Math Teachers at Play #66

[Feature photo above by Franz & P via flickr. Route 66 sign by Sam Howzit via flickr. (CC BY 2.0)]
Route 66 Sign

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.

By tradition, we start the carnival with a couple of puzzles in honor of our 66th edition.

Let the mathematical fun begin!

Puzzle 1

how crazy 66

Our first puzzle is based on one of my favorite playsheets from the Miquon Math workbook series. Fill each shape with an expression that equals the target number. Can you make some cool, creative math?

Click the image to download the pdf playsheet set: one page has the target number 66, and a second page is blank so you can set your own target number.

Puzzle 2

Did you know that 66 is a triangular palindromic number? The “triangular” part of that description makes for an especially cool pattern: 66 = 1 + 2 + 3 + … + 10 + 11. And 66 is also the number of 8-iamonds, which leads to our second puzzle:

Print out several sheets of triangle graph paper so you can play with polyiamonds — patterns made by connecting equilateral triangles along their sides.

  • A single triangle can make only one pattern, itself.
  • Two triangles still make only a single diamond, no matter how you connect their sides. (Patterns that can be moved or flipped to align exactly are considered equivalent.)
  • What about three triangles? It seems like they should make more than one type of triamond, depending on how you connect them. But once again, every option turns out to make the same design, only rotated or flipped to different positions.
  • Finally, the 4-iamonds (or tetriamonds) get interesting. Can you find all three of them? Are you sure there aren’t any more? What kind of shapes can you make if you laminate your graph paper and cut the tetriamonds out to use like puzzle pieces?
  • How many 5-iamonds (pentiamonds) and 6-iamonds (hexiamonds) can you find? What kind of shapes can you make with those pieces?
  • For more fun with polyiamonds, check out The Poly Pages.

Answers can be found at the Wolfram MathWorld definition page: Polyiamond.

And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; others were drawn from the immense backlog in my rss reader. Enjoy!

Early Learning Activities

Name the Shapes

Elementary Exploration

Wicked Good

  • There are so many interesting things to learn in math! Lula B talks about the positive changes she has seen since her family started their “living maths experiment” and shares her ideas for a new school year in Living Maths Curriculum 2013-14.
  • Have you tried Bedtime Math puzzles with your children? Check out Laura Overdeck’s Lego puzzles in Way Larger Than Life.
  • Yan Kow Cheong poses a slew of impossible problems in To Count or Not to Count. Can your students figure out what’s needed to solve them?

Middle School Mastery

Following Instructions

Adventures in Basic Algebra & Geometry


  • So many kids struggle with the abstraction inherent in simple equations, but Cheesemonkeysf’s students have fun mastering algebraic Substitution with stars.

Advanced Mathematical Endeavors

Elvish Calculus

  • Shireen D wants her students to struggle in this lesson for Calculus Day 1.

Puzzling Recreations


  • What makes a pattern a pattern instead of a design? John Golden’s students investigate a few possibilities: Creative Pattern.
  • Exercise your mind daily with a problem from the AMC-8, AMC-10, or AMC-12 at MAA Minute Math.

Teaching Tips

Word Problems

  • How can you help a math-phobic student who is falling farther and farther behind grade level? Angelicscalliwags shares her family’s journey in a wonderful series of blog posts: Helping a Struggling Maths Student.

Final Comments & Credits

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

But Dad, They're Almost Finished Rebuilding from Last Time!
But Dad, they’re almost finished rebuilding from last time!

Photos are from the I Can Has Cheezburger? family of blogs. If you click through to see additional jokes, be aware that these blogs celebrate internet humor, which is often tasteless and sometimes offensive. Browse at your own risk.

The next installment of our carnival will open in early-to-mid October at Moebius Noodles. To send in a contribution to the carnival, 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 math blog carnival information 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!

Finally, if you enjoyed this month’s MTaP posts, treat yourself to more mathy fun at our sister carnivals:

carnival acrylicartist 7231200052
[Photo by Rodney Campbell via flickr (CC BY 2.0).]

2 thoughts on “Math Teachers at Play #66

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