/v/t1.0-9/12728860_1684142441803284_5627299127368925474_n.jpg?oh=a40ea533a1850272b9cdf270b0efee34&oe=575F0295

This is a totally cool animated gif that shows the development of the formula for area of a trapezoid and how it relates to the area of a triangle. So awesome. Thanks to @mathletepearce for this one
Curriculum Tags: Gr7
Yup, and another "Only for geniuses" question on order of operation.
Curriculum Tags: Gr7, Gr8

## Friday, February 19, 2016

### Math Links for Week Ending Feb. 19th, 2016

A few years ago I was a facilitator at MathCAMPPP for teachers in Barrie. It was pretty awesome. The theme for the week was fractions and I was helping to facilitate the Gr9-12 session. One of the things we discussed was how useful a number line was and used a clothesline to create it. We did some cool things with functions but I digress. The point is that I love when anyone ever uses a clothesline in math. The general idea in this activity from @MrOrr_Geek is that students get random card with a line on it to calculate the slope from. Once they calculate their slope, they place their card on the number line in its appropriate spot and what you end up with is a visual that shows how the lines look as the slope increases.
Curriculum Tags: MPM1D, MFM2P
http://mrorr-isageek.com/slope-clothesline/

I love it when teachers take it upon themselves to create a whole new genre of math problems. Not that fractions are some new invention but @NatBanting has created his new site Fraction Talks where he posts images where students have to determine what fraction of the image is shaded. Or as he describes it:
"I introduce the structure much like a number talk. I project an image, choose a section to be shaded, and ask students, “What fraction is shaded?”. Students develop an answer (and reasoning) individually, and signal to me when they are done (usually with a thumbs up). I then extend invitations to share."
The images are categorized by type so that you can have your own fraction talks in your classes. Plus you can submit your own images. Check it out.Thanks to @marybourassa for pointing this out
Curriculum Tags: Gr7, Gr8
http://www.fractiontalks.com/

We created this activity years ago and finally are just getting around to posting it. The premiss is simple, students sort cards that have algebraic equations and expressions and matching statements. There are also Explain Everything versions as well for those of you who have iPads.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
http://engaging-math.blogspot.ca/2016/02/number-sentences.html

It's no surprise to anyone who knows me that I am a big fan of the Five Thirty Eight site. Lately they have been posting a weekly Riddler. They are math and logic related, like this one that has it's basis in the circumference of a circle. They post the new riddler every Friday and have the solution to the previous week's on that Friday post. You have a couple of days to submit your answer (if you are into that sort of thing). But if you are looking for some brain teasers for your class, then this might be a great place to start.
Curriculum Tags: All
http://fivethirtyeight.com/?s=the+riddler

There are a lot of reasons to love Wolfram Alpha. I was reminded of one of them this week. Type in the phrase "planes above" and you get info on aircraft in the area (based on your IP address). How does that connect to math? It's a great application of trig ratios. You get the altitude, slant distance and angle of elevation. All of these can be used to verify the properties of trig ratios.
Curriculum Tags: MPM2D, MFM2P, MBF3C, MCF3M, MCR3U
http://www.wolframalpha.com/input/?i=planes+above

The first part of this video from @standupmaths is a neat application of parabolas (image, a building that lights things on fire). The rest of the video is a derivation of the definition of the parabola (including some calculus). So you might want to just stick to the first part.
Curriculum Tags: MPM2D, MFM2P, MBF3C, MCF3M, MCR3U

Here is a great Expected value question from @MathGarden. I love how he points out that a great math question doesn't need asking.
Curriculum Tags: MDM4U
And the "Only Genius" posts keep showing up on Facebook. I'm with @mathletepearce with the idea that all we have to do is pose our questions to kids this way and they will do them without complaining.
Curriculum Tags: Gr7, Gr8
https://scontent-yyz1-1.xx.fbcdn.net/hphotos-xfa1/v/t1.0-9/12744213_342667029402340_8251468416875614500_n.jpg?oh=180506ab4de25bd3d6941cc85ebbaaa1&oe=57346CBF

And another one on order of operations
Curriculum Tags: Gr7, Gr8
https://scontent-yyz1-1.xx.fbcdn.net/hphotos-xap1/v/t1.0-9/10273978_1728727597451510_565607596159149094_n.jpg?oh=4249c54e33bee6240d4fffe050eb2847&oe=5765DBCE

## Friday, February 12, 2016

### Math Links for Week Ending Feb. 12th, 2016

Some great action via Twitter for those who teach calculus. First I helped out a bit on a Desmos Activity created by @mjfenton on rates of change with non linear functions as well as looking at non linear regression can function concavity and modelling with real data. Give it a try
Curriculum Tags: MHF4U, MCV4U
https://teacher.desmos.com//56bba82b4b336120062011da

The second one is about derivatives of exponential functions from @Thalesdeciple. It starts out like a Match My Graph activity and then quickly moves into the comparison of the graph to it's derivative. I think that when we are dealing with teaching calculus, having these sorts of dynamic activities are just the thing to help students visualize the ideas that Calculus brings. And because calculus, in my opinion, is the pinnacle of high school math, having more of this sort of thing is great. So keep it up, Internet. Thanks to @marybourassa for pointing this one out
Curriculum Tags: MCV4U
https://teacher.desmos.com/activitybuilder/custom/56bcb32ac8141921063d02ba

A classic problem turned into a 3Act task from @mathletepearce. No matter how often you give students this problem, it is always a great way to exemplify the nature of exponential growth. It's also good to deal with geometric series due to the discrete nature of the problem.
Curriculum Tags: Gr7, Gr8, MCR3U
https://tapintoteenminds.com/3act-math/penny-a-day/

