## Saturday, November 29, 2014

### Math Links for Week Ending Nov. 28th, 2014

More of the same "Why is the common core good" stuff. We don't have the Common Core here in Ontario but we have expectations that have a lot of the similar properties. So this video tries to address some of the reasons that learning for meaning is good. I like the bit here about parents saying that because these methods are so foreign to them that they can't help their kids as proof that algorithms don't actually teach math.
Curriculum Tags: All
http://vimeo.com/110807219

I love getting out there and doing stuff with kids. One of my favourite things to do with grade 10 students is to use a clinometer to measure the height of tall things (flagpoles, buildings etc). But often you don't have clinometers in your schools. But this post shows how you can easily use a smart phone as a clinometer (with the right app). The only thing I might add is putting a straw along the top edge to help with siting. Thanks to Lisa Coughlin and Borden Hasiuk for this one
Curriculum Tags: MPM2D, MFM2P
http://gabrielhemery.com/2011/05/15/how-to-calculate-tree-height-using-a-smartphone/

I like this post about how data can help you write a better screenplay. Although the individual data sets are things that could probably be used in grade 7 or 8, I really think that this is more appropriate for grade 12 Data Management since it is really about bringing different sets of data together to do things better. That being said there
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U
http://fivethirtyeight.com/features/how-data-can-help-you-write-a-better-screenplay/

I have continued to add to my collection of videos on using algebra tiles. I didn't put these in the Student link section because I really intend them for teacher. Honestly to try to convince them that a conceptual understanding of algebra is better for students (at least in the beginning). I am not suggesting that the tiles are good for everything (or should be used for everything) but for the first parts of any concept I think they are good for everyone. That is why in the videos I keep the examples to simple ones as I think that once the questions become too complex then the rules for using algebra tiles get in the way of the understanding. And yes, takes a bit longer to use algebra tiles to, say, subtract a bracket but when we just tell students "change the sign of everything inside the brackets" its faster but its also no wonder that kids forget it. There is no connection for them. That being said here are three more that I made. The first is on adding and subtracting monomials
Curriculum Tags: MPM1D, MFM1P

The second is on simplifying polynomials

and the third is on subtracting polynomials

Now the narrator isn't so dynamic here but this series of videos is all about the math that is needed for construction. There is area, volume, unit conversions and more.
Curriculum Tags: Gr7, Gr8, MFM1P, MPM1D, MPM2P, MBF3C, MAP4C
https://www.youtube.com/watch?v=NiB2w_X23Rc&list=PL030CA42B814DE8B9

I think you could do something interesting in grade 12 Data Management with this visualization of chess piece survival rates.
Curriculum Tags: MDM4U
http://priorprobability.com/2014/10/22/chess-piece-survival-rates/

Another one for data management. This time a nice interactive visualization of all of the known satellites that are deployed.
Curriculum Tags: MDM4U
http://qz.com/296941/interactive-graphic-every-active-satellite-orbiting-earth/

Need a bar graph? Why not this one on the most popular names in the US? I am sure that the data is pretty similar for Canada. But beyond the first name, check out the other sets of data on names, there is some cool stuff.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

More Data from 538 and, again, I know that this is US data but it still is a nice data set to really get to the idea of a multiple bar graph (stacked in this case)
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

## Friday, November 21, 2014

### Math Links for Week Ending Nov. 21, 2014

I like this new site, Agree or Disagree. It's geared towards math but starts by showing you something and asking you a question that you have to agree or disagree on. They cover different topics (so far Quadratics, rates, volume and more) and every one comes with ppt file that has a full lesson and question suggestions. So for example, the first one has the video seen below. Then the lesson starts with the statement "The man's maximum height was no more than 50 ft. Agree or disagree" Then it gives potentially useful information and asks leading questions. The video itself is great for parabolic motion as it is done with a perfect side view so if you wanted to analyze it using something like Tracker, then you could. The PPT file has the video plus images with grids on them and even a strobe image for analysis
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MPM2D, MFM2P
http://www.aodmath.com/home

Kate at the f(t) blog has been laying down a bunch of good activities. The first of which is a game like Apples to Apples. The difference is that this game is used to connect students understanding of domain and range, it's called Graphies to Graphies. Check out her link below to get all the downloads and instructions.
Curriculum Tags: MCR3U, MCF3M
http://function-of-time.blogspot.ca/2014/11/graphles-to-graphles.html

Her next activity is dealing with parallel lines. It's a cool problem that takes advantage of a simple piece of paper that is folded on top of itself and the natural parallel lines that exist when done. It's definitely a problem they would have to chew on for a bit.
Curriculum Tags: MPM1D, MFM1P

And I love her approach to inverse functions. Starting with code breaking and then snaking her way into actually reversing operations. Then leading students to an activity. The cards and instructions are at the link below.
Curriculum Tags: MCR3U

