88
votes
Accepted
What's a replacement for "married couples" in combinatorics problems?
I've been using "pets" and "owners" (as in: possible pet-shelter adoptees) in recent years.
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83
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What's a replacement for "married couples" in combinatorics problems?
In the stable marriage problem, you can introduce the problem as it is. But then you ask your students how things change if you assume there are not only heterosexual but also gay and lesbian people (...
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What's a replacement for "married couples" in combinatorics problems?
A few possibilities off the top of my head:
Students and chairs. How many ways are there for $n$ students to sit in $k$ chairs. The game of musical chairs might be fun to play around with. One can ...
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37
votes
What's a replacement for "married couples" in combinatorics problems?
The issue is not making problems about heterosexual married couples. The issues are:
Implicitly making the assumption that all married couples are heterosexual.
Making problems about heterosexual ...
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34
votes
What's a replacement for "married couples" in combinatorics problems?
Try objects that often occur in pairs but are distinct from each other: forks and spoons (or forks and knives), left and right shoes, salt and pepper shakers, and so on (where each fork has an ...
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26
votes
What's a replacement for "married couples" in combinatorics problems?
When I taught a class about the stable marriage problem last week, I replaced "men" and "women" with "medical students" and "hospitals": the classical instance in which the Gale-Shapley algorithm is ...
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Examples of arithmetic and geometric sequences and series in daily life
I tutored a student who came with a kind of problem I had never seen before and found quite refreshing. It was something like:
A child is being pushed on a swing by their father, reaching a maximum ...
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14
votes
What's a replacement for "married couples" in combinatorics problems?
Protons and electrons (form hydrogen atoms)
Or cations and anions (form salts), e.g. Na+ and Cl-
Pens and pen-caps
Bottles and bottle caps, etc.
Textbooks (for the course being taught) and ...
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14
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Nice examples of limits to infinity in real life
If you are willing to take some time to explain the model and do some simulation, I really like to show students a logistic growth model (in discrete time). The basic setup is something like the ...
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12
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What's a replacement for "married couples" in combinatorics problems?
An idea I find interesting is to use abstract objects: "given X squares and Y circles, in how many ways it's possible to pair one circle with one square?"
If the students are at kindergarten or ...
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11
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Inspirational Mathematics Books for Teenager
If you looked at those other topics, you saw the links to the books page at my blog, Math Mama Writes. There are a number of books there that would work for a teen. One of my favorites is Carry On, Mr....
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10
votes
Electronic devices to replace pencil and paper
Taking a break from a convoluted computation...
To me the key limiting factor is space. I can spread out several sheets over the table and have various bits and pieces directly visible. I cannot do ...
quid♦
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10
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Accepted
Examples of arithmetic and geometric sequences and series in daily life
Here are a few more examples:
the amount on your savings account ;
the amount of money in your piggy bank if you deposit the same amount each week (a bank account with regular deposits leads you to ...
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What's a replacement for "married couples" in combinatorics problems?
I like several of the answers which found clever sets that avoid assumptions about genders and sexes. Just to provide an alternative, what about keeping the assumption about sexes, but changing ...
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9
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Examples of arithmetic and geometric sequences and series in daily life
I like to explain why arithmetic and geometric progressions are so ubiquitous. Using the examples other people have given.
Geometric progressions happen whenever each agent of a system acts ...
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9
votes
Math Everywhere Activities
I would recommend activities that can be done at least once a day (instead of once a month).
When setting the dinner table (especially when guests are present), request the child to help get the ...
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8
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What's a replacement for "married couples" in combinatorics problems?
I'm just thinking out loud here, but one possible option is to keep it as men and women, but have it be about ballroom dancing, or figure skating, instead of dating or marriage.
That way, it might ...
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7
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Inspirational Mathematics Books for Teenager
"(Books in German or with German translation are a plus)"
and "she is particularly interested in geometry."
The OP's notes suggest:
Ziegler, Günter M. Do I Count?: Stories from Mathematics. CRC ...
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7
votes
What's a replacement for "married couples" in combinatorics problems?
Nuts and bolts? You'll need to specify bolts which are only long enough to accept one nut each, but that's brief enough to do.
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7
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Nice examples of limits to infinity in real life
Deeba and Rushkady Go to Town: A Fanciful Real-Life Story
A festival was just starting in town, and Deeba and Rushkady walked toward the square headed to the Infinite Pancake Eating Contest. The ...
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6
votes
Accepted
Electronic devices to replace pencil and paper
Here's a sample of the iPad's resolution. The original is a page wide (8in) but clipped a bit short. The writing tends to be a bit bigger than I'd have with pencil and paper. The graph was just a ...
6
votes
Entertaining and fun books about mathematics for (basically) liberal arts students
I'll suggest the book Flatland by Edwin A. Abbott. It's an interesting read about geometry and thinking in a higher dimension.
The downside is that this book is, well, antiquated to put it nicely. ...
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6
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Examples of arithmetic and geometric sequences and series in daily life
This is a nice demonstration that
$$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\cdots
= 2 \;.$$
(Image from Wikipedia ...
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6
votes
Impressive common misleading interpretations in statistics to make students aware of
This fallacy is probably less well-known than others: large samples always mean better confidence. This turns out to be false in the presence of even the slightest bias.
Imagine an experiment to ...
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6
votes
What's a replacement for "married couples" in combinatorics problems?
Simply state that the question is purely in the context of purely heterosexual couples right out of the gate, then make reference to homosexual couples who are also pairing off but are not included in ...
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5
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Examples of arithmetic and geometric sequences and series in daily life
They might be interested to know about both Moore's Law and "Nielsen's Law". You've probably heard about Moore's Law, where computer complexity doubles about every two and a half years.
Internet ...
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5
votes
What real-example of modulo-arithmetic would work for American students?
Casting out nines is a good way to check arithmetic calculations.
Most American students are unfamiliar with casting out nines, but it is very easy to teach the method.
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5
votes
Accepted
Inspirational Mathematics Books for Teenager
For your particular case, I highly recommend "The Joy of X" by Dr. Steven Strogatz.
And although you didn't request it, for higher level students and adults I also recommend "Mathematics for Non-...
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5
votes
What’s a practical daily application of each times table?
A few off the top of my head:
7: calculating how many days away an event is when you know how many weeks it is (or vice versa)
All of them: estimating costs while grocery shopping
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Only top scored, non community-wiki answers of a minimum length are eligible