Though @AlexOverwijk first posted this activity 3 years ago, I'm glad @wheeler_laura pointed it out with some Desmos activity builder additions and a Pear Deck slideshow (plus I like the Google Doc version of the squares). We have a similar activity on our blog but we don't have 26 squares and certainly don't extend it to anything beyond the Pythagorean relationship like they do here.
Curriculum Tags: Gr8, MPM1D, MFM1P, MPM2D, MFM2P
https://mslwheeler.wordpress.com/2016/02/08/26-squares-perimeter-mfm2p/
http://slamdunkmath.blogspot.ca/2013/04/26-squares.html

I'm always looking for Geometer's Sketchpad resources. Last week this site was pointed out to me by Chris Kunkel. It is sort of a one stop shopping place for some of the best GSP resources. Links to the Dynamic Number site as well as links to many of the Web Sketchpad sketches. There is stuff on transformations of geometric shapes all the way up to trig functions. Take a look
Curriculum Tags: All
http://www.geometricfunctions.org/index.shtml

I am not sure how long this has existed but if you are new to Desmos, then the Learn.desmos.com site will probably help. I like the fact that it has different levels of learning depending on what grade level your students are. These are not just videos but interactive activities that walk through some of the many features.
Curriculum Tags: All
http://learn.desmos.com/

Many of you are Smartboard users and possibly CLIPS users. Well apparently Smart is dropping Flash support in the latest version of their software. This video from @4GBrotto gives us the 411 on ways to work around this issue. Thanks to @rossisen for pointing this out.
Curriculum Tags: All

Awesome animated gif to show the connection between radians and degrees.
Curriculum Tags: MHF4U

Yep, another "only a genius" Facebook post
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P

I love how these all seem to include some reference to Einstein. The order of operations ones are my least favourite
Curriculum Tags: Gr7, Gr8

The Superbowl was last week but here are some data posts that relate. The first is from @stupidcalc
Curriculum Tags: Gr7, Gr8, MDM4U
http://www.stupidcalculations.com/blog/superbowl

And of course you can't have a Superbowl without one about consumption. Thanks to @mark_esping for pointing this one out.
Curriculum Tags: Gr7, Gr8, MDM4U

## Friday, February 5, 2016

### Math Links for Week Ending Feb. 4th, 2016

I am now on the hunt for a laser cutter. There is certainly a lot of buzz around 3D printing but you don't have to get that technically. I don't even think you need a laser cutter. Maybe just a CNC machine. I think many schools have those. And then you can make some of these cool geometric shapes that have so much versatility. So many tessellation possibilities that start from three identical quadrilaterals that come from a triangle.
Curriculum Tags: Gr7, Gr8

I was reminded of Row Games last week for some reason and remembered that we had made a bunch years back. So I thought I would blog about them. The premiss is that you pair kids up and they each get a column of questions. As they do the questions the answers are the same for each row so if they come out equal the kids have done them correctly, if not, it's back to the drawing board. It's self checking in this way and tweaks the idea of practice just enough for it to be a bit more engaging for students. Curriculum Tags: MPM1D, MFM1P
http://engaging-math.blogspot.ca/2016/01/row-games.html
When we can take simple math concepts and turn them into games then we have won. I love this little game that deals with plotting points on an Cartesian plane that was made with Web Sketchpad. It starts with an explanation of the rules. You are trying to find a "treasure" and are given how many segments away you are from it. You put in the coordinates of a guess and given more clues. Hopefully eventually finding the treasure. There is a board with just points in the first quadrant and one with all four quadrants. Have fun.
Curriculum Tags: Gr7, Gr8

Although I don't necessarily agree with the sentiment that "we don't spend enough time on limits" (I always did - I think) in our Calculus & Vectors course, I do love all the beginning of the semester activities that @marybourassa has given to her students. The Desmos one on create graphs was nice and the one on calculating the area of a circle using polygons reminded me of this older Nick Jackiw sketch (from Key Curriculum) on Archimedes method of exhaustion. A fun way to start the semester.
Curriculum Tags: MCV4U

We have recently been talking a lot about digital manipulatives vs physical ones and we specifically were talking about digital snap cubes. We like the app by Braining Camp (in fact we like their whole suite of manipulatives) but I was lamenting that it could only be used in 2D but I love this idea from @matthewoldridge to use Minecraft to do the same thing but in 3D. Great idea
Curriculum Tags: Gr7, Gr8

This post from @dsladkey totally resonates with me. I have long thought that graphing is a great way to check algebraic work. Although there are certainly times that I might want students to not use a calculator, more and more I think that there are ways you can ask questions that require students to show their work and only use the calculator for checking purposes. So often when ever I see a student do some algebraic work and ask "is it right?" I answer with "let's make a graph". I especially like to tell students to get a visual proof when they are doing trig identities. They literally could do it every step of the way to see if they have made an algebraic mistake or not. The one quote from this post that I liked the most was
"No Calculator questions strip the students of their best and most visual resource:  THE GRAPH. What No Calculator questions do is get students to forget that GRAPHING is a GREAT way to solve almost anything.  Don't we want to encourage graphing?  I don't mean graphing by hand either.  I mean a really fast way to analyze a problem.   Are we discouraging graphing because that is too easy?"
Sometimes that is the problem that I think teachers have with this. Almost as if solving a question without a calculator there is a right of passage. Times they are a changin'
Curriculum Tags: All
http://teachhighschoolmath.blogspot.ca/2016/01/getting-rid-of-no-calculator-questions.html

Sometimes understanding the normal distribution is tough. This video and website might help
Curriculum Tags: MDM4U
https://learnandteachstatistics.wordpress.com/2016/01/18/the-normal-distribution/

A great image for dealing with addition (or multiplication) with fractions: How many watermelons were used to make this image?
Curriculum Tags: Gr7, Gr8