Though I don't agree with the use of "controversial" in this article (I would use the word surprising instead), there are some nice summaries of some classic math problems. From infinity, to Benford's law, to the birthday problem, to Pi to the Monty Hall Problem, there is something for everyone here. Thanks to @mathletepearce for this one.
Curriculum Tags: Gr8, MCR3U, MDM4U, MHF4U http://www.businessinsider.com/the-most-controversial-math-problems-2013-3?op=1
I have been known to say that we humans are bad at understanding probability. And it may also be true that maybe we don't take it seriously enough when we teach it. If you believe Arthur Benjamin then its way more important than calculus and I think I agree. Well NPR's All Things Considered have a special series called Risk and Reason about how we deal with probability in the news. For example, if the forecast calls for a 20% chance of rain, what does that mean? You can get them all at the link below.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U http://www.npr.org/series/333708682/risk-and-reason
The first video from Numberphile this week is on Friedman Numbers. These are numbers that can be made up by taking their digits and creating a math problem with them (eg 25 = 52). And as these numbers get bigger the expressions get more complex. Seems like a perfect opportunity to talk about order of operations.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P https://www.youtube.com/watch?v=I7v2wAXFQpc
The second is about a great geometry problem with 54 solutions. See one of them here that fits well with properties of angles. Its a very cool and elegant solution.
Curriculum Tags: Gr8, MPM1D, MFM1P https://www.youtube.com/watch?v=m5evLoL0xwg
I was in a workshop this week and they showed this video from Marian Small. The video itself might cause a bit of controversy as she suggests that for most calculations beyond one digit by one digit kids should just use estimation and a calculator. I kind of reluctantly agree. Anyway, she tells it better so watch below. But the real reason I mention this is to point out a relatively new resource from the Ministry of Ontario called Learn Teach Lead. The Learn Teach Lead Vimeo page has literally thousands of videos that have been uploaded in the last 6 months. This particular series was recently released and is called Leaders in Educational Thought: Mathematics K-12 and features speakers such as Damian Cooper, Jo Boaler, Dan Meyer, Cathy Fosnot, George Hart, Sugata Mitra and of course Marian Small. Given the group I suspect that all of these were recorded at OAME this year. They are part of a series Each speaker has a bunch of short video clips on things like assessment, mindset, the art of mathematics and more. Go to the link below for all of them.
This is a cool thing that you can do with fractions. Basically the post is about decimal expansions of fractions and their special cases ( eg repeated decimals). But the cool stuff showed up in the comment section. For example if you divide 1/99980001 you will get the counting digits in the following way 1.0002000300040005....x10-8. Check out the one that generates the Fibonacci sequence too. Note that to show these expansions you will definitely have to use Wolfram Alpha. Curriculum Tags: Gr7, Gr8
I like this post on sampling error. I think when we teach this topic it can often get glossed over but here are several resources (including a video lesson) to help get the idea across on types of sampling error.
Curriculum Tags: MDM4U http://learnandteachstatistics.wordpress.com/
I don't think this article is saying anything really ground breaking: "Make math interesting for students by showing them the beauty and by making it relevant". It's not a new article either (last year) but it sources both Steven Strogatz and Dan Meyer and points out that just by making a question about Justin Bieber, that won't make it relevant to students. They can see through that.
Curriculum Tags: All http://blogs.kqed.org/mindshift/2013/10/finding-the-beauty-in-math/
I was in a workshop this week and we were given four different shapes (3 rectangles and a triangle of different colours) and asked to completely cover a regular piece of paper (without overlapping) using the pieces to create a "flag". At first thought this might have seemed like a lame activity for kids but further discussion revealed many different ways this could be connected to the elementary curriculum (fractions, percents, area, spacial geometry and more). The activity was developed by Dr. Cathy Bruce and you can download the instructions and template for cutting the shapes out here and the student BLM here that includes questions that can be asked.
Curriculum Tags: Gr7, Gr8 https://twitter.com/davidpetro314/status/511939184098283520/photo/1
I think it is interesting to let students in on the history of mathematics. And as it turns out we have Marcus de Sautoy to help us out. Here is a nice article from the latest magazine for IB teachers (turn to page 11). He also has a four part documentary called the The Story of Maths which you can view here (the first episode is below). He also has a 10 part BBC radio series called A Brief History of Mathematics an can be listened to and downloaded here. And if you find by now that you are into de Sautoy then you might like his TED talk on symmetry. Thanks to Steve Chevalier for reminding me of these.
Curriculum Tags: All
Making the Internet rounds recently is Randall Munroe, creator of XKCD. He is hocking his new book which is an expansion of this blog What if?. Here you can read an interview with him on the 538 blog and he was also on Science Friday recently too. Listen here. He was apparently also on the Colbert Report as well (Canada at 15:00, US). And I had mentioned this before but he has a TED talk as well. Thanks to Mark Esping for the last two.
