Playful Math Carnival 103 at Math Misery? Blog

Check out the new carnival of playful math for all ages at Math Misery? blog. You’re sure to enjoy this month’s collection of mathy fun.

The carnival features prime numbers, self-referential logic, calculus puns, word problems, Pythagorean triples, arithmetic games, geometric coloring designs, and more.

Click here to go read the carnival blog!

Past carnivals are still full of mathy treasure. Check them out:

New Hundred Chart Game: Jigsaw Gomoku


Counting all the fractional variations, my massive blog post 30+ Things to Do with a Hundred Chart now offers nearly forty ideas for playing around with numbers from preschool to prealgebra.

Here is the newest entry:

(34) The Number Puzzle Game: Rachel created this fun cross between the hundred-chart jigsaw puzzle (#7) and Gomoku (#23). You can download the free 120-board version here or buy the complete set at Teachers Pay Teachers.

CREDITS: Photo by geishaboy500 (CC BY 2.0).

A New Graph-It Puzzle

Since I’ve been posting new Alexandria Jones stories this week (beginning here), I’ve gone back and re-read the old Christmas posts. I noticed that the original Graph-It Game included a religious design, but nothing for those who don’t celebrate Christmas.

So I updated the post with a new, non-religious puzzle. Here it is, if you want to play…

Graph-It Game Design

For this design, you will need graph paper with coordinates from −8 to +8 on both the x- and y-axis. Connect the points in each line. Stop at the periods, and then start a new line at the next point.

(-8,8) – (-8,0) – (0,8) – (-8,8) – (-4,4) – (0,4) – (0,8) – (8,8) – (4,4) – (0,8).

(8,8) – (8,0) – (4,0) – (4,-4) – (8,0) – (8,-8) – (0,-8) – (4,-4) – (0,-4) – (0,-8) – (-8,0) – (-8, -8) – (0,-8).

(-8,-8) – (4,4) – (0,4) – (4,0) – (4,4) – (8,0).

(8,-8) – (-4,4) – (-4,-4) – (0,-4) – (-4,0) – (-8,0).

(0,-2) – (0,-4) – (4,0) – (2,0) – (2,-2) – (-2,-2) – (-2,2) – (2,2) – (2,0) – (1,1) – (1,0) – (2,0) – (0,-2) – (-2,0) – (0,2) – (1,1) – (-1,1) – (-1,-1) – (1,-1) – (1,0) – (-4,0) – (0,4) – (0,-1) – (-1,0) – (0,1) – (1,0) – (0,-1) – (0,-2).

Color in your design and hang it up for the whole family to enjoy!

Now Make Your Own

Of course, the fun of the Graph-It Game is to make up your own graphing puzzle. Can you create a coordinate design for your friends to draw?

Want More?

You can see all the Alexandria Jones Christmas posts at a glance here:

CREDITS: “Love Christmas Lights” photo by Kristen Brasil via Flickr (CC BY 2.0).

The Mysterious Block Puzzle

3-way-block-puzzleFor toddler Renée’s Christmas gift, Alex and Leon crafted a puzzle set of wooden blocks.

First, they made a sturdy box with circle, square, and triangle shapes cut in the lid.

To make the blocks large and baby-safe, Alex and Leon bought a 4-foot 2×2 board. Then they asked Uncle Will to help them create a set of special blocks to fit through the holes.

Each block was round and square and triangular, so it could fit exactly through any of the three holes.

How can that be?

To Be Continued…

Read all the posts from the December 2000/January 2001 issue of my Mathematical Adventures of Alexandria Jones newsletter.

CREDITS: “Christmas Tree Closeup” photo by Zechariah Judy via Flickr (CC BY 2.0).

A Polyhedra Construction Kit

To make a Christmas gift for her brother Leon, Alex asked all her friends to save empty cereal boxes. She collected about a dozen boxes.

She cut the boxes open, which gave her several big sheets of thin cardboard.

Then she carefully traced the templates for a regular triangle, square, pentagon, and hexagon, as shown below.


Click here to download the polygon templates

She drew the dark outline of each polygon with a ballpoint pen, pressing hard to score the cardboard so the tabs would bend easily.

She cut out shapes until her fingers felt bruised: 20 each of the pentagon and hexagon, 40 each of the triangle and square.

Alex bought a bag of small rubber bands for holding the tabs together. Each rubber band can hold two tabs, forming an edge of the polyhedron. So, for instance, it takes six squares and twelve rubber bands to make a cube.

