Koch Snowflake cards

Like most self respecting nerds, I love fractals. So what better way to celebrate winter than creating a fun card based on the famous Koch Snowflake (also know as the Koch star and island)!

A fractal is a geometric figure that has some pretty awesome special features. They have "self symmetry," creating detailed repeating patterns that are often described as "the same from near as from far." They're found all over the place in nature and are used in math and science in a variety of applications. 

One of the easiest to create by hand, and also one of the easiest to understand, is the Koch Snowflake. First described by Helge von Koch in 1904, this fractal is based on an equilateral triangle. To build it one, you create an equilateral triangle, then remove 1/3 of one side of the triangle and replace it with an new, smaller equilateral triangle. You repeat this process on each side, then repeat it on each side of each new triangle, and so on. The result is a shape that can literally have infinite perimeter, but finite area. Cool right?

So, for an extra nerdy card, I used the Koch Snowflake shape and created a fun, glittery pop up.

The process is simply to make a Koch snowflake template, trace that into a card and cut around the shape with a craft knife, leaving the shape attached to the base at a few points. Then fold the pop up in the opposite direction of the card, creasing the contact points carefully. Finish by backing with contrasting cardstock to create the front of your 4.24" x 5.5" card.

To make it more festive, I created snowflake "covers" that were just the Koch snowflake. These I embossed and glittered to make them stand out beautifully. I also used the inside of the double snowflake to create a custom stamp, simply tracing it onto craft foam and cutting it out, then adhering it to an acrylic block with some double-stick tape. I used it as I would any other stamp. This card reads "Baby, it's cold outside."

Now, I'll have really detailed instructions up on CRAFT soon, I hope, but in the mean time, why not just grab my templates and make a card the easy way?

Print the PDFs below onto cardstock and cut until your heart's content!

• Single Koch snowflake pop up card
• Single snowflake cover
• Double Koch snowflake pop up card
• Double snowflake cover

If you have a digital cutter, like I do, this all becomes very easy, indeed! I have an old first generation Silhouette from Quickutz. You can pick them up for about $100 on eBay, and they are amazingly useful. I use the free software Inkscape to design my digital cutting files and then the free software for the Silhouette to manipulate and cut the shapes. It's totally awesome!

Anyway, if you have such a machine, all you need to do is download the appropriate DXF or SVG file and let your computer do the work for you! You may opt to throw in a perforation or scoring line down the center when you cut to make folding easier, but I just used my Scoring Board. Now you can make cards for all your nerdy friends!! Huzzah!

• Single Koch snowflake pop up card (dxf)
• Single snowflake cover (dxf)
• Double Koch snowflake pop up card (dxf)
• Double snowflake cover (dxf)
• Single Koch snowflake pop up card (svg)
• Single snowflake cover (svg)
• Double Koch snowflake pop up card (svg)
• Double snowflake cover (svg)

Anyway, I hope you have fun. Be sure to share pictures of your cards!

MORE fractal cards!

After I made the last fractal Christmas card, my daughter pointed out that it also looked a lot of like a pile of present. (Kids!) So I decided to play with that idea a bit.

I selected a set of coordinating scrapbook papers, and cut the inside of the card just as I did last time. For a quick review...

For this version, it's important to measure and cut accurately, so that the pieces we cut for "presents" fit well. That said, go ahead and cut a second insert from a piece of plain or scrap cardstock. We'll use this for templates. Just cut along the folds.

Then it's time to trace and cut. We'll need one large piece as the central present. Then cut three of the mid-sized present, one from each of three types of paper. Lastly, cut nine small pieces -- two each from the three different papers and three from the last.

Now, we get to play paper tetris. Ink the edges of all the the present pieces, so that they have some depth when attached. Use a bit of glue stick to attach the paper pieces onto the base. Then attached the base to the outside of the card. Ink the edges and you're nearly done.

I added some strips of paper for "ribbons" and attached the inside to the outside. Then I gave the front a bit of decoration.

Add the sentiment and I'm good to go! This got me thinking, what other fractal-based patterns can I cut and make into cards. As it turns out, I am not the only one who is obsessed with this technique. Yale offers a fun free pattern using blocks. They actually have a whole lab activity using Cantor sets to make fractal folds. There is also a book called "Fractal Cuts" by Diego Uribe, that you can buy new or used on Amazon. (Yea, I totally ordered it.) So I played with another boxy design.

Then using the same template method as above, I made another "present" card.

Fractal Christmas Card

We've been studying fractals with the Kaleidoscope Cooperative for Science and Math. As part of that study, we explored Sierpinski's Triangle, a fractal in which equilateral triangle shapes are removed according to a specific set of rules, forming a repeating pattern.

