Friday, December 18, 2009

Math Teachers at Play #21

Welcome once again ...
to the Math Teachers At Play blog carnival. Puzzlers, riddlers, thinkers, doers, novices, experts, come one
, come all!

[photo by santarosa]

First off, in honor of the number 21, is a puzzle, fresh from the oven.

The Numberland News
runs personal ads. 21 was looking for a new friend and put an ad in.
Two-digit, semi-prime, triangular, Fibonacci number seeks same. I'm a binary palindrome, what about you?
Will 21 find a friend?


Kendra at Aussie Pumpkin Patch has written about the estimation lesson she did with her sons, which they started by reading Counting on Frank. It sounds like fun!

What is your child's favorite small toy? Will it help them learn division? Ashley at HyperHomeschool headed for the Legos, and here's what happened.

A really good way to understand place value is to work with other number bases. A book I recently discovered, How to Count Like a Martian, by Glory St. John, tells a detective story in which the history of other number systems plays a starring role. The last few chapters discuss place-value-based systems. Want a more hands-on approach? Sol, at Wild About Math!, offers us some math magic with index cards, based on binary numbers.

Megan Wong has written some books she'd like to share with us: Math Power is Fun and Brain Power is Fun are part of her Mind Power series.

Algebra and Geometry
At Let's Play Math, Denise gives another algebra lesson in Pre-Algebra Problem Solving: 4th Grade. I'm thinking this would be a good first step even for adults just learning algebra. I've seen mention of bar diagrams plenty, but this is the best illustration of their use I've seen so far.

Maria Miller offers us 3 videos of her proofs of some basic geometric relationships in Angles in a parallelogram and a triangle.

John Golden at Math Hombre shares his geogebra sketches (available as webpages and geogebra files) at Net Results. Students can use these to create their own prisms and pyramids. Print the nets, fold them up and see the funky solids.

One of my favorite things about MTAP is discovering new blogs. Here's one: Guillermo presents a Tutorial on Geometer's Sketchpad.

Calculus and ...
Pat's Blog has Fun with Parabolas.

Dan at Mathrecreation offers us a curious population model, with directions for exploring the logistics functions in Fathom.

Our Favorite Proofs
Brent, at The Math Less Traveled, presents a proof that pi is irrational. He thinks calculus students should be able to follow it. I've treid to follow this proof in other places and not had the patience for it. So far, his explanation is right up my alley.

The Count, at Discrete Ideas, gives us Discretely Simple, on his two favorite proofs.

On Teaching
Simple things can make such a difference. “What’s a question that someone else might get wrong?” So simple, and such a good way to get students thinking. Here's JD's post on it.

Riley Lark, at Point of Inflection, offers us his index cards. Well, the students get the cards, and some quickie interaction.

Then they can review with Trashketball. Post by Dan Greene at The Exponential Curve.


The Holiday Connection
When mathematicians hear about the gifts "my true love gave to me" on the 12 days of Christmas, they start counting. How many gifts would that be altogether? Sol at Wild About Math! wrote this post a few years back. And John at The Endeavor wrote this post more recently. One of the commenters on John's post wondered: "Funny that the 12 days of Christmas turn out to have just short of one gift per day for a full year. A coincidence?"

Remember the Soma Cube? Rachel, at Minds in Bloom, gives directions for making it here, and thinks a home-made puzzle would make a great gift. If you'd like to do that for this holiday season you may not have time to wait for the cubes to be shipped. But if you can wait, the cubes are pretty inexpensive online: 100 1" plastic cubes on Amazon for about $15, 100 1" wooden cubes for about $10 here, or 1000 centimeter cubes for $25.

Between Maria and JD and a few others around here, I've started to think that creating puzzles (or authoring math, as Maria would say) is something I too can do. So last week I made a logic puzzle, Holiday Logic. I hope you'll enjoy it.

This edition of MTAP was composed in Richmond, California and Chicago, Illinois. It's coming out late in the day because leaving home and flying here yesterday, even though uneventful, did take up my whole day. May your holidays be peaceful. May peace spread exponentially from our hearts through our actions to the world around us.


  1. "I'm a palindrome, as well. In two bases, but not binary"

  2. Great carnival! Thanks for stepping in and doing it on short notice. I love your puzzle, and Jonathan's extension of it.

    Now I'm off to do some serious browsing...

  3. Maybe that's three bases (of course excluding all bases greater than the number itself. How boring: 2 reads the same backwards and forwards in every other base...)


  4. I think 21 will find a friend. But the friend is 10111 in binary, so not a palindrome.

  5. Brent at The Math Less Traveled gives a bunch of links to help with the puzzle here.

  6. thanks!

    &happy holidays to you
    & yours (kid, & tutees,
    & saloners, & penpals &...).
    g-d bless us every one.

  7. @jd and Maria, Sorry your comments didn't show up when you posted them. I turned on moderation because of the spam, which I am still getting.

    I thought all comments came to my gmail. I just discovered these 2 here at blogspot, which had never shown up in my email. Hmm...

    So jd, I think you're saying you found a 3rd base that makes 21's friend a palindrome. I'm trying to figure out a painless way to search for that...

  8. Sue,

    Fun puzzle.

    > I'm trying to figure out a painless way to search for that...


    You will see the other base in which it is a palindrome as well.


  9. Ahh, yes. I guess I still think of Wolfram Alpha as cheating somehow. ;^)

    Now I guess we should ask if there are others. Is there any way to check algebraically?

  10. Hi I'm available a middle school math teacher
    who runs a website:

    -Michael Edlavitch

  11. Hi Michael, If you're saying you'd like to have a blog post of yours included in the math carnival, that's easy: go to the blog carnival site to see who the current host is, or to submit a post (at top left is 'submit an article').


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