Michael Ross did an interesting analysis of McDonald's Monopoly game and Tim Horton's "Roll Up the Rim to Win" (not living in Michigan anymore, I had kind of forgotten that Tim Horton's existed...)
http://regressing.deadspin.com/the-math-behind-mcdonalds-monopoly-1642081131
http://www.mikerobe007.ca/2013/02/the-economics-of-roll-up-rim-to-win.html
I like the data displays he uses in his Monopoly analysis are nice (2-way table vs. pie chart), and I like the comparisons used in his analysis.
Not sure exactly what math I would have kids do with this, but it's fun. Maybe it would give kids another mathematical reason to not eat at McDonald's.
Showing posts with label Probability. Show all posts
Showing posts with label Probability. Show all posts
Wednesday, October 8, 2014
Tuesday, September 23, 2014
Estimation 180 and Confidence Intervals
I love Andrew Stadel's Estimation 180 collection and sequence, for all the reasons why lots of people have been praising it. Estimation is an undervalued skill! Kids are terrible with units of measurement! It's super-accessible across multiple grade-levels! It's quick! It's fun! Etc!
One of the features is that Stadel always first asks for a guess that is too low and a guess that is too high, before asking for a the final estimate. I initially liked this because of how it increases accessibility for students and also trains them, in the long-term, to get more specific and accurate with their estimates and reasoning. Now I found a new reason why I like this practice: preparing kids for confidence intervals. Confidence intervals are just a more systematic way of making estimations, and really what the confidence interval is saying is "here is my range of guesses that are neither too high or too low." I imagine that when having kids share to high/low guesses for Estimation 180, there will sometimes be guesses that are actually correct, especially as students get better at their estimation and try to get "just a little bit" off in their too high/low values. That, in a lot of ways, is like a confidence interval! A 95% CI is saying that it is possible--5% of the time--that our interval doesn't capture the true population statistic (mean, proportion, etc). The too high/low guesses for whatever population statistic fall in those outer 2.5% tails. They're possibly correct, but it's highly unlikely. You'd be really surprised a value from those tails turned out to be the true population statistic.
Somewhere in here there has to be a lesson/activity where we collect estimations from a bunch of people and find out that the mean estimation is actually pretty close to the actual value. This is true for people guessing about the number of jelly beans in a jar, and so on. Can we use estimations to set up a confidence interval for the real number of jelly beans in a jar? Is that legitimate statistics?
One of the features is that Stadel always first asks for a guess that is too low and a guess that is too high, before asking for a the final estimate. I initially liked this because of how it increases accessibility for students and also trains them, in the long-term, to get more specific and accurate with their estimates and reasoning. Now I found a new reason why I like this practice: preparing kids for confidence intervals. Confidence intervals are just a more systematic way of making estimations, and really what the confidence interval is saying is "here is my range of guesses that are neither too high or too low." I imagine that when having kids share to high/low guesses for Estimation 180, there will sometimes be guesses that are actually correct, especially as students get better at their estimation and try to get "just a little bit" off in their too high/low values. That, in a lot of ways, is like a confidence interval! A 95% CI is saying that it is possible--5% of the time--that our interval doesn't capture the true population statistic (mean, proportion, etc). The too high/low guesses for whatever population statistic fall in those outer 2.5% tails. They're possibly correct, but it's highly unlikely. You'd be really surprised a value from those tails turned out to be the true population statistic.
Somewhere in here there has to be a lesson/activity where we collect estimations from a bunch of people and find out that the mean estimation is actually pretty close to the actual value. This is true for people guessing about the number of jelly beans in a jar, and so on. Can we use estimations to set up a confidence interval for the real number of jelly beans in a jar? Is that legitimate statistics?
Wednesday, July 2, 2014
Guess My Weight
I've always been interested in those people at amusement parks and fairs who guess people's weight or age or birthday month or whatever. One interesting question from that situation is which variable you should have the person guess for the best chance of winning. On one hand, birthday month feels nearly impossible for someone to guess by just looking at you, but the guesser does have a 1/12 chance of being correct. I can't remember the usual ranges for age and weight that let the guesser win, but it would also be interesting to think about how the amusement park sets those and if they're fair. To complicate things even more, how do social factors change what the guesser guesses (e.g. does the guesser under-guess age and weight for older people and women respectively, because that's what our society says is better?)
This problem is super-interesting:
http://nrich.maths.org/6957
I like that there is a lot of open-endedness to the solution and "correct answer." Unfortunately I am not sure what unit it might fall in because it involves a ton of different possibilities. Just a fun math problem? That's okay with me too!
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Update: I tried this task with a group of approximately 80 secondary math teachers (6th-12th grade). My version was slightly modified to (1) give it a little bit more of a hook and make it look pretty; and (2) obscure the task name so no one could google it... Teachers are sneakier than students. They shouldn't get to do what I did and just go straight to the sample student solutions!