I wanted to extend the 2D version we made in class to a 3D project. Luckily, I found the Fractal Foundation and their instructions to create a triangle fractal cutout. By making repeated cuts in folded paper you can create a shape similar to a Sierpinski's triangle. And when you're done, it looks like a Christmas tree. Which makes it a most excellent holiday card!

The kids had a great time making these, but I wanted a little more refined version for my nerdier friends and family members. So I pulled out my craft supplies. For this project you need: colored cardstock, a ruler, a pencil, scissors, a glue stick, a star punch, an embossing folder and embosser, and assorted inks.

I started by cutting a piece of green cardstock to 8.5 x 5.5 inches. I folded this in half to create a 4.25 x 5.5 inch card. Using my ruler I marked the middle of the card and drew a line from the folded side to midway across.

Then I cut along the line, folded one section away from the folded edge and creased well. Then I unfolded the flap and inverted the tab, pushing the fold inwards.

Refolding the paper, and tucking the tab inside, I once again used my ruler to measure the halfway point on each of the side "steps." I drew a line halfway across the step. Then it was cut, fold, invert.

 I repeated the cycle once more. After this point the paper was too thick to fold and cut neatly. I you used copy or origami paper you might be able to get more detail.

Once all the tabs were done, I used the edge of my ruler to crease them really well. Then I un-inverted the folds to flatten the paper and ran the card through an embosser. I also trimmed the paper by 1/4" all around and inked the edges. When that was done, I carefully refolded the tabs to create the pattern and sprayed the front with gold ink.

I cut a piece of red cardstock to 8.5 x 5.5 inches, folded it into a 4.5 x 5.5 inch card and embossed that as well, inking the edges when it was done.

I applied glue to the back of the triangle tree and carefully attached it to the inside of the red card, pressing down well and being sure to center the green card. I punched a little star from yellow cardstock, folded it in half and used the glue to attach it to the top of the tree. I then decorated the front of the card with some scrap green cardstock and another yellow star.

All I need to do is add a cheery sentiment and this card is ready to add a bit of geek chic to someone's Christmas.

Math Fun with Dice

I hear it a lot. "I hate math." "Math is boring." "I'm no good at math." "I just don't get it." It really doesn't have to be that way. I swear!

One of the best things about math, especially at the elementary and middle school levels is that so much can be learned through game play. Addition, subtraction, multiplication, division, negative and positive integers, exponents, currency, probability and even basic algebra can all be practiced through game play.

For this post, I'm going to focus in on dice games, because they are inexpensive, extremely portable and offer tremendous variety. That last one is really important. Any game gets boring after a while, and for kids that hate math, keeping game play fresh is vital.

One of the most popular commercially available games is aptly called "Math Dice." Using three six-sided dice and two ten-sided scoring dice, students can play a variety of games. The most popular scenario is to roll the die and figure out how to add, subtract, multiply or divide to reach a "target" number. This type of game encourages the kind of problem solving and mental math skills the students need. It can be played independently, collectively or competitively, and has been used in classrooms and for math tournaments for years. At only $6/set, Math Dice is a great addition to any game shelf. There is also a Math Dice Jr. for younger children.

There are other less well-known math games available out there as well -- 4-Way Count Down, Even Steven's Odd, Double Shutter -- just to name a few! And don't forget other games that, while not being specifically made for teaching math, do contain elements that practice important skills. For example, Yahtzee requires a great deal of number play and addition, as do the fun variants on the theme, like Flash and Yamslam.

One of my personal favorites, that you may not have played before, is call Cosmic Wimpout. "In this game that consists of five dice and nothing else, play proceeds by rolling the five Cosmic Wimpout cubes and get points for each 5, 10, or Flash (triplet) that you roll. You can accumulate points towards the Winning Total by ending your turn or risking it all, because if you roll and don't score, you lose all the points for that turn and the next player goes." It's fast-paced, challenging, exciting and tons of fun. Kids will not know they're practicing math. I keep this tube of dice in my backpack at all times. It's just that good. Farkle tends to travel with me too.

Now, say you don't want to have to buy a bunch of games. Maybe you have some dice sitting around at home, lonely and unused. Perfect! You're ready to start playing some math games!

Start with a visit to Scholastic's 4 Great Math Games. There you'll learn favorites like Pig. A player rolls two dice and mentally adds them. This player can keep on rolling and adding to their total for as long as they want. However, if they roll a 1 before they choose to stop, they're total for the round is 0. If they roll two 1's, their entire total is reduced to 0. The first player to reach 100 points wins.

Teachers will appreciate the printable instructions and score sheets at Math Salamanders. My favorite is "Spot the Calculation." In this game, a student roles three dice and makes a calculation. The other player must guess what operations they used to get that answer.

