Math Hombre

Doesn't this look like that door from the story problem?

by mag3737

The Number Dictionary reveals two particularly interesting facts about 47.

• 47 is a prime and a Gaussian prime.
• 47 is the difference between two squares.

Don't these make you wonder?

I mean 7s and 3s show up in the ones places of many primes, of course.  (What is the frequency of one's place digits in prime numbers anyway?  Are 7s and 3s more common than 1s and 9s?)  But 47 is so nicely nestled between 43 and 53. What's the next 7-prime that's the only prime between two adjacent 3-primes? Jim Loy has a nice page on Gaussian primes - that's extending the idea of prime numbers to complex numbers. Surprising things happen then - like 2 and 5 are not Gaussian primes. In fact there are only 12 integers that are Gaussian primes less than 100. Aren't there 24 primes less than 100? Is there a reason that it's half the number? There's some nice complexity.

Being the difference of two squares is also interesting. Is there a triangle connected to that? (Bet I could illustrate that in GeoGebra...) The difference of two adjacent squares - is there a pattern to those numbers?  How would you quickly estimate which squares? Can you tell precisely just from knowing they're adjacent? Could the difference of adjacent squares pattern help you find more Pythagorean triples?

I don't think I've appreciated 47 nearly enough before this carnival. But we should move on since there are a lot of neat entries this month.

by Eva the Weaver

About teaching 
David Coffey sent in Whose problem is it? from Delta Scape, which is good because it saved me poaching it for the curator's corner below. He's thinking about supporting students in being problem finders not just problem solvers.

Bon Crowder instructs How to Create an Inquiry Zone for Math Learning from Math is Not A Four Letter Word.  Making learning safe for students - even in math class.

Peter Price blows Are Wind Farms The Solution? Do the Math! our way from Classroom Professor, How math should be used to inform students' learning about the environment and how to protect it, using video about wind farms and the challenging questions they raise.  

Peter Rowlett asks Have you used maths in the news in school? posted at Travels in a Mathematical World Blog. He would be interested in hearing from people who have used maths in the news to enrich their teaching.
 
Becky Johnston shares a young learner's Metamorphosis pictures Wide Open Campus, and argues for a broader view of mathematical thinking.



Rodi Steinig explains What We Did in Math Circle, AND Why We Did It posted at Talking Stick Math Circle Blog, presenting Math Circles' pedagogy via a session with 8-10 year olds.


Natasha Chen from IMACS persuades us to avoid teaching tricks and instead urges us to make sense of word problems.
 
Balazs Koren (kobak) presents digitális bennszülöttszelidítés (digital teaching tools) posted at kobak pont org. (The Google translation; there's a slideshare which doesn't translate but which you can read most of.)

by Leo Reynolds

Algebra and Geometry 
Alexander Bogomolny presents Finding a Parallelogram in 3D posted at CTK Insights, with three solutions based on the definition and properties of parallelogram.He de "Almost a classic problem of finding a parallelogram cross-section of an irregular pyramid. " Plenty of his insightful and excellent visualizations.


Denise at Let's Play Math!, the founder of this here carnival here,  writes Understanding Algebra: How Many Roots? because "I wish my algebra teacher had explained it like James Tanton does. It makes so much sense!"

Fawn Nguyen presents Playing with Barbies posted at her self-titled blog, which uses Barbie dolls to teach proportions. "The kids really get into the activity and are proud of their work."


Cassie Becker is developing 16 algebra activities based on the Common Core to promote student engagement. The first 5 are available already.

Luis R. Guzman, Jr. presents A Complex Problem looking at roots of Complex numbers at Guzman's Mathematics Weblog, using standard and Euler notation. But he's not afraid to get negative, too.


Guillermo Bautista also speaks C, and investigates Complex Conjugates at Math and Multimedia.