I haven't looked at feedback from the session yet, but I personally enjoyed listening to what people came up with. There as a great deal of disagreement in the room about who should "win" and lots of different takes on a scoring system. Unfortunately we didn't have as much time as I wanted to, so I didn't get as much of an opportunity as I would have liked to push on some of the justification aspects, especially about why a scoring system is fair or ideal.
A lot came out about mean and standard deviation that I also didn't get a chance to make sense of. I wanted to ask people mean and standard deviation of what? What's their sample? Is mean or median a better measure of center? Part of that last question might rely on an assumption about guessing whole number weights. What happens when this task changes from discrete to continuous mathematics? I doubt the answer changes, but the questions you ask will definitely change.
This problem is super-interesting:
http://nrich.maths.org/6957
I like that there is a lot of open-endedness to the solution and "correct answer." Unfortunately I am not sure what unit it might fall in because it involves a ton of different possibilities. Just a fun math problem? That's okay with me too!
--------------------
Update: I tried this task with a group of approximately 80 secondary math teachers (6th-12th grade). My version was slightly modified to (1) give it a little bit more of a hook and make it look pretty; and (2) obscure the task name so no one could google it... Teachers are sneakier than students. They shouldn't get to do what I did and just go straight to the sample student solutions!
I haven't looked at feedback from the session yet, but I personally enjoyed listening to what people came up with. There as a great deal of disagreement in the room about who should "win" and lots of different takes on a scoring system. Unfortunately we didn't have as much time as I wanted to, so I didn't get as much of an opportunity as I would have liked to push on some of the justification aspects, especially about why a scoring system is fair or ideal.
A lot came out about mean and standard deviation that I also didn't get a chance to make sense of. I wanted to ask people mean and standard deviation of what? What's their sample? Is mean or median a better measure of center? Part of that last question might rely on an assumption about guessing whole number weights. What happens when this task changes from discrete to continuous mathematics? I doubt the answer changes, but the questions you ask will definitely change.
Sunday, February 9, 2014
When are Babies Born?
Are births evenly distributed across time of day, day of the week, and time of year?
http://journals.lww.com/greenjournal/Fulltext/2004/04000/Timing_of_Birth_After_Spontaneous_Onset_of_Labor.8.aspx
The raw data is in the tables. I think kids would be interested in this question, and the results are kind of surprising.
http://journals.lww.com/greenjournal/Fulltext/2004/04000/Timing_of_Birth_After_Spontaneous_Onset_of_Labor.8.aspx
The raw data is in the tables. I think kids would be interested in this question, and the results are kind of surprising.
What Are the Odds of Twins Born in Different Years?
The best thing about teaching probability and statistics, in my opinion, is that it's so much easier (and fun!) to find interesting contexts for problems. I feel like I don't have a good sense of what data is actually interesting to kids, but this question seems like it would capture some imaginations:
http://freakonomics.com/2014/02/05/what-are-the-odds-of-twins-born-in-different-years/
This also feels like a Fermi problem in some ways.
Rather than having kids actually answer this question, I think it would be more interesting for them to try to make sense of the methodology described in the post, the comments, etc. Analyzing someone else's process is a big part of evaluating is reasonableness. Oh, hey SMP #3...
http://freakonomics.com/2014/02/05/what-are-the-odds-of-twins-born-in-different-years/
This also feels like a Fermi problem in some ways.
Rather than having kids actually answer this question, I think it would be more interesting for them to try to make sense of the methodology described in the post, the comments, etc. Analyzing someone else's process is a big part of evaluating is reasonableness. Oh, hey SMP #3...
Wednesday, November 20, 2013
Where's Waldo?
If this isn't real-world math, I don't know what is.
http://www.slate.com/articles/arts/culturebox/2013/11/where_s_waldo_a_new_strategy_for_locating_the_missing_man_in_martin_hanford.html
I like what you can do with this around probability and area. It also makes me think about what kids hear/understand when they use and read the word "random." Do they think that Waldo is placed randomly? Why or why not? What would the pages look like if he were to be placed randomly?
I also like that it takes something that looks like it has little order, and uses math to help you see something you wouldn't otherwise be able to notice.
http://www.slate.com/articles/arts/culturebox/2013/11/where_s_waldo_a_new_strategy_for_locating_the_missing_man_in_martin_hanford.html
I like what you can do with this around probability and area. It also makes me think about what kids hear/understand when they use and read the word "random." Do they think that Waldo is placed randomly? Why or why not? What would the pages look like if he were to be placed randomly?
I also like that it takes something that looks like it has little order, and uses math to help you see something you wouldn't otherwise be able to notice.
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