I came across a lovely way of folding stars. It was in a youtube video by someone named Tobias.

As lovely as these stars are, what really caught my attention was the way Tobias showed how to use paper folding to make a pentagon from a square. This square-to-pentagon transformation was in a separate video, and since it will take me about two days to forget everything I saw in the video I drew out the directions.

How to fold a Pentagon from a Square

How to fold a Pentagon from a Square. For the Video of this that Tobias made, go to https://www.youtube.com/watch?v=4kJmJUQVbO0

 

After the novelty (but not the thrill) wore off of making a pentagon from a square I began to look at the angles that I was making and figured that I could make the star with less steps (and perhaps with more accuracy) if I just started out with the net of the shape, so I made this map of the paper star’s fold lines:

Lines for a Folded Paper Star

Lines for a Folded Paper Star

If you make Tobias’s stars, after you get the hang of which lines fold in which direction, I highly recommend printing out lines above, score the lines with an inkless ink pen, and make that same star using just its essential folds.

The back of the paper sta

The back of the paper star

The photo above shows the backside of these stars. Quite a nice backside!

I’m sure that there are all sorts of things to do with pentagons, but something I want to mention is something that is fast and impressive, sort of the pentagon version of snowflake cuts. If you cut off an angled slice at the bottom of the folded up pentagon (step 12 in my tutorial drawing) there are all sorts of star possibilities.

36-54-90 triangles, with cutting lines on their tips

36-54-90 triangles, with cutting lines on their tips

These little beauties turn into:

Stars in Pentagons

Stars in Pentagons

The stars inscribed into these pentagons were made by cutting through all layers on the tips of the folded shapes.

 

And look, below there’s something extra for my friends who teach Geometry, and who might like a holiday themed angle activity. Part of the working out the folding pattern for the star was deciphering certain angles.

Find the Angles with degrees of 90, 45, and ~72, 18, 36, 54, and 108

Find the Angles with degrees of 90, 45, and ~72, 18, 23, 36, 54, 63 and 108

I had a good bit of help with the especially tricky parts of understanding the angle relationships. I’m sharing two twitter threads here, just because it was such a pleasure to get help from my friends.

and

That’s about it for now. Oh, and if you need to directions on how to fold a square from a rectangle, take a look at https://bookzoompa.wordpress.com/2014/12/10/paper-folding-squares-and-equilateral-triangles/


 

To be two cubes

To be two cubes

I wanted to transfer this image to a big piece of paper. Way too big for my printer. It’s just under 24 square inches.

One the way to being two cubes

One the way to being two cubes

I made the pattern with the intention that it would fold into two cubes. BTW, I recently learned that the correct term to use here is net:” A pattern that you can cut and fold to make a model of a solid shape. This is a net of a cube.” (quoteth from the internet)

While I was scheming how to break the net into prints that I could piece back together, it occurred to me to just overlap the artboards in Illustrator. Set them up to be negative one inches apart. Here’s a snip of what the Illustrator workspace looked:

Six overlapping artboards in the Adobe Illustrator workspace

Six overlapping artboards in the Adobe Illustrator workspace

All I did, after setting up the six artboards was to overlay my net onto the artboards. No figuring, no scheming, just laid it right on top. Honestly I didn’t know what would happen. Would the overlapped parts not print? Just didn’t know.

Amazing. Everything printed everywhere. What I mean is that the parts of the image that were on the overlap printed on both papers. This made it really easy to piece together. Of course the best use of this technology is to print Happy Birthday banners. But what I did was piece them together, cover the back of the paper with blue crayon, and, using a ballpoint pen, trace over the lines to transfer to my larger paper.

net of the Cubes, cut out

I didn’t take any more photos of the process, but here’s my fully cut out net.

On the way to cubeness

The blue crayon showed up just enough, but what was really great is that the force of the tracing created score lines, making this easy to fold.

Weighted by a train

Weighted by a train

Here’s the cube. Hard to imagine how that image becomes these two two-inch cubes. So I made a video:

 

Paper-quilting sqaure

Paper-quilting sqaure

Yesterday was paper-quilt square day with second graders. This is the central graphic of the Western Expansion project that this group started last week.

Although this project is designed to align with this class’s curriculum, I have to say, this quilting part has great possibilities for as a summer project.

Templates and samples

Templates and sample

Although I’ve been playing around with rhombuses in squares (along with my friend Malke)I hadn’t yet mixed rhombi and squares together within the same square. This may sound like a small detail, but it creates the possibility to make many new decisions. What I provided was some samples to hint at the wide range of  choices students could make, colorful papers that had squares and rhombuses on them ready to cut, and a kind of complex looking white template.

 

I tried to get these second graders to see the rhombuses as well as the squares and the triangles in this map of shapes. I wasn’t sure if they’d get it. Maybe second grade is too young to be able to make sense out of all these lines?

Ha! Some students struggled more than others, but they absolutely were able to make sense of this, and make some great designs. 

Some students added their own graphics to the papers that I gave them.

Quilting square, journal and compass rose

Quilting square, journal and compass rose

Some students created miniature designs for the covers of the journals that they made during a previous class.

Starting the quilting square

Starting the quilting square

Here’s a nice sequence, showing the first steps of one student’s work…..

Paper Quilting square nearing completion

Paper Quilting square nearing completion

…and here it is, nearly done. For the most part students used cut-paper as their medium, but finishing off some of the small spaces with marker was a great way of working.

 

The students in the classroom went wild over the piece in the above photo. . The young man who created it had a long explanation for the choices he made, and his classmates were riveted by his reasoning.

Paper-Quilting square in book

Paper-Quilting square in book

Students needed only about forty minutes to design and assemble their squares.

We finished off this project by making the crisscross which held their journal in place (I gave very little direction on how to do this: mostly I just said, “can you figure this out?’ to which to replied yes or no, but in either case they did figure it out themselves. I just helped them make a knot in the back that kept the yarn from being saggy)

Then students glued on their title, added in the writing they had already created, and most of them drew a covered wagon on the front, which I had done with my sample, but I hadn’t anticipated that they would want to do as well. Without further explanations, here are some more close ups of the rest of this really engaging project.

 

 

 

 

And, last photo, here’s what the paper table looked like when we were done.

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