Kyle at the Tap Into Teen Minds blog continues to turn them out. This time a 3Acts about the percentage increase of a photocopied cheque. It is similar to this one by Dan Meyer but getting bigger rather than smalller.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MAT1L, MAT2L
http://tapintoteenminds.com/3act-math/big-cheques/

I like this activity from Misscalculate about trig calculations in word problems. The premiss is that students get cards with problems on them and then also hint cards that they can use if they need them. All the cards are ready for download at the link below
Curriculum Tags: MPM2P, MFM2D
http://misscalculate.blogspot.ca/2014/11/word-problems-with-hints.html

This is an awesome video from Numberphile on the math behind the computer animation of Pixar movies. Now I had mentioned a TED talk a while back about this. Well this is the same guy but he goes into much more detail. Just like the previous TED talk, there is mention of midpoints but more than that there is mention of types of polynomial function, limits, tangents and more.
Curriculum Tags: MPM2D, MHF4U, MCV4U
https://www.youtube.com/watch?v=mX0NB9IyYpU

I saw this at the mall today. So many different questions you could ask. Maybe volume, definitely percent. It's not a cut and dry problem.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P, MAT1L, MAT2L
https://twitter.com/davidpetro314/status/535871465141575680/photo/1

A top 10 of the most beautiful math equations. Most of them are technically from physics but I am OK with that.
Curriculum Tags: All
http://www.cbsnews.com/news/the-11-most-beautiful-mathematical-equations/

## Friday, November 14, 2014

### Math Links for Week Ending Nov. 14th, 2014

I am a big fan of collecting real data in math class and if you can do that and have fun at the same time then even better. Mr. Orr noticed this great video on Jimmy Fallon and quickly noted the connection to scatter plots. I realize that it is no longer pumpkin season but he has created a Google form so you can add your own data and then summarized it on a Desmos Graph. All harnessing the power of Twitter to make the activity better. Thanks to Kyle Pearce for this one.
Curriculum Tags: MPM1D, MFM1P, MDM4U, MAP4C
http://mrorr-isageek.com/?p=3397

I just added a new Geometer's Sketchpad sketch to our Engaging Math blog. This is a fun one that has students guessing the size of a percent by sliding a point to create the shaded area. It was designed for the iPad (using the Sketchpad Explorer) but of course works in the desktop version of GSP as well. Download the sketch at the link below.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
http://engaging-math.blogspot.ca/2014/11/geometers-sketchpad-percent-guesser.html

Here is another new one from our blog Engaging Math. It's another one that can be used to create groups. In this case, groups of three in grade 9 academic or grade 10 applied. Students are each given a card that has either a table, equation or graph of a linear function and they are asked to find the other two people with the same relationship.
Curriculum Tags: MPM1D, MFM2P
http://engaging-math.blogspot.ca/2014/10/sort-students-into-groups-using-linear.html

This video was part of Mathalicious' Kickstarter campaign. When you watch it, it seems like a great connection to area of a circle and unit rate. Perfect for grade 8. But on the Mathalicious blog they have repurposed it to look at modelling the relationship between the pizza and the proportion of the crust. They have done it dynamically with some interactive applets and modelled the function. This would be great for modelling in Advanced functions. But you could also make connections to quadratics as well so you might be able to fit it in in grade 10 or 11 too.
Curriculum Tags: Gr8, MPM2P, MFM2D, MCR3U, MCF3M, MBF3C, MHF4U
http://blog.mathalicious.com/2014/11/02/pizza-pi/

The Sign of the Times blog have had a bunch of new interactives based on GSP sketches. And the good thing for some is that you don't need to have GSP to run them. They are puzzle based and could be used. The first is one that is a guessing game gives clues about a number between 1 & 25 by stating whether it is a multiple of any digit from 2-12. This is good for any time you just want to practice factors
Curriculum Tags: Gr7, Gr8
http://blog.keycurriculum.com/reasoning-with-multiples-to-find-the-mystery-number/

This one is not clear right away but there are 10 unknowns. Drag the circle over any number of them and it will show the sum of those unknowns. Your job is to determine what the unknowns are. And to make it more difficult, the numbers are moving. I see this as a great introduction to systems of equations in grade 10.
Curriculum Tags: MPM2D, MFM2P
http://blog.keycurriculum.com/dancing-unknowns-you-havent-seen-simultaneous-equations-like-these/

The third one is a neat little puzzle that requires students to create an isosceles triangle with the only stipulation that one of the vertices must be in a random location.
Curriculum Tags: Gr7
http://blog.keycurriculum.com/isosceles-triangle-puzzles/

Another nice one from Kyle at Tap Into Teen Minds. This time a student video on solving proportions. I like the visual way that he went about doing this and that he didn't jump right to the balance method.
Curriculum Tags: Gr8, MPM1D, MFM1P
http://tapintoteenminds.com/2014/10/17/visualizing-proportional-reasoning-working-ratios-proportions/

