## Friday, December 26, 2014

### Math Links for Week Ending Dec 26th, 2014

This is a relatively new site dealing with diagnostic questioning with multiple choice questions. Now most MC question sites are pretty standard. Ask a question, show some answers, tell the person if they got it right, move on. This is different. First of all, the questions are written with good MC design. That is, the wrong answers are based on misconceptions. So this means that even if someone chooses the wrong answer they can learn something. Also as they answer, they are encouraged to explain their reasoning for making that choice. Once they answer then they can see the correct answer and all the explanations (of the correct and incorrect answers) created by other students. So that means they can self medicate. Teachers can create classes and questions and there are more than just math questions (though math currently has the most). Thanks to Dan Meyer for pointing this one out. Curriculum Tags: All
http://www.diagnosticquestions.com/

A new activity from my Engaging Math. This one is about the geometric (area) model of the Pythagorean Theorem. Students are given sets of three numbers (some are Pythagorean Triples) and then sets of squares with side lengths equal to the numbers in the sets. Through the activity, students then discover the Pythagorean relationship.
Curriculum Tags: Gr8, MPM1D, MFM1P
http://engaging-math.blogspot.ca/2014/12/the-area-representation-of-pythagorean.html

Kyle at Tap Into Teen Minds, has a new three acts that deals with cylinders and jelly beans. I actually saw it independent of the jelly bean video below. But if you are doing anything with cylinders then this could be good. There are two here actually, the original and the sequel. So check them both out.
Curriculum Tags: Gr8, MPM1D, MFM1P
http://tapintoteenminds.com/3act-math/guessing-gumballs/
http://tapintoteenminds.com/3act-math/guessing-gumballs-sequel/

This site has been around for a while but they have added some new activities since the last time I have been to it. My favourite activity is the Music in Math Challenge where students work with music samples in rate and ratio in a fun and interactive way. There are other challenges dealing with percents, graphing, parabolas and more.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MPM2D, MFM2P
http://www.thirteen.org/get-the-math/

Do you need to know when all the major math holiday's are? Then look no further. From the most popular "Pi Day" to the lesser known "Fibonacci Day", get the info here. Thanks to Michael Lieff for this one.
Curriculum Tags: All
http://tetrahedral.blogspot.ie/2012/12/14-math-holidays-every-math-major.html

I always like having examples of quadratic relations in real life. This animation was made in 2008 to demonstrate the power of a new video card and it has balls flying in parabolic motion all over the place. And if you look closely you can also pick up some spots with sinusoidal motion (eg when the cymbal is crashed).
Curriculum Tags: MPM2D, MFM2P, MCF3M, MCR3U, MBF3C

A math parody of Gagnam Style. This time dealing with intro to Trig. Thanks to Michael Elliot and Alessadra Perruccio for this.
Curriculum Tags: MPM2D, MFM2P, MCF3M, MBF3C, MCR3U

This was a contest that ran last year out of Australia. The premiss was being able to guess how many jelly beans were in the cylinder. You could pay \$5 to make a guess and the person who guessed close enough could win \$100,000. As it turns out, the contest was cancelled and everyone got their money back and we never did find out what the amount was. But you could try it in your classes, just for fun.
Curriculum Tags: Gr8, MPM1D, MFM1P
http://vimeo.com/26603533

My sone made this dodecahedron for my wife for Christmas out of cans of Coke.
Curriculum Tags: All

I like this little problem that deals with both perimeter, geometry and number sense.
Curriculum Tags: Gr7, Gr8

I thought this would be a good for exploring exponential functions and modelling. When you try to model the size of storage space over time then you should see an exponential relationship (probably closely following Moore's Law). You could probably also do some research and look at how the price per Mb has also changed.
Curriculum Tags: MCR3U, MAP4C, MCT4C, MHF4U

## Friday, December 19, 2014

### Math Links for Week Ending Dec 19th, 2014

So many good things this week that it was hard to pick the thing that I would feature. So I narrowed it down to two. The first is a new one from that graphing juggernaut Desmos. This time a new activity for recognizing and describing linear, quadratic and rational functions as well as hexagons. They have done it in a way that is very much like the kids game Guess Who? The way it works is that kids login to a game (that you initiate with your account). They are then paired up and both are presented with a grid of graphs(each from their own computer or tablet). One of the students picks one of the graphs and then the other starts asking yes or no questions. As the questions are answered the graphs can be crossed off until the chosen graph is revealed. Check out their blog post about it for more info. Thanks to @marybourassa for this one.
Curriculum Tags: MPM1D, MFM1P, MFM2P, MPM2D, MBF3C, MCF3M, MCR3U
http://blog.desmos.com/post/105283812542/polygraph

