1.  Five Triangles - @Five_Triangles - for challenges, puzzles, problems, and fun math facts

A lot of these are appropriate for middle school as well as high school - Share a few fun challenge problems with your students (integers, geometry, and more!)

2.  Algebra Fact - @AlgebraFact - for higher level math facts

Postings include Abstract Algebra, Number Theory, and higher level Algebra.  These would be interesting for advanced students or higher grade levels.

3.  Math Giraffe (of course!) - @TheMathGiraffe  - for the #WeeklyMathematician series plus teaching articles, math education links, and more

New Mathematicians are posted each Friday.  Just put the fact on the board for the week, and then download the free crosswords to review at the end of each semester -- an easy dose of math history for your class!  Read more about how your class can join us for the Weekly Mathematician here.

4.  Geometry Dad - @GeometryDad - for really cool animated images to inspire Geometry appreciation

Any grade level will enjoy these neat GIFs that Geometry Dad puts together for his kids.  They show the beauty of Geometry in a fun way!

5.  NCTM Illuminations - @NCTMIllum - for lesson plan links

These games, investigations, and lesson ideas are so helpful!  I love all the content on the Illuminations website, but can never browse through it all.  Through the tweets, I find myself slowly being exposed to fun new ideas over time.  The lessons are wonderful for inquiry / discovery learning.

6.  On This Day in Math - @OnThisDayinMath - for daily math history facts

These mathematician bios and math history facts (often more than one per day!) are great for students or classes that are interested in what happened on today's date to impact mathematics.

7.  Ben Orlin - @benorlin - for humor and funny drawings

There may not be as much to share with younger students, but older ones may appreciate the humor, and at least you'll get a grin as you browse through.  I just love these fun math cartoons. 

Related Articles:

You can adapt this idea to other topics too, but these are the ones I have made so far. 

After trying a few different topics with these puzzles, I noticed that they really motivate students to find more efficient mathematical methods and develop their own shortcuts to try to solve them faster!  ... Awesome for critical thinking!!

Here's how to do it:

Three of these are puzzle-style activities in which students have to spin three layers of plates.  The goal is to line up the numbers so that each set of three numbers will meet the criteria.

For these ones, I pressed a paper between two plates to get an imprint of the circle.  I cut it out to the right size and made a little template.  I folded to make 8 sectors.  I traced a candle for the center circle, then eyeballed the halfway point from that circle to the edge to make the three layers of numbers. 

I kept this template and now I re-use it each time.  I just lay it under the plates while I create each activity.

Once you have a template set under the first plate, go around and copy the innermost set of numbers (see my photos below for sets of numbers that work for each puzzle).  Set another plate on top and do the next circle of numbers, then lay the third plate for the outermost set of numbers.

For the puzzle-style activities, I try to make them only have one correct answer (If one ends up with more than one solution, no problem - you'll just get a good conversation going about it!).  I found it helped to put a little arrow on one layer to point out one row to record as a "check row."  This makes it easier to grade.  If you use this as a station, the students just need to record that set of 3 numbers, and you can check answers in one second.

For the Triangle Inequality Theorem one, students must spin the three layers of plates until they can get ALL 8 sets of numbers to represent the 3 side lengths of POSSIBLE triangles at the same time.

This offers a great critical thinking challenge and really reinforces the concepts behind the side lengths of triangles.  By the time they test and spin a few times, the students get a ton of practice with the theorem. 

They start analyzing patterns in an attempt to test cases more quickly.  It's a pretty good challenge!

The image shows the solution, so the "check row" for students to record if they get it would be 818.

This one is similar, but takes even more thinking.  Two of the layers have angle measures, and the third has the triangle classification.

As they spin and test to find the solution to this puzzle, students have to first determine what the third angle measure will be (using triangle sum theorem - 180 degrees).  Then, they can think about the classification.  Again, they will develop shortcuts on their own as they work. 

The motivation to solve the puzzle leads them to find their own ways to become more mathematically efficient!

Again, the solution is shown here.  The set for a "quick check" would be 64, 58, acute.

You can never have too much practice with integers in Pre-Algebra.  I love this one for switching it up.

The 3 layers have to be arranged so that each set of 3 numbers adds up to 10.  You can easily make a huge set of these, each with different "goal" numbers. 

These work a little differently.....
Once I discovered the joys of my little plastic plate rotation stations, of course I could not get enough.  I decided to make a few to add a little fun to Algebra 1.

Instead of using a table on a worksheet, students can manipulate the plate and try to figure out the rule. 

It's not too fancy, but you can use basic or more challenging function rules and show the idea of a function in a different way for those hands-on / visual learners.  Some kids enjoy using these for practice.

I just draw the function machine on the top layer, and arrange my input and output values on the bottom layer.  As the kids spin it, they try to find the function rule that defines each relationship.

The colored one is a "basic" level.  The rule is f(x) = 2x + 1.
The other is more challenging.  The rule is f(x) = x^2 - x.

These are a fun addition to transformations.  I put the coordinate plane on the bottom of one plate, and the students use a dry-erase marker on the top plate.

Everything spins so smoothly and stays aligned.  It is the best way I have found so far to do rotations manually.

It helps to mark off a line every 90 degrees for reference.  You can do more marks if you want to do other rotations.  Click here to download the jpg image file for the coordinate plane if you do not have a printable one in this size already.

This video shows a little more detail if you are interested in making a set for your class.  Click the image to head over to the "Tools for Teaching Teens" video blog site to watch!

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I like to use online applets and manipulatives for virtual algebra tiles, but before kids get the hang of it, you really need something that everyone can see and touch.

These giant ones are easy to use on a magnetic whiteboard.  After a few demonstrations, students can come up and work through a few practice problems to learn how these manipulatives work. 

After that, of course they can get into a technology version of some kind, but I have found that the first introduction just has to be hands-on.

Download the algebra tile pages.

So far, I have only assembled positive sets to demonstrate the basics, but if you want them to be reversible like regular algebra tiles, just print a set of red tiles too and place the card stock pieces back-to-back with the magnets between the layers.  (Make sure your magnetic tape is double-sided.)

• adding and subtracting integers
  
• solving equations
• adding and subtracting polynomials
• multiplying polynomials
• factoring

This online file shows how to model different concepts with algebra tiles:
http://www.eastside.k12.ca.us/commoncorestatestandards/Using_Algebra_Tiles_Effectively.pdf

This hands-on applet is a great way to let students explore as a follow-up to using the giant board tiles together:
http://illuminations.nctm.org/activity.aspx?id=3482

Here is a free download of standard-sized printable algebra tiles for student desks:
http://www.regentsprep.org/regents/math/algebra/teachres/ttiles.htm