Category Archives: Problem Solving

Number Gossip

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“Can you believe what 56 did?  It’s just so…odious!”

“Oh I know.  And 43 is so lucky, I can’t even stand it.”

You probably know a lot of properties of numbers like “even”, “odd”, “prime”, “square”…but there are so many more that you might have never heard of!  Head on over to Number Gossip to get the scoop!

BADGING:

Pick a favorite or interesting whole number.  It might be your uniform/jersey number for a sport you play, or your home address, or your lucky number, or something else entirely.  Enter it into the search field at Number Gossip.

  1.  List all of the “common properties” of your number that Number Gossip lists.  If any of those properties are unfamiliar to you, you should be able to click for an explanation.   Explain in a sentence next to each property why your number belongs to that property (Where applicable, give a specific reason for *your* number, not just a definition of the property).
  2. Pick one “rare property” (if your number has one; not all do) and do the same thing as in step 1.
  3. Pick one “unique property” (if your number has one; not all do) and do the same thing as in step 1.
  4. Search Number Gossip for the whole number directly before and after the number you chose.  How are the search results different?  How are they similar?  Write a few sentences comparing and contrasting, as well as your thoughts as to why they compare the way they do.

 

 

 

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The Math Of Roasted Potatoes

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Chefs in Great Britain have used “maths” to determine the best way to cook roasted potatoes.  See the magic formula here (courtesy of the Sun).

BADGING:

Watch the video and read the accompanying article.  Write a paragraph that explains the difference between the “traditional” way of making roasted potatoes and the “new, mathematical” way.  What changes were made and what is the advantage?  How did chefs determine that the new way was in fact “better”?

In a second paragraph, describe another food that you think might be improved using mathematics to aid in the preparation.  Describe a hypothesis you might have about how  that food might be improved using mathematics and why you think it would be an improvement.  Give a diagram if it helps your explanation.

Are You Eating Tennessee or New Jersey M and M’s?

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Did you know the color distribution of M and Ms has changed over the years?  Quartz has a breakdown, and how you can which factory your candy originates from (including one right here in Tennessee)!  (Thanks to Bowman Dickson for sharing this link on Twitter!)

BADGING:

Read the article linked here or above.

Answer the following questions in a couple of sentences each.

  1.  Compare the color distribution for M and M’s in 1997 compared to the color distribution in 2008.  What changed?  Why do you think it changed (hypothesize)?
  2. Why does Mars no longer publish the color data for M and Ms?  (In other words, what’s true about the two different plants that manufacture M and Ms?)
  3. Buy a bag of M and Ms and before you eat it, count the colors.  Create a data display (bar graph, pie graph, etc) to show the color distribution in your bag (you can use Excel or some other program to help you do this, or you can do it by hand).  State whether or not you think you are eating New Jersey or Tennessee M and Ms based on your results, and explain your reasoning.

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.

 

Noise Cancelling Headphones

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Ever wonder how noise-cancelling headphones work?  Is it just more insulation than other headphones?  Or is there more to it than that?

Turns out it is mathematical.  And we have one Joseph Fourier (1768-1830) to thank for the equation that makes noise-cancelling headphones work.  Check it out here:   https://www.wired.com/2011/05/st_equation_noisecanceled/ (via WIRED)

BADGING:

Read the brief article linked above.

Print off this picture of a sound wave:

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Use the information from the article to answer these questions on the page where you printed off the above sound wave:

  1.  Under the picture of the sound wave you printed off, draw another wave that would be higher-pitched sound than the one you printed off.  (NOTE:  When the article mentions “frequency”, it is referencing the wavelength).
  2. Underneath that picture, draw another picture of a sound that would be quieter than the one you printed off.
  3. Explain in your own words how the article describes how an engine roar is “like an ocean in a storm”.
  4. In your own words, explain what noise-cancelling headphones do in order to reduce outside noise.