Math Teachers at Play #35

Pyramid_of_35_spheres_animation — 35 is a tetrahedral number

Welcome to the Math Teachers At Play blog carnival — which is not just for math teachers.

Do you enjoy math? I hope so! If not, browsing these links just may change your mind. Most of these posts were submitted by the bloggers themselves; others are drawn from my overflowing Google Reader. From preschool to high school, there are plenty of interesting things to learn.

Let the mathematical fun begin…

TRY THIS PUZZLE

By tradition, we start the carnival with a puzzle in honor of our 35th edition:

Take a piece of graph paper with 1/2″ squares, and cut it apart along the lines. Separate these squares into sets of six.
Arrange each set so that all the squares touch sides with at least one other square. These are called hexominoes.
Glue them to a piece of construction paper, so they don’t get mixed up. Try not to make any two patterns the same. Patterns count as the same if you can rotate or flip them to make them match.
Can you find all 35 possibilities?
Which of the hexominoes have an axis of symmetry? Which have rotational symmetry?
Which of them could be folded up to make a cube?

ELEMENTARY CONCEPTS

[Photo by Pink Sherbet Photography.]

There was an old man who said, “Do
Tell me how I should add two and two.
I think more and more
That it makes about four —
But I fear that is almost too few.”

The Professor said, “Now I’ll tell you
A fact known to only a few
Men and women alive.
Two plus two equals five!
For large enough values of two.”

— Donald E. Simanek

Sally Haughey applies her imagination to “number recognition, one to one correspondence, counting, taking turns, and beginning addition” in Make Your Own Math Games – Fit for Royality!

Jennifer teaches the value of coins in a hands-on way in Math Lesson: Money with Cuisenaire Rods.

Technology In Class shares a collection of links to Free Math Activities Online: Money Math.

Risa Kawchuk plays a variation on Rock, Paper, Scissors for practicing addition and multiplication facts: Fingers! – A Math Game.

Umm Ahmad says the activities in his Interactive Math Calendar are for 5- to 10-year-old children, but Kitten (12yo) and I both enjoyed several of them.

ARITHMETIC

[Photo by pranav.]

A dozen, a gross, and a score
Plus three times the square root of four
Divided by seven
Plus five times eleven
Is nine squared and not a bit more.

— Leigh Mercer

Jeff Trevaskis shares a worksheet puzzle/game for practicing Order of Operations.

Mike Dimond asks for input: How would you calculate the product? Share your ideas at How do I love thee? Let me count the ways… of solving 95 * 95.

Sue Downing finds a wonderful visual for creating Equivalent Fractions, which would also be helpful for an older student doing unit conversions.

And speaking of unit conversions, Michael P has “fun with some weird-sounding units, such as butts, nibbles and siriometers, culled from wikipedia” in his blog post I like butts.

I love the games that John Golden invents, and his Integer Games were perfect to round out Kitten’s math lessons this week.

BASIC ALGEBRA & GEOMETRY

[Photo by EricGjerde.]

If A equals B (so I say),
And we multiply both sides by A,
Then we’ll see that A squared,
When with AB compared,
Are the same. Remove B squared. Okay?

Both sides we will factorize. See?
Now each side contains A minus B.
We’ll divide through by A
Minus B, and ole!
A plus B equals B. Oh whoopee!

But since I said A equals B,
B plus B equals B, you’ll agree?
So if B equals one,
Then this sum I have done,
Proves that two equals one. Q.E.D.

Caroline Mukisa gives a video review of an online algebra-for-beginners program in Conquer Mighty Algebra! A Review.

In a word problem Tuesday, Kitten forgot how to find the area of a circle. Time for a hands-on lesson, cutting up a paper plate — and together we’ll read Alexander Bogomolny’s post: Area of a Circle.

John Chase tells the world Why I hate the definition of trapezoids: “In this post I take on the problematic ‘exclusive’ definition of trapezoid which plagues many geometry teachers, and I argue that it should be abolished.” Amen! Follow-up post here.

Dan M constructs angle bisectors and parallel lines in simple origami and math – paper cup.