Maria Miller shares a triangle area problem (with her own solution) from gogeometry.com at her Homeschool Math Blog.

by Leo Reynolds

Arithmetic 
Mainul Maksud posts an algorithm for Extracting Square Roots with several examples. From Mental Math with Tricks and Shortcuts.  Does his method apply to Luis' method for complex numbers?

Yan Kow Cheong shares Social Media Math posted at Singapore Math, 8 exercises using social media as a context.
 
Santo D'Agostino has been writing a series, How Much Mathematics Should A Student Memorize? Part 5, The Multiplication Table is up at QED Insight Most of the post is in an 18 page pdf file that quite thoroughly investigates multiplication facts and properties. It even addresses one of the 47 problems from up above!

Christy presents A few more math books and activities from Just another step to take.... Instead of following their regular math curriculum, they've been reading some math books and doing math play.


Peter Rowlett has Favourite popular mathematics books posted at Travels in a Mathematical World Blog, saying, "I collected this list of favourite popular mathematics books from people on Twitter and Google+ and there's more in the comments." (Love these kinds of lists, and there's lots of overlap with my list, but definitely new stuff, too.)

Chintamani Gadre further develops some divisibility rules in this post.


I recently wrote up one of my favorite games, Fraction Catch. Pretty good game, and some constructive mathematics.
 

by Ruth Hill

Early Learners  
Karyn Tripp presents What Equals What? With Math Fables posted at Teach Beside Me, adding some quick representation to Greg Tang's book.

Teaching My Baby Math from Jennifer Bardsley's Teaching My Baby To Read. She wonders: can two year olds identify and name the quantity three?  Even after all of my trials and errors with my own daughter, I’m still not sure. Can your two year old do this?


Christy has Math and Graph Games. posted at Just another step to take.... With bonus connections to flow charts and Rock, Paper, Scissors, Lizard, Spock.

Amy Bowers paints numbers with art grids posted at mamascout. I'd be curious to see the math side of this more explicitly. The art is beautiful.

Lilac shares Homemade Math Manipulatives - Sorting Hearts for teaching grouping and sorting skills to preschoolers, at Learners in Bloom. Also a game, Blocks in Socks - Early Math Game.

by mafo

More!

Colleen Young presents World Maths Day 2012 posted at Mathematics, Learning and Web 2.0, saying, "With World Maths Day approaching, it seems appropriate to have a post on the topic as part of the carnival." Some info on the day and links to lots of resources.

Dan MacKinnon programs better late than never: Mandelbrot Set  at mathrecreation. He's using the open source programming language called Processing. 

Sunday at the Park with Guillermo results in a post from his Mathematical Palette blog on Points, Pixels and  Pointillism.


Opening a whole can of worms, Misty presents Free High School Math and everything else you ever wanted to learn posted at Homeschool Bytes, saying, "We've been using Khan Academy almost exclusively for our math work lately and the kids love it."  I'll share a counterpoint here from Frank Noschese.  That said, Khan is a huge resource that there must be good ways to use.

by Eva the Weaver

Curator's Corner
Sam Shah started a conversation on planning. Read the comments.

Jason Buell lays out some nuts and bolts of complex instruction. Strong stuff.

Derek Bruff has a nice probability lesson, but moreso builds a case for using student prediction in your teaching.



 
...and out!

by pieplate

That concludes this edition. Submit your blog article to the next edition of math teachers at play using our carnival submission form. Past posts and future hosts can be found on our blog carnival index page. Next time around Bon is hosting at Math Four. Could get crazy.

47 lb.s? We do like this wine in my house... but supposedly this was a real rooster from a turn of the 20th century Texas carnival. A typical rooster weighs about 10-18 pounds and about a foot tall... so how big was HRM Rex Goliath?

 Image credits: mostly captioned under photos, all from Flickr. But I want to especially point out Eva the Weaver at Flickr who has many math themed photos, geometry and counting as well as numerals. The title graphic is from DizzyGirl, altered with Skitch.

by Eva the Weaver of course

Welcome to the 36th edition of

How many rhombs can be traced on the edges of this figure?

