http://wtfviz.net/
The title may not be school-appropriate, but the awful data representations are a goldmine of "What's wrong with this?" problems.
Friday, September 27, 2013
What's Number Are You?
http://www.bbc.co.uk/news/world-15391515
According to this website, of all the people living on Earth, I was the 4,611,347,584th person to be born. Can you figure out how old I am???
There are lots of other interesting mathematical things about this. First, just the fact that the population of the Earth increased by about 2.5 billion people in my lifetime--more than half of what it was when I was born--is just staggering. I know that large numbers are hard for kids to conceptualize (adults too! me (non-kid, non-adult) too!), but there's something in here that makes you say WOAH. Even if you put in a kid's birthday (I picked a random 15 year old), there were still about 1 billion people born in their lifetime.
Of course there's also interesting stuff with exponential growth, how we would calculate this number, and so on. I'm also interested in the statistic of how many people have been born on Earth since the beginning of time. This website gives an interesting summary of that calculation, including this video:
According to this website, of all the people living on Earth, I was the 4,611,347,584th person to be born. Can you figure out how old I am???
There are lots of other interesting mathematical things about this. First, just the fact that the population of the Earth increased by about 2.5 billion people in my lifetime--more than half of what it was when I was born--is just staggering. I know that large numbers are hard for kids to conceptualize (adults too! me (non-kid, non-adult) too!), but there's something in here that makes you say WOAH. Even if you put in a kid's birthday (I picked a random 15 year old), there were still about 1 billion people born in their lifetime.
Of course there's also interesting stuff with exponential growth, how we would calculate this number, and so on. I'm also interested in the statistic of how many people have been born on Earth since the beginning of time. This website gives an interesting summary of that calculation, including this video:
The World Bank has a shorter video on the same topic:
I like the stat in this video that 7% of all the people who have ever lived are alive today. Holy smokes!
Monday, September 23, 2013
Record Setting Stupidity
http://recordsetter.com/
This is a proportional reasoning teacher's dream. All of those problems I've used about competitive eaters, giant foods, and other world records, here are videos to match! Those weird facts are already a good hook for kids, but reading about someone cramming hot dogs down their throat will never top actually seeing it.
This is a proportional reasoning teacher's dream. All of those problems I've used about competitive eaters, giant foods, and other world records, here are videos to match! Those weird facts are already a good hook for kids, but reading about someone cramming hot dogs down their throat will never top actually seeing it.
Saturday, September 21, 2013
Biggest Trig Warmup Ever
This looks so fun! What a way to get kids to think about the composition and decomposition of the "sweet 16" triangles on a unit circle. I haven't found many get-up-and-move-around activities that feel appropriate to high schoolers, so I love this. The materials prep isn't even that bad because you only need the two triangles.
Extra challenge for when you have more students in the class: throw in the angles an increments of 15degrees that aren't already part of the key unit circle angles. Really this is a physical variation on the question of how many angles you can build from just from a set of drafting triangles.
Extra challenge for when you have more students in the class: throw in the angles an increments of 15degrees that aren't already part of the key unit circle angles. Really this is a physical variation on the question of how many angles you can build from just from a set of drafting triangles.
Elevator Math
Eli Lansley of the Lansley Brothers Blog posted these pictures of interesting floor numbering systems in buildings.
The first he found in Israel, the second in Hackensack, New Jersey
I have definitely taught kids to think about negative numbers and number lines by thinking about elevators. I don't know much about teaching younger grades or teaching negative numbers for the first time, but I can totally imagine giving kids a picture like this and asking them to describe the building where this elevator lives. Or some kind of problem about a building that adds an underground garage with the question "How should they label the number on the elevator button?" Even with the standard US systems for labeling underground space (P1, P2, P3 and stuff like that), I think it's interesting to talk about what order those should go in. Maybe it's not that exciting, but it feels like there's a little something there.
Also thinking about elevator numbering, I feel like there might be something with the way that many European countries label their floors by having floor 1 as the floor above the lobby. Or with Americans skipping the 13th floor. Is there some kind of function rule you can write to figure out how many floors the building actually has? It would be a piecewise function because the rule for calculating how many floors for buildings above 13 would be different than for buildings with fewer than 13 floors.
The first he found in Israel, the second in Hackensack, New Jersey
I have definitely taught kids to think about negative numbers and number lines by thinking about elevators. I don't know much about teaching younger grades or teaching negative numbers for the first time, but I can totally imagine giving kids a picture like this and asking them to describe the building where this elevator lives. Or some kind of problem about a building that adds an underground garage with the question "How should they label the number on the elevator button?" Even with the standard US systems for labeling underground space (P1, P2, P3 and stuff like that), I think it's interesting to talk about what order those should go in. Maybe it's not that exciting, but it feels like there's a little something there.
Also thinking about elevator numbering, I feel like there might be something with the way that many European countries label their floors by having floor 1 as the floor above the lobby. Or with Americans skipping the 13th floor. Is there some kind of function rule you can write to figure out how many floors the building actually has? It would be a piecewise function because the rule for calculating how many floors for buildings above 13 would be different than for buildings with fewer than 13 floors.
Tuesday, September 17, 2013
Upgrading & Early Termination Fees
Here's an interesting story about a guy trying to negotiate upgrades for his family to the latest iPhone. All comments aside about the scam that constant upgrade "opportunities" offer, the story is an interesting mix of straight math and emotion. So basically, economics. Homo Economicus might have just skipped the upgrade altogether (or took his family back to flip phones).