Do you want to mess with your kids. How about proving that all triangles are equilateral. It might fit into grade 7 since they talk about triangles there but really maybe anywhere. Thanks to Mike Lawler for this one.
Curriculum Tags: Gr7
http://mikesmathpage.wordpress.com/2014/11/06/using-numberphiles-all-triangles-are-equilateral-to-talk-about-constructions/

A proof without words of the cosine law. Follow the link for more details
Curriculum Tags: MPM2D, MFM2P
http://www.cut-the-knot.org/pythagoras/CosineLawMolokach.shtml

So fun. Fractal Silverware
Curriculum Tags: All
http://boingboing.net/2012/10/01/fractal-cutlery-that-fringes-o.html

## Friday, November 7, 2014

### Math Links for Week Ending November 7th, 2014

This video from Phil Daro suggests why in North America our math students do so poorly compared to other countries.
When I look at hundreds of hours of videos of Japanese classrooms where they get high performance from ordinary teachers and hundreds of hours of US classrooms where we get ordinary performance from very good teachers. I see the goal of the Japanese teacher is different from the goal of the US teacher. The American teacher looks at a problem they are going to use in a lesson and asks themselves, "how can I teach my kids to get the answer to this problem?" The Japanese teacher asks "what's the mathematics the students are supposed to learn from working on this problem?" - Phil Daro
Answer getting, that seems to be the issue. Watch the video and then take a look at Keith Devlin's post on it.
Curriculum Tags: All
http://devlinsangle.blogspot.ca/2014/11/against-answer-getting.html

A new video from TED-ED. And although it may not seem like there is a connection to a specific math problem, when they talk about the model for the turbulence it is shown to vary as the 5/3rds power. So when kids are asking where rational powers fits in the world, here is an application that comes from the art world
Curriculum Tags: MCR3U, MCF3M, MAP4C, MCT4C
http://ed.ted.com/lessons/the-unexpected-math-behind-van-gogh-s-starry-night-natalya-st-clair

We really like this activity which is basically a tweak of a very common activity done by most teachers when having students learn about scatterplots. In this case we normally have students measure their various body parts and then compare them to see if there is a relationship. The twist here is that we include comparisons that kids can make to real people about their heights, arm spans, foot size and hand size. See all of our templates here
Curriculum Tags: MPM1D, MFM1P, MDM4U, MAP4C
http://engaging-math.blogspot.ca/2014/10/how-do-i-compare-to-michael-phelps.html

Annie from the Math Forum talking about apps to help support conceptual learning. Apps include a sketchpad sketch that deals with types of triangles, an app that introduces the idea of distance time graphs, an app that introduces the idea of systems of equations and algebra tiles.
Curriculum Tags: Gr7, MPM1D, MFM1D, MPM2D, MFM2P
http://mathforum.org/blogs/annie/2014/11/06/using-technology-to-increase-conceptual-understanding-in-algebra-and-geometry-pctm/

I love this activity by Nat Banting. There are all sorts of ways you can demonstrate the concept of conditional probability. But playing egg roulette might be the best of them all.
Curriculum Tags: MDM4U
http://musingmathematically.blogspot.ca/2014/10/egg-roulette.html

For a free download (for a limited time) you can download this journal from the Association of Teachers of Mathematics.
MT243_Full_Journal.pdf

Kyle at Tap into Teen Minds has been producing these videos which are intended for students. They look slick and could easily be referenced as review or remedial or for a flipped classroom model. In this one the idea is the trend line of a scatterplot.
Curriculum Tags: MPM1D, MFM1P, MDM4U, MAP4U
http://tapintoteenminds.com/2014/10/10/visualizing-two-variable-relationships/

Leave it to Dan Meyer to take a boring pseudo math concept and add a tweak to make it more palatable. Take the coin problem "You have 50 dimes and quarters and they total \$11. How many of each do you have?" Why not start with a real application of this in the video below. Then get to the actual problem incrementally. IE just ask how many of each could add to \$11. And then move on. Take a look at the blog post.
Curriculum Tags: MPM2D, MFM2P
http://blog.mrmeyer.com/2014/these-horrible-coin-problems-and-what-we-can-do-about-them/

So fun, why not use hashtags when commenting on student assessments?
Curriculum Tags: All
http://www.mathycathy.com/blog/2014/10/just-playin/

I know that Halloween is over but still I like this interactive graph of the most popular costumes over the last few years. Click on any item and see the broken line graph appear.
Curriculum Tags: Gr8, MDM4U, MAP4C
http://www.npr.org/blogs/money/2014/10/27/359324848/witches-vampires-and-pirates-5-years-of-americas-most-popular-costumes

Want some data on weight loss. Here are a couple of bar graphs that try to determine which are the most useful diets.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U
http://fivethirtyeight.com/features/which-diet-will-help-you-lose-the-most-weight/

And one more for Halloween. This time an infographic on the healthiest candies
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U
http://lifehacker.com/halloween-candy-ranked-by-healthiness-1652824186