36 has long been one of my favorite numbers, but faced with this carnival, it was hard to figure out why.  It's a square number that's a product of two squares, but that's not too rare.  (Why?)  It's the 6th perfect square and the sum of the first six odds, but that's not too remarkable.  (Why?)  It's the 8th triangular number, but not a Sierpinski step or anything... wait!  It's a square triangular number?  How common is that?  1, 36, then...?

8+9+9+10... will numbers like that have a special property?

Number
Denise, the founder of this here carnival here, has an activity on Times Tac Toe at Let's Play Math.

Erlina at Mathematics for Teaching (formerly keeping Math Simple) has a nice introduction to integers based on sorting.

Can you see the four 9-squares and nine 4-squares in this brick?

Guillermo has posts on addition and subtraction of integers.  He updated recently from his old wordpress ___domain to mathandmultimedia.com.

Marilyn at Mad Kane's Humor Blog had a Pi Day limerick.  Given Pi Day's proximity to St. Patrick's Day, that's a double score. Bonus: Math Jokes 4 Mathy Folks had mathy St. Patrick's jokes.

Pat blogged at Pat's Blog, hmmm, about Pi from a classic Venn illustration in 1888 to an internet meme cartoon from 2011. 

John has fascinating info on a class of prime numbers called the Limerick Primes at the Endeavor.

How can you quickly determine if 1926 is a multiple of 36?  Is it close?

Algebra
Mimi at I Hope This Old Train Breaks Down... has a complete activity on (beyond) composition of functions, adapting and extending an NCTM activity, and also an idea for a neat telephone function composition activity.  She's prolific, so poke around the blog while you're there.

Alexander, author of the amazing Cut-the-Knot, has a great discussion of inverse functions, relating three different Mathematics Teacher articles at the CTK Insights blog.

How big is this 36 in real life? Why do you think so?

Geometry
Becky at Wide Open Campus has a quick little activity called Nature's Pattern Blocks.

Chris at M.O.B. has an activity on Mirror Imaging Monsters.  Arrrgh, reflectional symmetry.

Maria at Homeschool Math Blog has an excellent problem with a chord. Good challenge with a different perspective.




 
Connections
Katie has a travel site, Tripbase, with the nine most mathematically interesting buildings.  I might make it ten for either the Plaza de España or the Alhambra in Spain, both of which have some great tessellations.  What would you add?

Cheong ponders Are You a Number? at Singapore Math.

Representation
Caroline at Maths Insider has a post on strategies for your visual, auditory or tactile learner.

Sue, writing at Math Mama Writes...,  use graphs to make connections to increase her understanding of trig identities.

I never got a chance to clean up and make pretty this 36 knot that I designed for this carnival.  Why on earth would I think that this somehow related to 36?

Why would 36 degrees be newsworthy?

Teaching and Learning
Rachel at Quirky Mama has monthly math activities for preschoolers.

Maria at The Math Mom recommends a short post with 5 tips for not transferring your math anxiety or a long and serious post on if it's okay to be smart.

Peter has a collection of links to enthuse about math at Travels in a Mathematical World.  Peter is half of the Math/Maths podcast.

Jacob tackles memory vs. mastery learning at License to Teach.


What about this?
Carson shared a nice graphic relating math to careers at When Am I Going to Use This?  But it's at an online education site, which Dan Meyer wrote quite forcefully against, in terms of predatory recruitment, at dy/dan.  He was writing specifically about the Top N lists.  What do you think?

 The other issue to be on the look out for is the EduSolidarity online rally, March 22nd.  If you don't stand for something, you'll fall for anything.

So Long and No Longer
Sorry this was a wee bit late.  I had a busy couple of days between Knot Fun (Celtic knot activity on axioms) and a Tech Symposium presentation, for which I assembled this glog (interactive poster) about the Tech I Use.  See you next month inside Maths Insider hosted by Caroline.  Submit an article!