The second neat site is one that helps with solving equations is SolveMe. On this site students are given a symbolic representation of an equation using a balance and shapes to represent unknown numbers. This is similar to the series of Geometer's Sketchpad sketches that did the same thing years ago but now can be done without the special software. Perfect for beginning algebra.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
http://solveme.edc.org/

We have a couple of new activities on our Engaging Math Site. The first one is a Christmas themed review activity for decimals, exponents and Pythagorean Theorem in grade 8. Students are put in group to grab questions. When they get a question correct, they can earn a present on the SmartBoard tally board. There are special cards for extra points as well and as an extra bonus, if you tap on any tree, it places a different Christmas song.
Curriculum Tags: Gr8
http://engaging-math.blogspot.ca/2014/12/christmas-review-activity.html

The second is another Sketchpad activity. This time for kids to practice their knowledge of perfect squares. The sketch generates a random number under 150 and students have to decide whether it is a perfect square or not. To help, they can actually try to construct a literal square with the same area as the number given.
Curriculum Tags: Gr7

We have, for a long time, in Ontario had a great resource in the CLIPS package. The problem is that it's a flash based app and thus won't work on an iPad. Well it still won't work on an iPad but a new app associated with the Puffin Browser has been developed that has taken CLIPS as well as a bunch of other flash based resources and combines them in what is now called the Puffin Academy. Go there with the app and you can choose CLIPS from the choices and it runs almost as it would on a regular computer. Read more about it here on the CLIPS blog
Curriculum Tags: All
http://mathclips.wikispaces.com/Using+MathCLIPS+on+Mobile

CueThink is an iPad app that is kind of like an interactive notebook that students can use. Given a problem students can start by saying what they have noticed and wondered and eventually get to a video solutions (similar to what might be done on Educrations). Then as a teacher you can go in and annotate those solutions from their dashboard. Check out Andrew Stadel's blog post on the topic. Thanks to @marybourassa for this one.
Curriculum Tags: All

Although the data might be controversial, there is some good probability based math here for grade 12 data management. The interactive graphs show the chance of pregnancy for various forms of birth control. It's a perfect demonstration of the binomial distribution for probability.
Curriculum Tags: MDM4U
http://www.nytimes.com/interactive/2014/09/14/sunday-review/unplanned-pregnancies.html?_r=0

People really can't wait for the new Star Wars. So much so that they are analyzing to death the first trailer to come out. In this post, they use the free tracker software to determine the approximate speed of this new R2 droid. Most of the math needed isn't too hard but the main idea pivots around angular velocity in terms of radians. So this probably would be best for modelling in advanced functions or calculus.
Curriculum Tags: MHF4U, MCV4U
http://www.wired.com/2014/12/fast-rolling-droid-star-wars-vii/

It's always good to find real world applications for math topics that seem to have none. In this case, the concept of least common multiple is the topic and the application is hotdogs and hotdog buns and the scenario is taken from the movie Father of the Bride.
Curriculum Tags: Gr7, Gr8

Do you need something that might be interesting for student when having them work with formulas. In this case, the formula is one that takes all the data and uses a formula to determine the most popular albums of all time. It's a pretty interesting algorithm and produces some interesting results.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
http://www.besteveralbums.com/howitworks.php

The Centre for Education in Mathematics and Computing (CEMC) at the University of Waterloo has just released a great resource for students in grade 12 Advanced Functions and Calculus & Vectors. This is an interactive student resource with interactive tutorials and quizzes that is sorted by topic. No login is required and students are free to use this as often as they wish. Right now it is about 50% functional with new modules being added all the time. Thanks to Mark Esping for this one.
Curriculum Tags: MHF4U, MCV4U
http://courseware.cemc.uwaterloo.ca/

Do you want to know why those in the UK use the term maths and we over her don't use the 's'? Then read on.
Curriculum Tag: All
http://www.slate.com/blogs/lexicon_valley/2014/12/08/math_versus_maths_how_americans_and_brits_deploy_the_collective_noun.html

The idea that there are math people and non math people has long since been disputed. Here is some more evidence.
Curriculum Tags: All

I have always thought that the area of a trapezoid formula was pretty useful. That is, it can be used to find the area for a parallelogram, rhombus, rectangle, square, and even a triangle. So I create a GSP sketch and this video to demonstrate that.
Curriculum Tags: Gr7

Some Christmas cheer for you
Curriculum Tags: All
http://visualizingmath.tumblr.com/post/104961540336/submitted-by-naked-geometry-math-inspired

At first this seems very cool but a second look gives you pause and of course it can't be. But it can be a great opportunity for your students to answer the question: What would need to be include in the equation in order for it to be true. Here is the answer if you are interested. Thanks to @ecokrisb for this one.
Curriculum Tags: MPM1D, MFM1P, MFM2P

## Friday, December 12, 2014

### Math Links for Week Ending Dec. 12th, 2014

This is the 100th Math links. That is some sort of milestone I guess. I will continue to wait for my award. In the mean time....

