Gerrymandering

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Gerrymandering is the term for when political borders (shapes of districts, etc.) are set so that one political party/group gains an advantage.  It’s widespread, but there are some cases in the court system now trying to address the issue — and mathematicians are helping.  From The Nib comes a comic the describes mathematicians’ roles when it comes to Gerrymandering.  Check it out!

BADGING:

Read the comic linked above.  Answer the following questions in a couple of sentences each.

  1.  Using the cartoon of red/blue houses, explain how gerrymandering can take an evenly split vote between two parties and make it a “majority win” for one of the parties.
  2. Courts have rules against districts in the past for racially-based gerrymandering.  But why have the court systems been mostly powerless to rule on partisan gerrymandering cases to this point?
  3. Mathematicians are tackling the unresolved question of how “compact” districts can be and how to define that compact-ness.  What are two ways that “compact” can be defined mathematically?
  4. In your own words, describe what is meant by “negative curvature”.  Why is this a red flag for districts?
  5. How are mathematicians using “maps that could have been” as a way to frame the gerrymandering discussion?

 

 

 

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She May Not Look Like Much, But She’s Got It Where It Counts, Kid.

 

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From Nerdist comes an infographic outlining the fastest space craft in the known universe — both real and fictional!  Check out the picture here! (Nerdist)

BADGING:

Look at the infographic linked above.

Pick out two of your favorite ships from the “relativistic” category.  Calculate their acceleration in m/s^2 (meters per second per second).  Compare those to a roller coaster in our very own Dollywood called the Tennessee Tornado, which reaches 3.7G.  How is it possible that a roller coaster achieves the same G-force as a space shuttle?

Then, pick out two of your favorite ships from the “faster than light” category (Note:  These are *all* fictional, as this type of travel is not yet possible).  Calculate their speed in miles per hour (You need to know that there are 1000 meters in a kilometer, and 1.62 km in a mile to do this calculation).  Please note that you may put your answers in scientific notation, and that you may not choose the Heart of Gold for this exercise.

*If you liked this badge, thank Eleanor for sharing the infographic with me!

 

 

What Are The Most Likeable Prime Numbers?

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So there’s this Twitter feed that tweets out the prime numbers…in order…on the hour…every hour.  Friend of Pre-Algebra.info David Butler analyzed the data from this Twitter feed to see which prime numbers were the most popular (via Likes and Re-Tweets).  See the results in his blog post.

BADGING:

`1.  Before you visit the blog post linked above, visit the Twitter feed that lists primes.  Out of the most recent 15 primes listed, which one is your “favorite”?  (You can decide how to interpret “favorite”.  Just decide which of the most recent 15 primes you like the best).

2.  Now visit Dr. Butler’s blog post where he analyzes the prime data.  Read the blog post and look at the data displays.  List at least four characteristics he noticed about the “most liked” primes, and give an example from the data to support each claim.

3.  Refer to your prime choice from question #1.  Does your choice fit any of the four categories from the second question?  Which ones?

4.  Hypothesize: Why do you think certain patterns or arrangements of primes are more “likeable” than others?  What might this have an impact on subjects like cryptography (internet passwords or even locker combinations)?

5.  Here’s a link to ten random ten-digit prime numbers?  Using what you’ve learned so far, which one do you think would be the “most liked”?  Explain your reasoning.

The Difference(s) Between Pro and Amateur Soccer Players

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With GPS data being used in a variety of sports, we have more data than ever to compare professional athletes.  More than just stats like goals and assists, we can actually measure distance traveled and top speeds.   The folks over at SportTechie have analyzed the data comparing amateur and professional soccer players.  Check out the differences between the players here.

BADGING:

Read the article linked above and answer the following questions (You may use a calculator, but show your work!).

  1.  The English Premier League leader in distance covered in the 2016/17 season was Tottenham’s midfielder Christian Eriksen, who covered an average of 11.92 kilometers per match.  If there are approximately 1.62 km. in a mile, how many miles did he average per match?  How does that compare to an average professional midfielder (data included in the article)?
  2. Let’s say an amateur attacker and a professional attacker are both racing towards the same spot on the soccer pitch.  Both players are 100 feet from the spot.  Calculate how far away would the amateur player be from that spot when the professional player arrived there, assuming both players ran at their top speed the entire time.  (There are 5280 feet in a mile, and use the speed data from the article linked above).
  3. An English Premier League season is 38 games long.  Over the course of a 38-game season, calculate how much farther a professional defender would run when compared to an amateur defender.

 

Categorizing Flags

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Via CityLab comes a bunch of infographics that examine how different flags around the world are constructed.  Pretty cool stuff!

BADGING:

Pick the United States and one other country (Your choice!  Maybe this is a country that you’ve visited, one where you have lived at one time in your life, one where a family member lives, or just one you are interested in for any reason).

Look through the infographics at the link above and answer the following questions about the flags for the USA and the other country that you chose.

  1.  Do your countries’ flags (USA and the other one you chose) have any of the five most typical layouts?  If so, which ones?
  2. Do your countries’ flags have any of the most typical colors included in them?  Which ones?
  3. Research what the colors on your countries’ flags are used to represent. Are they the most typical meaning behind those colors, or a less-used meaning?
  4. Do your countries’ flags include any of the five most common symbols?  Which ones?
  5. How complex are your countries’ flags?  If they are more than just “Child’s Play”, what elements do you think made the flags more complicated?
  6. Finally, imagine you were going to create a new country and had to design a flag.  Given what you learned about flag design from these infographics, how would you design your flag so that it was similar enough to other world flags (doesn’t feel like a huge outlier) but still different enough to be recognizable and unique (doesn’t feel like a copycat) ?  Draw/color a sketch of your new flag after you print out your answers to the previous five questions.

 

Why Math Is The Best Way To Make Sense of the World

 

From the original article at Quanta, see the video above for Dr. Rebecca Goldin’s explanation for why mathematics helps the world to make sense.

BADGING:
Watch the above video.  Answer the following questions in a couple of paragraphs.

We define the term literacy as the ability to read and write (and understand what you read and write).  Using that as a basis, what do you think Dr. Goldin means by the term quantitative literacy?

Why does Dr. Goldin think quantitative literacy is so important?  What can individuals who are quantitatively literate accomplish?

In her Quanta interview (towards the bottom), they discuss her work with an organization called STATS.  Explain what STATS is hoping to accomplish, and how it is related to her views on quantitative literacy that you described earlier.  (You don’t have to read the entire article — you may — but you can skip ahead to where they discuss her work with STATS).

 

 

Who Cares If Math is Useful?

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The last time we saw Dr. Eugenia Cheng, she was on The Colbert Show cooking up some fun mathematical recipes.

This time, she’s on PBS talking about how the usefulness is math is…a burden?  What could she possibly mean?

Visit the video to hear what she’s talking about.

BADGING:

Watch the video linked above (less than 4 minutes).  Answer the following questions in a couple of paragraphs.

  1.  Why does Dr. Cheng feel that we should let go of the idea that math is “useful”?
  2. What are some adjectives Dr. Cheng uses instead of “useful”?
  3. Dr. Cheng gives a number of examples of math that wasn’t “useful” until centuries after it was discovered.  Describe a couple of those examples (internet cryptography, viruses, soccer balls, etc.).
  4. How does Dr. Cheng suggest we “break the cycle” of how students (particularly elementary students) view mathematics?