Math Teachers at Play #24

[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

• Responding to an article in the New York Times, Montessori Matters announces a News Flash: Pre-Schoolers Can Understand Math Concepts (no duh).

• Try Ticia’s Fun Quick Math Game for basic counting. What young child doesn’t love stickers?

• Maria takes a look at Subitizing – a video review.

• Wendy presents Spring Math Worksheets: Addition Color by Number.

• Crunchy Mama plays a number bonds game in Easy, Cheap Alternative to Drill & Kill.

• Nadene shares a set of downloadable Mental Maths Practice ~ fun worksheets! for basic addition and subtraction.

• Amy posts some links to Hundred Chart Activities, including a fun online game I hadn’t seen before.

• Ginger gives several creative ideas for teaching and reviewing geometry words in Lines, angles, and rays! Oh My!

• 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

• Kitten shares some of her favorite online multiplication practice in Math Games for Learning Times.

• 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.

• How well do you understand fractions? Challenge yourself with Jason’s Conceptual fraction test.

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. . .”

• Annarita solves an Ancient Greek fraction puzzle in Il Problema Del Sepolcro Di Diofanto. (If, like me, you need a translation, Google did a fair job.)

• Mrs. H introduces her algebra students to The Claw.

• Craig asks for some Word Problem Help.

• John offers several geometry games for K-8 teachers from the conference Math in Action 2010.

• 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.

• Meanwhile, Pat presents A Guest Blog (Rant?) from Dave Renfro about Pi Day in the news.

• Nick features a couple of algebra puzzles (and a link to the program he used to make them) in Puzzling Out Some Quadratics.

• Erlina gives ideas for Making connections through math investigation: polygons and operations with algebraic expressions-Part 1 and Part 2.

• Xamuel’s Inverse Graphing Calculator is a fun geometry toy, and I had to laugh at the equation for my blog name. High school teachers can increase the math-learning value of the calculator by studying The Equation of a Line Segment.

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?

• John challenges us to come up with a Twitter version of Euclid’s proof that there are infinitely many primes. (David’s entry is my favorite so far.)

• Jinna’s students have trouble with Michael’s Velocity Graph.

• Jonathan has been Having fun teaching Σ of geometric series and poses “a π question for you.” (Follow-up post here: Proof by taxation, and you might have fun with this puzzle.)

• Riley describes One way to convince kids of finite infinites.

• Cap reviews Mathematical Fiction: Riot at the Calc Exam and Reality Conditions. “I think there’s a lot more intrinsic humor in mathematics than many people expect. . .”

• And Dan (who did a great job with last month’s MTaP) offers up the Carnival of Mathematics 63, a wonderful collection of math blog posts for your browsing pleasure.

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)

• Julia presents several puzzles to challenge elementary students in Number Fun Week and Counterintuitive Problems Week.

• 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.

• Praveen likes to play around with math and logic. Can you solve the Hourglasses or Jelly Beans puzzles?

• 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. . .”

• Speaking of coffee, Jan challenges us with It may be a bit hot and Not a coffee maker, both of which are way beyond Kitten’s level of math.

• 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.)

• Dan notices his students’ struggle to remember what they’ve learned, and he gives review a creative twist in Language and Retention of Math Concepts.

• 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.

• Joanne encourages teachers to ask for proofs (even in elementary school) in Why is this answer right?, a post prompted by Coach G’s article Don’t Tell Students to Show Their Work—Make Them!

• Kate stirs up plenty of discussion with her Answer to the Monte Hall Problem.

• Alen recommends the National Library of Virtual Manipulatives (great site, whiteboard friendly).

• If your students need extra help outside of class, Rashmi presents 10 Places for online Math Help.

• And the multiplication/repeated addition debate breaks out again here, here, here, here, and here. I appreciated Michael’s analysis of Children Doing Mathematics, Terezinha Nunes and Peter Bryant Dole Out The Multiplicative Harshness.

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:

• 20 Shocking Stats on American Education
• The Ultimate Guide to ACT Test Statistics

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!