Meanwhile, Activity Village has lots of classic math games like Mountain and Mouse, many of which are perfect for young students who are still learning to identify numbers. For example, in Mountain, you make or print a drawing of the hill with the numbers 1-6 going up the side to the top and then 6-1 down the other. Students start at the bottom of the hill with a marker. The first student rolls a die, hoping for a 1, because they must roll each number in order to move up or down the mountain. If they don't roll the needed number, they can't move. This is great for kids to learn to recognize their numbers and to practice counting with the dots on the dice.

And Didax Education offers a small selection of dice games for algebraic thinking that are great for middle schoolers. You can use their samples, or make your own similar games. It's easy! Try this: Onto index cards, either copy a few simple algebraic expression from a textbook or  make your own. Mix up the cards and place them face down on the table. A student, flips the top card and rolls a die. She then substitutes the number on the die into the expression for the variable and solves. Each player rolls their die and does the same, writing down their answer. Play continues until all the expression cards are used. Players then add their solutions together. The highest number wins.

For teaching negative and positive numbers, I like this simple game. First print or create a simple number line and find a small marker that fits on it. Then find two dice, each a different color. One color represents a positive number, the other negative. The student rolls both dice and selects one to start with. They mark that number on the number line. Then using the other, they count from that spot the amount on the other die, moving in the correct direction. The place they land is the sum of the two numbers. I usually have them write out the equation then. Once they get the hang of this, I add dice, making the equations longer or swap in 10 or 12 sided die to practice with larger sums. This game is especially useful for students that don't understand how positive and negative integers work.

So I hope you have some new ideas for fun dice games to play with your favorite math student.

Making Mosaics

Last week we held a really fun Bricks4Kidz Mining and Crafting Camp at Kaleidoscope. Among the many online and hands-on activities were mosaics of popular Minecraft tools and mobs. They were really fun! And they're a great hand-eye, visual activity.

Of course, this can be done with any game, show, etc. With a little graph paper, most students can create their own mosaics of favorite characters. Not only is it creative, it develops a child's mind mathematically as they work over a plane, counting and placing colors and patterns. It's can be an especially interesting challenge to translate a 3D object to a 2D space.

We used Legos, but you don't have to stop there! Take out your melty beads and create custom suncatchers and ornaments. Or take up cross-stitching and translate your designs to fabric. Once you get the concept down, there are many directions you can go!

November Programs!

We have many exciting programs scheduled for November. Please join us!

Newton Winter Farmers' Market
Saturdays starting November 5, 10 am to 2 pm, Newton High School, 44 Ryerson Avenue, Newton, NJ! Free crafts and activities for children!

Recycled Geodesic Dome 
Monday, November 7, 3 to 5 pm
Patented by engineer and writer R. Buckminster Fuller, the geodesic dome is super efficient, fast to build and amazingly strong. When constructed, the geodesic dome uses the least possible material to create the largest possible structure, and because of the way weight is distributed, it can demonstrate amazing strength.  Use nothing more than recycled newspaper we’ll build a geodesic dome large enough to sit under! Geometry has never been this all-out cool. Hosted by Sandra Roberts. $5/person plus your own stack of newspaper (the more the better!). Ages 5-13.

Change the World
Wednesday, November 9, 1 to 4 pm
What do you want to change about the world? Civics is the study of the rights and responsibilities of citizenship. Everyone -- adult and child alike -- can and should be capable of making their voices heard by representatives at every level of government. In this civics class, the emphasis isn't on memorizing how our government works but, instead, on learning and practicing the skills needed to fully participate in our democracy.  By the end of this workshop, every student will come away with a sense that they have the power to change the world around them. Hosted by Elizabeth McCarthy. Best for ages 7-12. $25/person.

Rube Goldberg Machines

Wednesday, November 16, 1:30 to 3:30 pm

American cartoonist, Rube Goldberg, is best known for his detailed drawings of crazy contraptions that were able to complicate simple tasks. The idea has grown into a fun physics and engineering activity, with worldwide appeal and an annual college-level contest in its honor. We’ll use common household materials to create our own machines, learning about forces and simple machines as we go! Hosted by Sandra Roberts. $15/person. Bring some items to include in the machine! Ages 5-13.

Math MAGIC Land

Mondays, November 14 and 21, 3:30 to 5 pm

Based on the popular Disney Movie, Donald in Mathmagic Land, we’ll explore the ways that math is tied to music, architecture, nature, our bodies and much, much more! Students will apply math concepts through experience and hands-on projects. Depending on individual strengths, participants may choose to explore concepts through calculation as well. Hosted by Sandra Roberts. Best for ages 7 to 13. $30/person.

All programs are subject to change. Check the website at www.klcnj.com for changes. Most programs need at least five students to run. Programs may be cancelled or combined with lack of interest. We suggest registration. Full refunds will be provided if a class is cancelled. Programs in November will be held at EcoZOica Lounge, 23 Main Street, Blairstown, NJ. For more information call 908-283-0020.