Mathy pictures made in Geogebra.  Other pix from Flickr - the photographer's name for each is in the file name.  And a special MTAP shout out to Leo Reynolds, who has got to be the most prolific number photographer in history.

Welcome to the Mathematics and Multimedia Blog Carnival, 5th edition.  (Hope you enjoyed the Fantastic Fourth Edition.)  Five seems like a fortunate number, since we have five senses.  Our five fingered hands are a good start to mathematics.  We all love a high five, are happy to take five or are glad when it's five o'clock (somewhere).  But my favorite five fact features 5 for the fifth Fibonacci number.  Far out!


This blog carnival seeks to promote seven principles:
1. Connection between and among different mathematical concepts


Sol Lederman at Wild About Math shares a video of an Incredible Magic Square.

Antonio Gutierrez at Go Geometry has a fascinating golden rectangle puzzle that connects with the Droste effect.




2. Connections between math and real life; use of real-life contexts to explain mathematical concepts


John D Cook at the Endeavor shares that there isn't a googol of anything.

 Grrrl Scientist suggested this article from her guardian.co.uk blog about "How the leopard got its spots" that has some literally beautiful mathematics.

Consider this beautiful film by Cristóbal Vila - Nature by Numbers.  Or this collection of Hands On Math Movies.

David Cox has just been sharing a ridiculous amount of great stuff lately.  For example, projectile motion.

It's been widely shared, but you have to check out Kate Nowak's money take on special right triangles at f(t).


 3. Clear and intuitive explanation of topics not discussed in textbooks, hard to understand, or difficult to teach

James Tanton has two videos explaining the principles for math genius thinking.  Hat tip: Denise at Let's Play Math.  You might also like Sue Van Hattum's interview of Dr. Tanton for the Math 2.0 interest group.

For that matter, Sue's post at Math Mama Writes about E is for Eigenvectors and Eigenvalues belongs in this category.  Has the great first sentence: "This post is about fear."

I spent some time recently looking at trigonometric function visualizations and making a couple Geogebra sketches for them and their inverses.  Seems silly to link, since it's right down there.



4. Proofs of mathematical theorems in which the difficulty of the explanation is accessible to high school students

No one nominated entries in this category, but it makes me think of work like James Tanton's explanation of Euler's proof that every even perfect number is triangular, or Alexander Bogomolny's proofs at Cut-the-Knot of the addition and subtraction formulas for sine and cosine.  (Both of these sites I've had occasion to look up recently!)



 5. Intuitive explanation of higher math topics, in which the difficulty is accessible to high school students


Derek Bruff has put together a fascinating interactive Cryptography Timeline.  I'd love to see some of these for some important math concepts.






6. Software introduction, review or tutorials

Guillermo Bautista, the founder of this here carnival, at the Math and Multimedia blog, has a roundup of essential tools for every math blogger.  Also be sure to check out his terrific Geogebra tutorials while at his site.

Maria Anderson has video of her presentation from MAA-Michigan up, Math Technology to Engage, Delight and Excite.  Also watch as her new blog, Edge of Learning, gets up and running.

Chris Betcher has some terrific Scratch (the programming language) resources and videos.

You might try one of these 15 mind-mapping tools.  (Many are free.)






 7. Integration of technology (Web 2.0, Teaching 2.0, Classroom 2.0), in teaching mathematics 

David Wees has an interesting meditation on the importance of interactivity in math teaching.

Cybraryman has a long list of math/tech integration resources and lessons.







If you're looking for Five tunes, Take 5, or try Gimme 5 from Sesame Street, High Five from They Might Be Giants, Dino 5 (who also have a great counting rap called What About 10)?, or maybe the best (in terms of math) ...







If you have ever posted a blog carnival, you know that you receive a lot of obvious spam.  But some can seem relevant, so I like to have a Best of the Spam category.  For example, the Top 40 sources for open courseware video.

