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)]

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

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

• Christopher Danielson and his kids explore the concept of one-to-one correspondence in Holding hands at the market. I love Christopher’s stories, and I can’t wait to read his new book, Talk Math With Your Kids.

• Are you looking for creative ways to help your children play with math? Check out Maria Droujkova’s Baby algebra, toddler calculus: Adaptations for toddlers and young kids.

• Eclectic Homeschooler plays a silly-song game to help her daughter master Singapore Math – Making Tens.

• Or try a number bond game with Margo Gentile’s Addition Tambourines-Shake-a, Shake-a, Shake-a.

• Want to find some math manipulatives to help your children learn? The Girl Who Painted Trees shares her Friday Five – Favorite Math Materials.

Elementary Exploration

• 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.

• Lisa Ginet reviews two books that help children understand How “Big” is a Million?

• Jmommymom creates a printable playsheet for exploring multiplication patterns: Multiplication Circles.

• Caroline Mukisa reviews a new game her children have enjoyed in Questimate! – Quite Possibly the Coolest Math iPad App!

• 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

• Sarah would like to inspire your students to solve math problems with her colorful Kid Friendly Mathematical Practices Posters.

• Can people learn to “play math” the way they might pick up an instrument and play music? Jordan Shapiro interviews Keith Devlin about the new (free) math game, Wuzzit Trouble: Video Games Are The Perfect Way To Teach Math, Says Stanford Mathematician.

• Can you figure out why Maria Miller’s Find your age using chocolate math 2013 puzzle works? My daughter had fun with this.

• Michael Pershan treats us to A number theory problem that I modified a bit for primary schoolers.

• Julie Reulbach adapts an algebra problem for her 6th-grade students in Pizza + Linear Equations = Fun, Free Mathalicious Lesson.

Adventures in Basic Algebra & Geometry

• For my entry in this month’s carnival, my daughter and I discover Gordon Hamilton’s Puzzle: Algebra on Rectangles.

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

• Christopher Danielson helps his students come to terms with a system of linear equations in College Algebra with Christopher.

• Patrick Honner posts the details of his Rosenthal Prize Lesson — Sphere Dressing, a creative way to explore the geometry of polygons and their relationships to geometric surfaces.

• Jennifer Wilson’s students explore the mathematics of Translations, Reflections, Rotations, and Reflected Triangles.

Advanced Mathematical Endeavors

• Have you tried the Daily Desmos challenge yet? Justin Lanier explains how it works and gives a taste of fun to come in Daily Desmos: Phase Two and You.

• Bob Lochel encourages his new algebra 2 students to try Breaking Apart Sums and Differences of Perfect Cubes.

• Thaddeus Wert’s students learn about the power of mathematical models in Pennies, Circles, and Quadratics.

• Jonathan Newman asks for help in developing his Improved Lesson: Review of Function Families for precalculus students.

• 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.

• Don Steward offers an ever-expanding variety of puzzles. Here are a couple of my recent favorites: faces and elevations and square symmetries.

• Munizao poses an interesting variation on tiling puzzles in Hinged Polyforms.

• Gary Antonick introduces a new kind of challenge: Palmer Mebane’s Combonoku.

• Exercise your mind daily with a problem from the AMC-8, AMC-10, or AMC-12 at MAA Minute Math.

• If your brain is feeling a little bit stale, check out Maria Droujkova’s 60 ways to stay creative in math.

Teaching Tips

• 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.

• Malke Rosenfeld ponders how context and conversation affect children’s mathematical development Learning Math by Ear and Between 6 & 8: Learning Math by Ear, Part Two.

• Carollee Norris suggests Ten Uses for Sticky Notes in Math Class for practicing number sense, geometry, word problems, and more. Most of these projects would be good for homeschoolers, too.

• Ben Blum-Smith shares how asking students to summarize each other’s comments has transformed his classroom. I need to try this with my math club kids.

• Pat Ballew continues his series of tidbits from math history: On This Day in Math.

• Do the things that other teachers say confuse your students? Tina Cardone is looking for help to Nix the Tricks! (See also Nix the Tricks: An Update.)

Final Comments & Credits

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

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:

• The All-New Topical Math Monday Blog Hop
• Mathematics and Multimedia Blog Carnivals
• Carnival of Mathematics
• Carnevale della Matematica

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