Halloween: Mathematical Jack-o-Lanterns 

1. Buy some pumpkins and carving implements.

2. Cover a large table with plastic garbage bags. Provide paper towels.

3. Distribute the pumpkins and carving tools, and encourage your students to carve mathematical formulas or expressions.

4. Display the results – in the science building, in the dining hall, in the student center, at a community event for children. (Our Mortar Board chapter hosts a party for area children on campus.)

Christmas: a GeomeTree 

1. Gather construction paper and other brightly-colored paper, for the tree and the ornaments.

2. Identify a bulletin board or a blank wall in your math building or other campus spot.

3. Find patterns for polyhedral 'ornaments' online at sites such as Enchanted Learning or Origami Club and download and print copies.

4. Set up a work area with paper, scissors, tape, and string.

5. Construct the tree with large green paper triangles.

6. Make colorful mathematical ornaments and attach string.

7. Decorate and enjoy tree!                     

Valentine's Day: Mathematical Valentines 

1. Download and print instructions for constructing mathematical paper hearts from the German web site Mathematische Basteleien. Most of the constructions involve straightedge and compass constructions; others require the student to graph a curve on a computer. Some of them are quite beautiful and involve weaving paper of different colors.

2. Gather a set of compasses and rulers, pink and red paper, scissors, and perhaps markers or tape – depending on how much you want to decorate the hearts and what you plan to do with them.

3. Put everything on a table and watch your students make hearts! We had some interesting discussions about the relative beauty of several hearts, depending on what size isosceles triangle we began the construction with. And of course we all reviewed how to construct perpendicular line segments and isosceles triangles and semicircles and so forth, using the classical tools.

4. If you have access to a computer lab, you may want to let students graph some of the  two- and three-dimensional hearts described on the website. Alternatively, you could use Geometer's Sketchpad to do the ruler-and-compass constructions for you.

There is also a nice Valentine cardioid at the Math Forum.

Euler's Birthday

 A truly mathematical holiday! Celebrate Euler's Birthday on April 15^th:

1. If students in a particular class have studied anything related to Euler, get them to prepare presentations for extra credit -- short talks, an Euler-themed Jeopardy game (make copies of Euler Swiss francs for prize money), a trivia contest.

2. Decorate the area in Swiss flags and red and white streamers.

3. Bake a cake, and decorate it with symbols connected to Euler.

4. Show the movie "The Seven Bridges of Königsberg," if you have an old copy – and a projector.

5. Serve Swiss chocolate and Swiss cheese.

6. Hand out Euler trading cards. (Use a template like http://www.avery.com/avery/en_us/Templates-%26-Software/Templates/Blank-Templates/Cards/Business-Cards/Business-Card-_-tall-10-per-sheet_Microsoft-Word.htm?N=4294967206&refchannel=c042fd03ab30a110VgnVCM1000002118140aRCRD)

7. Make up and solve an Euler crossword puzzle. (Use an online puzzle maker: http://puzzlemaker.discoveryeducation.com/)