And if you are mistakenly put here, or your post did not appear, please let me know and I will correct it posthaste.

Images were obtained from Creative Commons search.  Attributions are in the picture title - click on the image and you will see the source from Flickr.

If you enjoyed the carnival, please consider nominating a blogpost, your own or someone else's, for the sixth edition, to be held at Great Maths Teaching Ideas by William Emery.  It's a very active blog with many K-12 activities, so don't wait a month to check it out!

Congratulations if you recognized the five connection for each of the images above.  I tried to slip in some tricky ones.

If the carnival is done, must be time to head over to the Five Bells.  Cheers!

lgb06 @ Flickr

I wanted to gather an overview of tech resources for students, and thought it would be worth posting for everyone.  Nothing completely new, really, but I'd like this to be a good overview.  Please add other relevant resources I overlooked or don't know about in the comments.

New teachers: don't overload!  Subtle shifts.  Look for something that will help you do what you want to do, and slowly incorporate or try out new things.

File storage and sharing:  have something to share with many people or everyone?  There are many free internet services.

• Dropbox - best for working with colleagues.  Simultaneously shares files and backs them up in the cloud.  Allows you to undo to previous saved versions for up to a month.  Invisibly syncs files on your computer with those in the cloud.
• Box.net - similar to dropbox without the seamless syncing.  May be better for sharing with the public, though.
• Scribd - document sharing that you can embed in a blog or other web 2.0 application.  Works with Microsoft Word and PDFs perfectly.
• Google docs - clearly the best for simultaneous editing and sharing from anywhere.

Presentations:

• Slideshare - upload powerpoint presentations to embed or share publicly or have available to students and yourself from anywhere.  Embeddable.
• Prezi - cool graphic-style presentation which is like a dynamic concept map.  You can embed youtube videos, present on or offline, embed the prezi and easily share them.  The editor is suprisingly easy to learn.
• Glogster - internet posters.  Multimedia possible.  Free to teachers and their students.  Easy enough for quick student projects.
• Animoto - turn powerpoint files into movies.  A little limited at the free level.  Also easy enough for students.

russelldavies @ Flickr

Math specific:

• Geogebra - my favorite, bar none.  Geometry, algebra and free.  That's just incredible.  Exports images for use in documents, exports sketches as a dynamic webpages, runs on any platform.  Becuase it's opensource, there's a large library of free resources developed by other teachers.  (Some of my sketches are on this blog.)
• Wolfram|Alpha - the app/webpage that makes a computer algebra system available to anyone with the internet or a smartphone.  Solve equations, access databases, investigate almost anything quantitative. (Here's my W|A think aloud for a question, but here's a better introduction to Wolfram|Alpha.)
• Core Plus math tools - free dynamic online applets shared freely from the authors of the Core Plus Mathematics Project curriculum, for algebra, geometry, discrete math and statistics.
• NRICH - a sortable, searchable problem bank of rich problems for K-16 mathematics from the national maths organization of the United Kingdom.  Updated with new problems monthly.  Many problems accompanied by a dynamic visualization.
• Virtual Manipulative Library -  good for computer demonstrations, smartboards, and students with internet access.  Some are clunkier than others, but many are quite smooth.

Other Tools

• Jing - free screen capture software and screen video capture software that allows you to save to your computer or share via their linkable website.  The souped up version is Snag It, and the same company makes Camtasia which is a quite nice movie editing software.
• Mindomo and Mindmeister - tools for online, sharable concept maps.
• Social bookmarking - Diigo, StumbleUpon, Delicious
• Of course, I'm a big fan of twitter and blogging, also. 

Rights and responsibilities

• Creative Commons - Finding copyright accessible material
• Fair use - video mashup completely explaining fair use.
• Copyleft - Licensing your work to share; Gnu public license or Sharealike

More reading:

• Maria Anderson
• Derek Bruff, expert on clicker use, among other things.
• Dan Meyer's What Can You Do With This? lessons.
• Math 2.0 Interest Group
• My week at tech camp - where I learned about or first had a chance to try many of these things.