The story in itself seems like more of a hook than the basis for a problem you'd actually spend the bulk of a class period on, but it opens up larger questions about early termination fees, upgrade costs, etc. Given deal X from company A that gives you free or cheaper phones with a new account, at what point is it "worth it" to leave your existing phone company and suck up the early termination fees?
There are lots of other interesting variables that could factor into the decision:
The story in itself seems like more of a hook than the basis for a problem you'd actually spend the bulk of a class period on, but it opens up larger questions about early termination fees, upgrade costs, etc. Given deal X from company A that gives you free or cheaper phones with a new account, at what point is it "worth it" to leave your existing phone company and suck up the early termination fees?
There are lots of other interesting variables that could factor into the decision:
- How many phone lines you have
- Variations in cost between the actual monthly phone plans of the two companies
- How soon you'd be eligible for an upgrade with your current company
- How soon the other phone lines would be eligible for an upgrade
- What kind of quantifiable measure you put on being cooler than your friends and/or having the latest thing. Would it change your mind about waiting out your time until an upgrade if you knew that all your friends would have the new iPhone before that? How many friends would you care about? Can you quantify how much you care?
Reminiscing about the Good Old Days of Gas Prices
http://consumerist.com/2013/09/17/you-will-probably-never-pay-less-than-3-for-a-gallon-of-gas-ever-again/
The Consumerist says that we will never again in our lifetimes pay less than $3/gallon for gas. When I first got my driver's license, I remember paying less than a dollar! I also remember when gas prices started to go up and I swore I would never pay more than $2/gallon. (Maybe the math problem in here is figuring out how old I am...). The Consumerists's logic seems to be that because today was the 1000th consecutive day that average gas prices are over $3, we can safely say that we've reached the point of no return.
Here are my mathematical questions about this situation:
- Are you convinced the 1000th day is "enough" of a pattern to say that we're never going back?
- Would you be as convinced if the 1000 days were not consecutive? What kind of pattern of conductivity would be "enough" for you?
- Does it matter that this about the national average of gas prices?
- Does it matter what that average price is for you to be convinced? For example, if the national average price of gas is $3.89, I'll probably be convinced that <$3 is unlikely. But if the national average is $3.02, I feel confident in saying that I won't have too much trouble driving around and finding a gas station where I can pay $2.99. --> This seems like a perfect opportunity to talk about the importance of standard deviation!
- How could looking at a graph of gas prices help add to an argument? I feel like there's a very powerful visual argument of showing the $3 line and looking at when the graph stops dropping below that.
- If you wanted to convince someone with a graph, what data would you show?
- National averages only, or the range?
- How often would you want to chart data points? Daily? Weekly? Monthly?
The Painted Cube, Revisited
I'm a big fan of the "Painted Cubes" problem (although to be honest, I don't think I have ever actually used it with kids...). I feel like most math-y people have seen the problem at some point: If you build an n x n x n cube out of unit cubes and paint all the faces, how many of the unit cubes will have one face painted? 2 faces? 3? 0?
This problem from NRICH Maths is a a cool extension. I love the use of the word "some"--it's so interesting how that word both increases access and makes the problem so much harder. I haven't actually done any work on the problem yet, but it just makes me want to play!
This problem from NRICH Maths is a a cool extension. I love the use of the word "some"--it's so interesting how that word both increases access and makes the problem so much harder. I haven't actually done any work on the problem yet, but it just makes me want to play!
Not-So-Easy Area
This seems to be called the Azulejos puzzle. I haven't actually gone through and figured it out yet (or cheated and watched the solution videos that pop up on YouTube), but it's super cool. I love that it takes a pretty straightforward area (a rectangle with obviously countable squares) and plays with it. I imagine that kids would have lots of non-mathematical theories about why this illusion happens. The YouTube commenters are thrilled to share their theories about how the person in the video is using slight of hand. But no magic, just math.
This task, "Doesn't Add Up" from NRICH Maths--my new favorite (or should I say favourite?) source of math tasks--feels similar to me. There's something going on that fools you, and it would be interesting to see what kids think is going on and how they solve it.
The NRICH Maths task also brings back memories of a long, painful evening I spent trying to write a shaded area problem for a test. I was trying to come up with a triangle that had parts shaded so I could ask kids to find the shaded area in at least two ways (getting at ideas of decomposition and recomposition). But the measurements I kept trying kept getting me different answers from different strategies! Even though I was trying to work systematically starting from one measurement and determining the others from there, it kept coming up weird. Finally I figured out that free-handing my triangles and adding values meant I wasn't actually accounting for angle measures and slopes of lines so the shape I was drawing was decidedly not drawn to scale. Finally I just got out some graph paper so I knew I was drawing to scale; I couldn't believe it took me so long to figure out what was wrong. On the plus side, at least I caught my error and didn't put an impossible problem on a test (wouldn't be the first time, won't be the last, but at least it wasn't another time).
Sunday, September 15, 2013
More Grocery Shrinking Options
- Change the shape of the packaging (box 1 in the comic above). Needs to be a change that's subtle enough that someone won't notice. Could be totally dramatic (changing rectangular package to a cylinder or frustrum). Could be subtle (shave a little bit off here, a little bit off here, no one will notice). Could be sneaky (when bottle manufacturers make the bottom of the bottle not flat).
- Make the actual product smaller (upper right box in the comic above). Seriously, how much could you save by making the holes in cheerios or bagels bigger?
- Filling the package with something else (the ice cream gnome above). Less ice cream, more toys!
(Yes, this is teaching kids to be corporate scammers, but hey, preparation for the real world, right? Maybe it will also teach them to be suspicious of corporate scammers!)
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