## Tuesday, June 12, 2012

### Math Teachers at Play #51

Noticing & Wondering

I'm a pentagonal number,
I have just two factors,
and if you put me in base 2, 4 or 16,
I'm a palindrome.
I wonder:
Is there anyone else like me in the number universe?

51 topics for your enjoyment...

 (from mandarintools.com/abacus.html)

Arithmetic

• Is counting on your fingers good, bad, or both? What do you think? Peter (Classroom Professor) analyzes the mathematical thinking in two classrooms, (giving finger counting a thumbs down, and visualizing a thumbs up) and Caroline (Maths Insider) says don't count on your fingers!  (In a series debunking math myths, I said go ahead, but these posts got me thinking. Now I'd say it's a starting point, and let's think about how to move on.)
• Liz (Homeschooling in Buffalo) posts on keeping it fun.
• Crazy Math Mom (Math Games ...) offers a fact family story.
• An (Motion Math) offers 3 games for place value (one is app-based, two are non-electronic do-it-yourself games).
• Carole (Mathematical Thinking) shares her missing part cards to lay a foundation for subtraction.
• Christy (Just Another Step...) shows her kids binary, with cards that look fun to make. She throws in some interesting history and a magic trick.
• When my son was younger, I searched for learning ideas that were good for very active, physical kids. He would have loved Kath's (Kath is Math) 'Swat those numbers!'
• While Gord (quantblog) was doing multiplication using coffee beans on graph paper with his young son, he started thinking about an applet he wanted. If wasn't out there, so he built it.
• John (Math Hombre) has made a game where you multiply and divide by fractions to make the superheroes shrink and grow, Size the Day.
• John Henry is the legend of a steel-driving man who competed against a steam engine. David (Delta Scape) shares this story with school children, and then they time each other doing multiplication worksheets with and without a calculator. "Students are asked to predict which method will take longer, gather data, and compare the results using box-plots." Sounds like a good way to help students decide when it makes sense to use a calculator.
• Christopher (Overthinking My Teaching) writes about his daughter's request for a 'real' math question, and how context is what helps us think.
• Michelle (The Rookery) used Incredible Comparisons: The World in One Day (only available used) to help her students understand rates. I've visited Michelle's classroom, and it feels magical to me. Here's a quote from a post on playing class games, "A child who has fallen on his knees to plead with another child to 'smile if you love me' does not feel inhibited when it's time to raise his hand and take a guess at how to solve a math problem."

 (from Christy's Game of Patterns)

Patterns & Logic

• Making up your own games is super-engaging. Christy (Just Another Step...) and her son made up a game of patterns that they had great fun with.
• Logic puzzles can be a great side door into the mansion of math. (Think about how Sudoku has swept the country.) The Island of Liars and Truthtellers is a classic setting for logic puzzles. Dan (mathrecreations) shares some background and 5 puzzles.
• Dr. Techniko's game, How To Train Your Robot, sounds like a blast, suitable for very young kids, whose 'robots' are their parents.

 (from britton.disted.camosun.bc.ca/jbsymteslk.htm)

Visual Math

 (by Anna Weltman)
• Becky (Wide Open Campus) shares photos from her son Z's Escheriffic day, along with a link to a tessellation maker and some thoughts on the magic.
• In Not Just Shapes, Malke (The Map is Not...) continues her delightful series documenting her daughter's math discoveries. "As the structure of the universe continues to emerge in front of her very own (and open) eyes, how much more fun will her world be to play in, explore, put together, and then take apart again?"
• Justin (Math Munch) shares Star Art with the readers of Math Munch (a weekly math links blog), along with some puzzle news. (Links to directions for making this beautiful blue star are in the comments.)
• When you check out Emilio's (Triangulation) Interactive Triangulation, make sure you move your mouse over the pictures.
• Rachel (Plus Magazine) wrote Shattering Crystal Symmetries. If I understand correctly, chemists used to think crystals were always organized in a repeating pattern; Dan Schectman analyzed the structure of a crystal that could not have a repeating pattern, and won the 2011 Nobel Prize for chemistry for this work, which is based on the mathematical work of Roger Penrose. Amazing!  "Not only had mathematicians extensively studied symmetry, but, as mathematicians are prone to do, they were also interested in how to break it."
• Mike and Ian wrote another great Plus Magazine article, this one on Visualizing Probabilities.
• Erlina (Mathematics for Teaching) gives a number of visual representations of the difference of two squares.
• In Perspective in Math and Art, Annalisa (at Inside Higher Ed) writes about how learning to draw in perspective can be a bridge to learning math. "If you sketch a picture of the rails of the train track going into the distance, and you know where the first two railroad ties go, where do you put the next one?"