This is not so much math but I still think it is good for all teachers to see. The premiss is that throughout the years there has been things that were touted to be able to "revolutionize education", though non have. That part is good but the part that resonated with me was the bit about what a teacher should do:
If you think the fundamental job of a teacher is to transmit information from their heads to their students then you are right they (teachers) are obsolete .......  The fundamental roll of a teacher is not to deliver information. It is to guide the social process of learning
Curriculum Tags: All

This was a quick little activity to do as a holiday treat. It is basically a colouring and patterning exercise with series, sequence and Pascal's Triangle. It could be kept light as it is or you could have kids determine the equations that represent each pattern to make it a little tougher.
Curriculum Tags: MCR3U, MDM4U
http://engaging-math.blogspot.ca/2014/12/the-12-days-of-pascals-triangle.html

A new one from Kyle at Tap Into Teen Minds. It's a 3Act Task dealing with composite volume. So it's perfect for grade 9 academic or grade 10 applied.
Curriculum Tags: MPM1D, MFM2P
http://tapintoteenminds.com/3act-math/mix-spray/

Often we ask "wrapping a gift" questions when we are trying to look at surface area of rectangular prisms but they aren't realistic due to all the overlapping that goes around. Check this out though, the mathematical way to wrap a gift with minimal waste.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
http://mentalfloss.com/article/60493/how-wrap-present-mathematical-precision-and-waste-less-paper

A new one from Numberphile. This one is pretty cool. They start with a sequence that is a modification of the Fibonacci sequence and then turns it into a representation of every rational number that exists, without repetition. Pretty neat.
Curriculum Tags: Gr7, Gr8, MCR3U

Curriculum Tags: All

Another web conference from the Ministry of Ontario. This time with Dr. Chris Suurtamm talking about myths in mathematics. This is a recording of an Adobe Connect session so it looks like it's interactive but it is not.
Curriculum Tags: All

Plenty of math in the Simpsons/Futurama crossover episode. Check out all the formulas. Follow the link for info on which ones
Curriculum Tags: All
http://www.simonsingh.net/Simpsons_Mathematics/simpsorama/

Need some Christmas data (who doesn't)? The crew at the 538 blog have got yer Christmas song data all ready for you in bar graph and tabular form. Whether it be the increase in Christmas themed Spotify channels or which is the most played Christmas song, you can find it here.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

## Friday, December 5, 2014

### Math Links for Week Ending Dec. 5, 2014

If you have a couple of hours to kill and want to think deeply about fractions then I suggest this Adobe connect from Dr. Cathy Bruce. Dealing with the conceptual ideas that relate to fractions.
Curriculum Tags: Gr7, Gr8

I have really been pumping out the Geometer's Sketchpad files lately. This latest one is meant for students to practice estimating square roots (without a calculator). The are four levels of guessing: Perfect squares under 100, Perfect squares under 500 (both appropriate for grade 7) Square roots under 100, and Square roots under 500. These last two require students to estimate the square root of non perfect squares without a calculator. The software generates all the random numbers and students can check their own answers. And as always this works really well with the Sketchpad Explorer app on the iPad.
Curriculum Tags: Gr7, Gr8

I like this post because it does a good job of taking something that we normally do and then giving it a little tweak to make it better. In this case it is in reference to all the distance time graphs and the tweak is to add a notice/wonder step at the beginning where students are asked no specific questions except what they notice and wonder. It's actually a good thing to consider when looking at any graph. As a bonus the worksheet downloads are included.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MFM2P
http://drawingonmath.blogspot.ca/2014/11/distance-graph.html

I have often said that sometimes all you need is a little tweak to get students to do something they normally were reluctant to. Here is an example. In both Grade 12 Advanced Functions and Calculus and vectors, we have to be able to describe functions and curve sketch. This tweak basically has students write personal adds for functions to describe them. Couple that with Desmos or GSP and you now have made that dynamic. Here's an example
I am a very negative and odd function. I have been working my way from quadrant 2 to quadrant 4. I have no curvy parts and I like to rest right at the origin. I am looking for a function to put a little more life in me. Two turning points is a must. I'm, looking for a positive influence in my life.
For more examples and some teaching suggestions, check out the post at the link below
Curriculum Tags: MHF4U, MCV4U

I am a big fan of using portable white boards in class. Years ago we used to go to the local hardware store and by 4'x8' sheets of tile board then have them cut them into 1'x1' pieces. But it never occurred to me to cut them in larger size pieces for group work. That is just what Andrew Stadel did and even came up with some suggested uses. Check them out here.
Curriculum Tags: All