Mimi Yang offers a hands-on Trick for Teaching Basic Trig to confused students. Read the comments for a bonus tip on introducing trig ratios, and then see day 2 of the lesson: Not Enough Information?

ADVANCED MATH

[Photo by quapan.]

When you cut Apollonius’ cone
There’s a circle, but it’s not alone.
A parabola, new,
A hyperbola, too,
And a perfect ellipse will be shown.

— Montgomery Phister

Shawn Cornally puts his foot in his mouth, and his students figure out exactly how far down it went, in How I Teach Calculus: A Comedy (The Papoose is Imminent).

Mr. H poses questions about the Dunning-Kruger Effect: Which “Average” is Used?

Maria Andersen creates a New Math Game: Antiderivative Block and says that “watching students play this game was the most fun I have ever had in a math class.”

Pat Ballew says, “Sometimes vectors make difficult problems look easy.” Check out his post Midpoint Madness for an example.

RECREATIONAL MATHEMATICS

[Photo by fdecomite.]

Limerick Problem #1:
Three different one-digit primes
produce me, if you’re using times;
If my digits you add,
Another prime will be had.
Two answers–and nothing else rhymes.

Limerick Problem #2:
There once was a cube ’twas found
Whose two digits, when switched clear around,
Was the product (quite fair)
Of a cube and a square,
And its name will most surely astound.

— John Gregory & Dale Seymour
Limerick Number Puzzles (Creative Publications, 1978)

Shecky offers up a “little quickie recursive brain workout” in Weekend Miscellany.

James Tanton takes on the challenge of Multi-Choosing: How can we count the possibilities when repeat choices are allowed?

Yan Kow Cheong shares the “lighter side of math” in his article Mathematical Clerihews.

Virtual Math Tutor poses a graph paper puzzle in Thinking geometrically.

Sue VanHattum tells how she began reasoning through a problem in Tin Ceilings, Triangles, and Loving Math: “Coming up with a formula for $n \times n$ squares is a hard problem (which I’m not done with yet). But just looking for different size triangles, and maybe coloring some in, would be fun for a young kid, I think.”

ABOUT TEACHING MATH

[Photo by jimmiehomeschoolmom.]

Fermat solved a problem with ease,
That most of us find quite a tease.
His margin so small,
Left no room at all,
For a proof as concise as you please.

A challenge for many long ages
Had baffled the savants and sages.
Yet at last came the light:
Seems old Fermat was right–
To the margin add 200 pages.

— P. Chernoff

Cassy shows how a common trick used by elementary teachers may backfire, causing a student to stumble: Understanding trumps tricks.

NerdMom shares her perspective on a frustrating review lesson in When Math is More Than Math.

In the “made me laugh” department: John Cook finds out that science education, too, is “much more complicated than you expected” (reference to quote by E. G. Begle) when he tries to solve for Final velocity with his daughter. And then Pat chimes in with a follow-up story about related rates.

I wish I could sit in the back of the room when Jonathan starts Teaching off topic (yet again). He follows up with a thought-provoking addendum on division of fractions.

And here’s my contribution to the carnival: What to Do When You’re Stuck. Does it work? Dave Lanovaz offers a great example in his post Looking for Wrong Answers.

BEST OF THE SPAM

[Photo by mrdodgy.]

There was a young fellow named Cole
Who ventured too near a black hole.
His dv by dt
Was quite wondrous to see
But now all that’s left is his soul.

— A. P. French

There weren’t any decent spam this time, but I really like that picture, so I left the category in. The good news, for those of you who might consider hosting the carnival, is that I received about 1/3 the number of spam submissions as the last time I hosted. I hope that means the blog carnival website is cracking down on spammers.

ALSO SHOWING…

MTaP is far from being the only math blog carnival in town. Check these out:

FINAL COMMENTS

Photos via flickr’s Creative Commons (Attribution) Search.

Math limericks are from Kayla’s Purlieu, Wikipedia, and Math NEXUS. I would like to link to the authors to give them credit, so if anyone knows a website associated with any of the names above, please tell me!

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

The next installment of our carnival will open on March 18 at Math Hombre. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.

Past posts and future hosts can be found on our blog carnival index page.

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!