Expanding Paper Fidgit Toy




About: I have taught math for 30 plus years. I am one of the crazy ones who actually think math is fun. I am still adapting to the loss of my husband of 18 years. He was the love of my life. I am returning to t...

This is simply made from paper. No glue, no tape, required. In fact you only need paper and scissors.

Ok. To be honest you need a bit of patience too.

I kept one of these on my desk for years. Students played with it almost daily. Occasionally a piece or 3 fall off--but they go right back on--no harm done. I have printed the pattern pieces many times and most of my high school students who tried were able to build one.

The simplicity of the design--all the pieces are exactly the same size and shape--is intriguing to me. The complexity of the finished toy--it bends, stacks, flattens, and rolls--fascinates kids.


Step 1: Print and Cut

I recommend printing on cardstock. It is thick enough to be durable but thin enough to cut easily. You can use anything that is a bit thicker than copy paper--cover stock, thin plastic sheets, etc.

I like the 2 color effect. That is a personal choice--use as many or as few colors as you like.

The software I used to draw the pieces insisted on my using wide margins. I like to cut out a piece and then trace it so I can get extra pieces from each sheet of paper. My sample was made from 2 sheets of paper.

First you cut the ovals.

The slits are a bit of work. You have to cut twice for each slit marked on the piece. You should cut just to the left of the mark and then just to the right of the mark (or right then left, doesn't matter but cut twice). If you do it right, there will be a tiny sliver of paper that kind of curls a bit. This sliver can just be pinched off.

It is important that you have these small gaps because they allow the paper to move a bit. If you make these gaps too wide, the pieces will still go together but they will slide apart more easily.

When you cut the slits, try to cut all the way to the end of the mark in one smooth motion. If there are tiny nicks in the slit (caused by stopping and restarting your cut), the other pieces will have something to catch on--not good.

Step 2: Assembly of Your Sliceform

This take a little patience to assemble. Take your time. All the green pieces will be parallel to each other with the slits opening down. All the white pieces will be parallel to each other with the slits opening up. The picture shows how to off set the pieces.

There are a lot of sliceforms if you look on line. The name is derived from the fact that the structure is created from a variety of different slices of the object. Some shapes are made from multiple different shapes. I encouraged my students to examine different objects from multiple different angles in order to understand the geometry. Math is fun!!!!

If you want me to post more sliceforms--let me know in the comments section below.



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    8 Discussions


    2 years ago

    Hey that's pretty cool. I'm gonna have to sit down and make one of those if I find myself bored with an hour or two of spare time. I voted for ya, hope you win the contest.

    3 replies

    Reply 2 years ago

    Hey, if you win, You should totally use that paper cutting machine to make one of these that is extremely long to celebrate. I've always wanted one myself. Put it to good use. Maybe make it a rainbow one out of a bunch of different colored paper =P


    Reply 2 years ago

    I will get on it as soon as possible. It may take a day or 2--something is wrong with my Microsoft word. When I save as puff it keeps coming out blank. Are word documents ok for you?


    Reply 2 years ago

    I will try that but in the meantime I tried typing 'sliceform' in the lets make box at the top of the page. There is an egg, a torus (doughnut), and a few other things if you haven't already seen them.