Finally, she stuffed the whole kit in a plastic zipper bag, along with the following instructions.

Polyhedra Have “Many Faces”

Poly means many, and hedron means face, so a polyhedron is a 3-D shape with many faces.

The plural of polyhedron is polyhedra, thanks to the ancient Greeks, who didn’t know that the proper way to make a plural was to use the letter s.

Each corner of a polyhedron is called a vertex, and to make it more confusing, the plural of vertex is vertices.

Regular Polyhedra

Regular polyhedra have exactly the same faces and corners all around. If one side is a square, then all the sides will be squares. And if three squares meet to make one vertex, then all the other vertices will be made of three squares, just like that first one.

There are only five possible regular polyhedra. Can you figure out why?

Here are the five regular polyhedra, also called the Platonic solids. Try to build each of them with your construction kit.

Tetrahedron: three equilateral triangles meeting at each vertex.

Hexahedron: three squares meeting at each vertex. Do you know its common name?

Octahedron: four triangles at each vertex.

Icosahedron: five triangles at each vertex.

Dodecahedron: three pentagons per vertex.

You can find pictures of these online, but it’s more challenging to build them without peeking at the finished product. Just repeat the vertex pattern at every corner until the polygons connect together to make a complete 3-D shape.

Semi-Regular Polyhedra

Semi-regular polyhedra have each face a regular polygon, although not all the same. Each corner is still the same all around. These are often called the Archimedean polyhedra.

For example, on the cuboctahedron, every vertex consists of a square-triangle-square-triangle combination.

Here are a few semi-regular polyhedra you might try to build, described by the faces in the order they meet at each corner:

Icosidodecahedron: triangle, pentagon, triangle, pentagon.

Truncated octahedron: square, hexagon, hexagon.

Truncated icosahedron: pentagon, hexagon, hexagon. Where have you seen this?

Rhombicuboctahedron: triangle, square, square, square.

Rhombicosidodecahedron: triangle, square, pentagon, square.

Now, make up some original polyhedra of your own. What will you name them?

To Be Continued…

Read all the posts from the December 2000/January 2001 issue of my Mathematical Adventures of Alexandria Jones newsletter.

CREDITS: “50/52 Weeks of Teddy – Merry Christmas” photo by Austin Kirk via Flickr (CC BY 2.0).

How to Make a Flexagon Christmas Card

tetra-tetraflexagonHere’s how Alex created tetra-tetraflexagon Christmas cards to send to her friends:

1. Buy a pack of heavy paper at the office supply store. Regular construction paper tears too easily.

2. Measure and divide the paper into fourths one direction and thirds the other way. Fold each line backward and forward a few times.

3. Number the front and back of the paper in pencil, lightly, as shown. Then carefully cut a center flap along the dotted lines.

4. Fold the paper along the dark lines as shown, so the center flap sticks out from underneath and the right-hand column shows all 2’s.

5. Fold the flap the rest of the way around to the front and fold the right-hand column under again. (Shown as dark lines on the diagram.) This makes the front of the flexagon show 1’s in every square.

6. Carefully, tape the flap to its neighbor on the folded column. Don’t let the tape stick to any but these two squares.

7. Gently erase your pencil marks.

Find All the Faces

A tetra-tetraflexagon has four faces: front, back, and two hidden. It is shaped like a tetragon — better known as a rectangle.

Here’s how to flex your tetra-tetraflexagon card:

  • Face 1 is easy to find. It’s on top when you make the card.
  • Turn the card over to find Face 2.
  • Face 3 is hidden behind Face 2. Fold your flexagon card in half (vertically) so that Face 1 disappears. Unfold Face 2 at the middle, like opening a book. Face 3 should appear like magic.
  • Face 4 is hidden behind Face 3. Fold the card (vertically) to hide Face 2, then open the middle of Face 3. Face 2 vanishes, and Face 4 is finally revealed.

When Faces 2 and 3 are folded to the back, you will notice that any pictures you drew on them will look scrambled. What happened?

Add Your Designs

Alex wrote a holiday greeting on Face 1. Then she drew Christmas pictures on the other three faces of her card.

To Be Continued…

Read all the posts from the December 2000/January 2001 issue of my Mathematical Adventures of Alexandria Jones newsletter.

CREDITS: “Happy Holidays” photo by Mike Brand via Flickr (CC BY 2.0). Video by Shaireen Selamat of