Note: if you're a college teacher of mathematics, you can go to tech camp next summer.

Well, I've made the Twitter jump.  I want to try twitter in classes this fall, and that means I need to be a user.  So far it has been interesting, and it's a slower fall down the rabbit hole than I expected.  Follow me as @mathhombre.  I would recommend it, as it has linked me to several interesting resources, and hasn't taken much time.  There's a whole social aspect I really don't get yet, but I'm a bit of a misanthrope.

A Reston Kid has a nice collection of math blogs to start with, all people who are on the mathteachers twitter list.

For example, Jim Knight tweeted: 35 web 2.0 educational resources.  Some are no brainers, some charge, but I found several new ones of use to me. 

Kate Nowak tweeted the MathFail website where the image at the bottom came from.

Reston Kid (blog link) also tweeted out Frink, a "practical calculating tool and programming language designed to make physical calculations simple."  As RK notes, the documentation is hilarious.

EDIT:  Cathy Campbell (@ccampbel14) points out this great post on Twitter for math teachers.

The first Math and Multimedia Carnival post is up at Guillermo Bautista's blog.  Lots of interesting stuff.  Sol Lederman's puzzles, Maria Drojkova's educational twitter uses, David Wees building off Dan Meyer's video problems and more.

For example, an Alexander Bogomolny post at C(ut)T(he)K(not) Insights, who's hosting the next Math Teachers at Play.  I'm excited as his Cut-the-Knot (a Gordian reference?) was one of the first worthwhile math sites on the internet.  (IMHO)


Of course, if you're on vacation, more power to you.  Maybe you'd be interested in trying our new family game... C'mon, please?

Guillermo Bautista is starting a new blog carnival on Multimedia and Math, focusing on technology and connections. Check his announcement on Mathematics and Multimedia, and post to the carnival here.

Kate Nowak is writing about starting your own blog.   Given me some food for thought.  She links to Sam Shah's worthwhile article on it, too.

Knowing my love for games, Sue Van Hattum (Math Mama Writes) sent me the link to this neat Geometry Taboo game at  Teaching ninJa, which had some other neat posts, also.  Sue just posted/linked an awesome/awful video about the L-Curve distribution of wealth in the US.  Has me wondering what a reasonable or equitable wealth/income distribution would look like.  Is the L-Curve necessary in any way?

Michael Paul Goldenberg (no relation) reordered Dan Meyer's What Can You Do With It? series chronologically, instead of the usual blog reverse order.  Hope neither he nor Dan don't mind me sharing it here - he sent it out on the MathTalk mailing list.  MPG blogs at rationalmathed.blogspot.com.  It was some drudge work on Michael's part, but cool idea.  I had the list here, but he's since put it on his blog.  So go there.

There's kind of a standards based grading theme going.  I've got to figure out some stuff about that and how it applies to process goals.  Shawn at Think Thank Thunk and Kate at f(t) (where does she get the time?).

Comic from the often quite funny Chuck & Beans at the shoeboxblog.com.  Like the card company.

My colleague Paul Yu and I (with a lot of help from colleagues) are trying to put together a grant for equipping a classroom with current tech for math teacher preparation.  In the course of this we have connected with many resources.  Really I should have posted this earlier to get feedback from readers, but better late than never.  (Probably the inscription to be on my tombstone.  Actually... not bad.)

Not to pander, but if you're a grant reviewer, welcome!

I'll continue to update this post rather than add new posts.  If you have suggestions, I'd love to hear them.