Curriculum Tags: All
I came up with this activity a few years ago to do with my data management kids. It's an open sort for types of single variable data. Even though I made it for grade 12 data management, it could easily be used for grade 11 college or even all the way down to grade 7 where they have to talk about different types of data (eg categorical vs numerical). Digital files are here to so it's ready to go as is.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U http://engaging-math.blogspot.ca/2014/09/sort-graphs-into-types-of-data.html
It's always great when teachers blog out there and do the heavy lifting for us. That being said, I like this activity, Transformation Telephone. If you may recall from childhood, the game telephone was played when one person whispered something into the ear of another, then they passed it on to someone else and so on until it comes back and you see how the thing has changed over all the retellings. That being said, at the Slightly Skewed blog they have developed this idea for transformations. The idea is that students are in groups of four and each are given a function to graph. They then pass their graphs to the right and the teacher gives them a transformation that they have to apply. The students graph the new function and then pass the graph again. Then a new transformation is given and graph and passed one more time to be transformed again. The reason I like this is that it is a self checking activity. That is, if the students have done it correctly, then after the last transformation the new graph will be the same as the original (I have done the first here in Desmos if you don't believe me). So the reason I say they have done the heavy lifting is that they have come up with several sets of transformations that all come back to the original function. The way it is set up, it could be used in grade 11 U or UC since they use function notation with parabolas but with a little tweak you might be able to adapt it for grade 10 as well (for example if all the transformations give were just described verbally (eg "translated to the right by 3"). Thanks to Dan Meyer for this one.
Curriculum Tags: MPM2D, MFM2P, MCR3U, MCF3M http://slightlyskewedteacher.blogspot.ca/2014/08/transformation-telephone.html
It's always good to have real examples of things to explain concepts to students. In this story from the Story Collider (storys of science and math), a woman tells of how cognitive bias lead her boyfriend to jail. The story doesn't seem to be related to that at all as you are listening but it comes around at the end. Caution: there is one use of the f-word. Listen below
Curriculum Tags: MDM4U http://storycollider.org/podcast/2014-08-22
I don't think anyone would argue that if you contextualize math for students, they will have a greater chance of internalizing those topics. The tough part is doing that authentically. Just making a question about a cell phone won't do it. None the less this article talks about doing just that to make algebra more accessible.
I think it's important for students to hear some of the stories of math. I like this one because it is about someone who most people would not have heard about but who was pivotal in the space program at the same time as breaking down race and gender barriers. Watch a series of videos about Katherine G. Johnson here
Curriculum Tags: All http://www.makers.com/katherine-g-johnson
Solving equations is not necessarily the most engaging of activities. Of course good math students love it because they can show that they are so analytical. But for the majority of students who struggle, changing things up a bit can at least engage them a bit so that they will do the work. Here the questions are on the wheels and the answers on the clothes pins and the clothes pins and wheels each have different sets of symbols. Once student clip the clothes pins where they think they go then they flip it over to reveal the pairs of symbols. An answer key then reveals if each pair is correct.
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
XKCD's What if blog always does something to employ calculations with large numbers. In this instalment the question that is asked is "What is the most expensive thing you could fill a shoe box with". The most interesting part of this is that the choice was not gold or some other precious metal but 64Gb SD memory cards. But not empty memory cards but those filled with $1 songs or software. So this could easily turn into a rate question of some sort (and maybe couple it with volume).
Curriculum Tags: Gr7, Gr8, MPM1D, MFM1P
When I saw this I immediately loved it. Show a graph and ask "Name that Data". That is, let students use the characteristics of the graph to try to deduce what it is about. This could work with any data management unit. On this blog they don't always do this but it seems to be a recurring feature. I am not suggesting that this graph is the one you should use but more the idea of this type of activity. You might want to have several graphs and then several sets of variables and have them match it. Thanks to @globeandtims for this one
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U, MAP4C http://www.washingtonpost.com/blogs/wonkblog/wp/2014/08/22/name-that-data-6
A simple fraction game that you play with standard playing cards. Pair students off and they each draw two cards. They then have to create the fraction that is closest but not equal to a predetermined number. For more details follow the link below.
As it turns out, we start out being pretty good at understanding probability. Maybe it's what we do to kids in school that makes them worse. In this article the researchers demonstrate that toddlers have a knack for probability.
Curriculum Tags: All http://www.sciencedaily.com/releases/2014/08/140825123315.htm
Not necessarily a really mathematical application for education here but this is Numberphile's take on the Ice Bucket Challenge
It looks like Yummy Math is moving into the 3Act math realm. This image based task deals with the fractions of drill bit size. This is good for re enforcing fractions on a number line.
Curriculum Tags: Gr7, Gr8 http://www.yummymath.com/2014/drill-bit-fractions/
Though I don't agree with the use of "controversial" in this article (I would use the word surprising instead), there are some nice summaries of some classic math problems. From infinity, to Benford's law, to the birthday problem, to Pi to the Monty Hall Problem, there is something for everyone here. Thanks to @mathletepearce for this one.
I have been known to say that we humans are bad at understanding probability. And it may also be true that maybe we don't take it seriously enough when we teach it. If you believe Arthur Benjamin then its way more important than calculus and I think I agree. Well NPR's All Things Considered have a special series called Risk and Reason about how we deal with probability in the news. For example, if the forecast calls for a 20% chance of rain, what does that mean? You can get them all at the link below.