 (from Fawn's area of a circle lesson)

Algebra, Geometry, & Trigonometry

 (from Haggis' puzzle)

Puzzles & Games

• Haggis (Knot Your Average Sheep) helped design some activities for an interactive evening at the museum (National Museum of Scotland), and included this:  "Can you colour the lines [on the star above] with 3 colours so that at each star 3 different colours meet?"
• Robert Abbott (inventor of the card game Eleusis) has shared some great online Logic mazes.
• Mike (Spiked Math Comics) asks, "What's wrong with this contest?"
• Here's a puzzle from Alexander (Cut the Knot): Given a sequence of numbers, pick any two, say A and B, randomly and replace the two with the result of A×B+A+B. Repeat the procedure until only one number remains. Try to predict the final result. You can play with it online. What's happening?

 (from Rick's blog banner)

Notation and Language

• Sometimes the notation makes a math topic harder than it needs to be. Take logarithms, for example. Where'd that word come from, anyway? Kate (f(t)) uses power2(8) = 3 to invite her students to figure out what the new function is. I used her idea, but changed it to  P2(x); it worked great.
• Rick (Exploring Binary) wanted a word for the portion of a binary number after the ... umm, "decimal" point. You know, the part that represents a fraction. He wants to know if 'bicimal' works for you.

 (from Brent's post)

Breaking News
(The MT@P Times)

 (from Bon's Geogebra post)

• Denise (Let's Play Math!) says, "What better way could there be to do math than snuggled up on a couch with your little one, or side by side at the sink while your middle-school student helps you wash the dishes, or passing the time on a car ride into town?" Mmm, tell me a math story, please.
• Colleen (Mathematics, Learning and Web 2.0) offers David's Powerpoint collections for Number, Algebra, Proof, Geometry, and Statistics.
• Erlina (Mathematics for Teaching) considers what a teacher needs to know to teach fractions and decimals.
• Bon (Math is Not...) asks teachers to reconsider the ways they use Geogebra. She hopes teachers will open lessons up so students can make their own discoveries. She says, "I discovered math when I used GeoGebra. Math I never knew."
• If you want students to learn math through projects (Project-Based Learning has its own acronym of course, PBL), you need to come up with projects that fit your subject and your teaching style. Bryan (Doing Mathematics) brainstorms some enticing ones. Geoff (emergent math) makes a plea for more inquiry-based lessons (is that the same as project-based?) He has set up a google docs repository for each course from algebra to calculus, and lots of folks have contributed ideas. You can use theirs or add some more.
• Sue (Math Mama Writes, that's me) posted on a way of structuring learning situations as games. Not the competitive sort, more like a treasure hunt where everyone can win.
• Paul (Lost in Recursion) on the inadequacies of grading, "The product of mathematical work is mathematical thinking. Trying to grade it is useless."
• Maria (busynessgirl) knows that getting students to participate actively is vital, and whiteboards are a great tool, but what if you don't have enough whiteboards? Betty solved that problem!
• Caroline (Maths Insider) shares some inspiring quotes.

And now we've come to the end of the 51st Math Teachers at Play blog carnival. Here's one last parting thought... I once read that, among the Tsilagi (Cherokee), you become an adult at 51. (Perhaps that's a bad translation, and you become an elder at 51?) That idea really stuck with me, and when I turned 51 I thought often about how much I'd matured since I was 18. With a 10-year-old in my life, I'm still working hard at maturity... What's 51 mean to you?

And one last question: "Are there coincidences in math?"

The next Math Teachers at Play blog carnival will be hosted at Denise's Let Play Math! blog in the 2nd week of July. If you'd like to be a host of this monthly carnival, check here for open dates. Until then, take your time to savor all these goodies, and when you're done here, check out the 87th Carnival of Mathematics at Random Walks.

1. Wow, what riches! I really love the categories. Can't wait to dig in! :)

2. Looks great! Thank you for hosting. I anticipate a lot of enjoyable browsing (so much for getting my chores done...)

I've always thought of 51 as something of a trickster, and 57, too. They feel like they ought to be prime, but they're not.

3. Look what I just found on mathchat: Find the smallest pair of pentagonal numbers whose sum and difference is pentagonal.

I wonder if 51 comes up in that puzzle.

4. Sue, thanks so much for hosting - I'm looking forward to reading what everyone's sharing!

5. I can't wait to read through the treasures you've included in the carnival.

6. I had a name and blog name wrong. (I got two people with similar names mixed up.) I fixed it, so now if you go to Bryan's (Doing Mathematics) brainstorm of some enticing projects, you won't be confused.

7. Thanks for the numerous collection Sue.

8. Lots more links to early math ideas, over at love2learn2day, in the 'blog hop' post. These happen every Monday.