Apple

• App Store Metrics 
• Apple iPad reaches 1 million sales faster than iPhone
• GetYaLearnOn - statistics app

Research

• Preparing teachers to use technology to enhance the learning of mathematics: A position of the Association of Mathematics Teacher Educators.  (pdf)
• Liz Kolb, Toys to Tools: Connecting Student Cell Phones to Education, International Society for Technology in Education, 2008 
• Mobile Computing category at T H E Journal
• Niess, M. L., Ronau, R. N., Shafer, K. G., Driskell, S. O., Harper S. R., Johnston, C., Browning, C., Özgün-Koca, S. A., & Kersaint, G. (2009). Mathematics teacher TPACK standards and development model. Contemporary Issues in Technology and Teacher Education [Online serial], 9(1).  Note that all of CITE is available for free.
• Schmidt, D. A.  , Baran, E.  , Thompson, A.  D.  , Koehler, M.  J.  , Mishra, P.  & Shin, T.  (2009).  Survey of preservice teachers' knowledge of teaching and technology.

Organizations

• Cell Phones in Learning (blog)
• Classroom 2.0, teaching with tech interest group (Ning)
• Math 2.0, Math teachers tech interest group (Wiki)
  Math Education 21C - 21st Century Project
• ON-Math, NCTM's online journal
• 
  

Uses/Tech

• Dan Meyer, My TEDxNYED Session — Math Curriculum Makeover.  (Really this blog has turned into the game of how many times I can reference this video.)
• Jill Laster, At Indiana U., a Class on Game Design Has Students Playing to Win, The Chronicle of Higher Education
• Instapaper
• Texting Poetry (article)
• Texting Education (article)
• Mobile Gaming/Learning tied to assessment
• MOBI Interwrite pads
• Cell Phones' potential - panel discussion

Just for Fun



(The iPad Tango?!)

Question 1: Do you know how many yards in a chain? Hint: 1 acre =1 chain x 1 furlong. OK, that's not a hint so much as a taunt. Hint2: a cricket pitch is a chain long. Blimey!

Elementary
Rachel Lynette presents Send your Kids on a Multiplication Scavenger Hunt posted at Minds in Bloom. She writes on a range of topics and you're sure to find other things of interest to you, too. For example, the Creative Classroom.

TIC presents Free Math Numberline Activities posted at Technology In Class. This blog features free resources of interest to teachers in all content areas, not just math.

Sue VanHattum presents Challenge: Write a Kids' Poem about Math posted at Math Mama Writes.... She has a fun comment thread started already as people start to investigate and respond with poems.

I once gave a class the challenge to write a number that when you say it out loud properly has haiku form. Got some fun answers. E.g. 22,220,220.

Crewton Ramone presents The Importance of Addends. posted at Crewton Ramone's Blog of Math. Crewton mixes an opinion piece with some advice about the importance of and how to compute addends.

Deb at math.about.com had a quick post linking to 10 100's Chart activities. I also quite like this representation.


Question 2: This edition is pentagonal. But where's the 22?

Secondary
Sue VanHattum presents Pythagorean Triples posted at Math Mama Writes.... This is the start to a fun investigation into the triples by doing some nice problem posing.

Denise presents 2010 Mathematics Game posted at Let's play math!. This is an interesting challenge that involves some non-standard arithmetic. Commenters have made some good inroads on it, but without giving anything away to keep you from trying the problem. As Denise said, "Did you know that playing games is one of the "Top 10 Ways To Improve Your Brain Fitness"? So slip into your workout clothes and pump up those mental muscles with the 2010 Mathematics Game!"

yofx has moved to its new site, and issued a nice Pieces of Eight challenge. Great order of operations problem. (G.o.o.o.p.?)

The Exponential Curve has been posting a series on graphing lines, including a nice one on multiple representations.

John Cook presents Roots of integers — The Endeavour posted at The Endeavour. John has a nice intuitive proof of an understandable and interesting theorem, and there's another in the comments.

Archimedes proof that 22/7 is greater than Pi involved circumscribing a circle with a 96-gon and then taking a ratio of its perimeter to the circle's diameter and showing that is less than 22/7.

The enlarged picture on the right shows the circumference of the blue circle to be less than the perimeter of the red 96-gon.

