Math Teachers at Play #24

found math triads wall hanging

[Photo by internets_dairy.]

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers! If you like to learn new things and play around with ideas, you are sure to find something of interest. Let’s start the mathematical fun with an arithmetic card game in honor of our 24th edition and a few number puzzles:

  • 24 can be written as the sum of three square numbers. How?
  • Can 24 be written as the sum of two consecutive integers? Can 24 be written as the sum of three or more consecutive integers? How many ways?
    [Which reminds me: Did you figure out the consecutive-integer puzzle from MTaP #22?]
  • How many ways can the letters M-A-T-H be arranged to form a 4-letter “word”? Okay, since there’s no 24 in the question, you’ve probably already guessed the answer — but can you prove it?
  • 24 is the largest number divisible by all numbers less than its square root. Can you find all of the other numbers for which this is true?
  • 24 is an abundant number, which means that if you add up all the numbers that divide evenly into 24 (except for 24 itself), the sum will be greater than 24 itself. How many other abundant numbers can you find which are less than 100?
  • What is the ones digit in the number 24^24?
    [That means 24 raised to the 24th power.]

And now, on to the carnival proper. Below are a number of math-related articles, submitted by the bloggers or drawn from my overflowing blog reader, along with quotes from the Handley Math Page and some cool pictures from MAA’s Found Math Gallery.

If my descriptions seem terse, it’s only because I was trying to crowd in so many wonderful posts. Have fun browsing!

ELEMENTARY CONCEPTS

[Photo by Marieshtela Villarroel, Universidad Pedagógica Experimental Libertador, Venezuela..]

From the very beginning of his education, the child should experience the joy of discovery.

Alfred North Whitehead

But in the new (math) approach, the important thing is to understand what you’re doing, rather than to get the right answer.

Tom Lehrer

  • Try Ticia’s Fun Quick Math Game for basic counting. What young child doesn’t love stickers?
  • And for those of you who dream of teaching elementary math without a textbook (perhaps using some of the games above), Kendra offers guidelines for Organizing a Math Lesson.

ARITHMETIC

[Incan quipu, photo by Lisa Kolbe, MAA, Peru Study Tour.]

Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency.

René Descartes

We use only 10% of our brains… Imagine how smart we would be if we used the other 60%!

Ellen DeGeneres

  • Cindy takes advantage of the winter weather for an outdoor math project in Cold Measurement.
  • Fëanor posts a story in which a hapless student struggles with a challenging word problem and “Nikolai Nosov demonstrates why he is possibly the finest expositor of mathematical pedagogy in children’s literature anywhere.” Check it out: Vitya’s Maths.
  • MathModels presents a series of videos to help you understand and teach Fraction Word Problems the Singapore Math way.

BASIC ALGEBRA & GEOMETRY

[Kenneth Snelson’s “Needle Tower.” Photo by I. Peterson, Geometreks.]

The length of your education is less important than its breadth, and the length of your life is less important than its depth.

Marilyn vos Savant

Circles to square and cubes to double would give a man excessive trouble.

Matthew Prior

  • Whit poses an interesting answer to the question What is Algebra? “Students should think of algebra not as a set of rules for solving things. . .”
  • Mrs. H introduces her algebra students to The Claw.
  • Sue and her friends have a fun time building the Platonic Solids and other shapes with polydrons at the Richmond Math Salon – Symmetry, and she shares a link where we can buy discounted polydron sets of our own.
  • If you haven’t been following the Opinionator math columns, take a look at the latest: Square Dancing. And then go back and read them all.
  • Abigail comes up with a cute entry: “a free knitted hat pattern, with the first ten digits of pi encoded in bands of reverse stockinette.” Check out Berry Pie/Pi beret.

ADVANCED MATH

[Photo by Mika Munakata, Montclair State University.]

I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn.

Archimedes

Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.

Johann Wolfgang von Goethe

  • Ryan and his students examine the physics of Up (I love that movie!) in How many balloons?

MATHEMATICAL PUZZLES

[Photo by Japheth Wood (Bard College).]

The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver.

I.N. Herstein

I was x years old in the year x2.

Augustus De Morgan
(when asked about his age)

  • NumberFest is offering pages of sample puzzles from their puzzle books. I think I’ll print a few of these for Kitten to play with.
  • Alison poses a math puzzle to her Facebook friends and gets a variety of feedback in A problem, and some responses. For the most enjoyment, work the puzzle yourself before reading the answers.
  • Eldhose posts a nice assortment of puzzles, too. Kitten impressed me by getting the Coffee machine right, and who wouldn’t chuckle at a rate puzzle which begins: “If a boy and a half eat a hot dog and a half in a minute and a half. . .”
  • For more math puzzling fun, exercise your mind daily with a problem from the AMC-8, AMC-10, or AMC-12 at MAA Math.

ABOUT TEACHING MATH

[Hand-stitched fiber art wall hanging by artist David Nerwen.]

The best teacher is not the one who knows most, but the one who is most capable of reducing knowledge to that simple compound of the obvious and wonderful.

H.L. Mencken

A math student’s best friend is BOB (the Back Of the Book), but remember that BOB doesn’t come to school on test days.

— Josh Folb
(I couldn’t find a link about the man himself, although many people like his quote enough to include it on their webpages.)

  • How can you tell whether a problem is due to a student’s personal issues or to the teacher’s faulty instruction? Mathew offers advice for Down and Dirty Data Analysis.

Finally, the “Might Be Spam” Category

The carnival received a grand total of 61 spam posts, mostly from online education blogs. Ads for nursing degrees have madly outpaced the real estate and how-to-pass-the-bar-exam spam we used to get. Still, I will share the following less-suspicious-looking entries, in the hope that they may be of interest to someone:

Concluding Remarks, and How to Join in the Fun

That rounds up this edition of the Math Teachers at Play carnival. I hope you enjoyed the ride.

If you’d like to know more about the math blog carnivals, Mike posted the FAQs. Past posts and future hosts can be found on our blog carnival index page.

The next installment of our carnival will open on April 16th at Point of Inflection. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics (that is, anything from preschool up to first-year calculus). Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

We need more volunteers. Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn hosting the Math Teachers at Play blog carnival, please speak up!

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13 thoughts on “Math Teachers at Play #24

  1. I thank you for posting “my” quote. Although it has gone viral over the past few years, I always thought that I borrowed it from someone else.

  2. I wouldn’t be surprised if you had, Josh, but when someone heard you say it, they wrote it down. And I’m glad they did! Your quote is a catchy way of communicating two very important ideas: that working backwards from the answer is a great way to learn, and that one has to keep at it until one understands the material.

    Do you have a website or home page that you would like me to link your name to? I try to give some sort of informational links for the people I quote.

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