Question 3: 21 and 22 are the 2nd pair of consecutive semiprimes. (A semiprime is the product of two primes.) Are there more?
UPDATE: Matt has a lot of information about this in the comments. Check out his post visualizing complex ___domain for functions - a dance!

Higher math
Pat Ballew presents Lotteries and Math posted at Pat'sBlog. Pat notes, "Lotteries seem to be more than just a tax on the mathematically illiterate.. they are a great source of math problems." Certainly these combinatorics can be confounding, but the context is so engaging to students that they will fight for it.

Math~Blog posted an interview with the author of the very interesting book Number Freak, Derrick Niederman.

Question 4: This is the first MTAP of 2010, a pleasing year because of its 2x*100+x structure. When was the last year with that pattern? When is the next?

Math Teaching
Maria H. Andersen presents How to Grade a Student Blog posted at Teaching College Math. She says, "I've been having students blog as one of their learning projects in Math for Elementary Teachers. This feels a lot more like play than work!" Maria's really doing some innovative things, and this is worth checking out.

Kate at f(t) has a good post on a simple assessment technique using red, yellow and green cards.

The Fun Math Blog had a neat caption contest with a still from A Serious Man, the new Coen brothers movie. It gave me the idea to make an assessment where you get at students' attitudes by having them caption some math images. 63 pretty fun captions were submitted.

Maria Miller presents Choosing a homeschool math curriculum posted at Homeschool Math Blog. Maria points to a resource for guiding a homeschooler through this decision.

For elementary, I can't resist plugging Contexts for Learning Mathematics here. Brilliant, and integrates well with literacy learning.

Question 5: 22 is expressible as a sum of 4 consecutive integers. (Which?) But it is not the sum of any other string of consecutive integers. Is that true for any sum of four consecutive integers?

End Note
This edition almost didn't come to pass because of the rare but deadly Blogcarnival Catch 22. Math teachers improve their teaching by sharing with colleagues. But you have to know there's room for improvement to be open to sharing. But if you seek improvement that's already proof of quality teaching. In more logical language:

Improve your teaching => Know you need improvement AND Are willing to share with colleagues
Not a good teacher => Not be willing to share with colleagues
By definition of an implication, this is equivalent to (Are a good teacher OR Not be willing to share)
By DeMorgan, that is equivalent with Not (Not a good teacher AND Be willing to share)
By the contrapositive of original statement, implies Not improving teaching.

So we were almost shut down by the Internet Blog Overlords. Luckily, we were able to make a case that Good teacher => Desiring improvement, thus escaping the Catch 22.

Question 6: The 12 pentominos are justifiably famous and interesting mathematically. If you used hexagons (like, say the yellow hexagon pattern blocks) how many non-congruent configurations can you make? (With the same edge-sharing matching rules as for pentominoes.)

Next Time
See Math teachers at Play #23 at MATHRECREATION. Dan posts some pretty serious mathematics, like recent explorations of Catalan numbers, and some other mathematical diversions, too, like his recent post More Folds.

Remember that you can submit posts from other people's blogs if you see something interesting or worthwhile. Submit your ideas at BlogCarnival.com.

Also be sure to check our sister carnival out: most recently the 61st edition of the Carnival of Mathematics.

Miscellanea
A few submissions seemed sortapseudorelevant, so I don't want to leave them out...

• OnlineCollege presents 100 Best Education Blogs of 2009 posted at Associate's Degree. You'll see some familiar blogs in the ranks, I'm sure.
• Herbert Aitken presents 50 Free Online Educational Games That Are More Fun Than You’d Think posted at How To E-D-U. A few of my kids favorites are in here.
• Scott Palat presents Online Math Games and Lessons |. This quick post by Meaghan Montrose links to 2 reasonable looking resources.
• Peggy Stoppelmoor presents 25 Tips for Students & Teachers Using Google Wave posted at Top Online University Reviews.

We'll consider that last one ... the wave goodbye!