Mar 9 2018

Exploration into Knitting

This winter I learned how to knit. I mean, I dabbled in making stitches a couple times over the past year, but this winter I finally made a real project. Each of my girls wanted short scarves. For the first two I just knit stitched over and over. For the third (pictured), I tried a stockinette style, which is alternating lines of stitch and purl (These are the only two stitches I currently know).


Anaya Scarf

During this process, I realized that rather always knitting from right to left and flipping the piece, I prefer to keep the ‘front’ of the piece always facing me and simply knit right-handed one line and left-handed the next.
After posting my little scarf on facebook, someone suggested I make a Catniss cowl (from Hunger Games) for Tiffany. That felt like too much of a leap for my abilities, but I wanted to make something for Tiffany and push myself another step. I decided on a birthday themed scarf. I needed two new skills for this. I still only needed to knit and purl as far as stitches go, but I needed to figure out how different combinations of those made different patterns. I also learned how to cable stitch, which is changing the order of the stitches on a line.

Tiffany Birthday Scarf
(click for larger)

Since Tiffany turns 35 today, I made a scarf with 35 stitches across. Also, beside some padding on each end, every row of the scarf represents two months of Tiffany’s life. So, six lines represents a year. The edges of the scarf mark out each year. The cables in the middle each represent a person in Tiffany’s family.
Aside: I should mention here that this is very simplified and stylized. Tiffany has a much bigger family and plenty of friends who are essentially family. You’ll have to cut me a little slack on that part.
The cables come in three widths (well, I guess four). One strand wide represent infants; two strands represents children (including adolescents); and three strands represent adults (four strands represent a pregnant woman).
The scarf starts at Tiffany’s birth with her mom, dad, and big sister. Six years later a new strand appears for her little brother. Several years down the line the older sister moves out. A few more years and Tiffany moves to college. Because Tiffany is the central agent in the scarf, this is seen as parents and brother moving out of the picture. I enter the picture and a few years later more strands enter the picture until the width of the scarf is well-stuffed with people.

Happy Birthday, Tiffany


Mar 18 2017

Subverting Solipsism

Watching TV several weeks ago, I happened to see AT&T’s ‘Everywhere’ commercial. It features a guy glued to his phone screen (figuratively) as he walks through his city. As he swipes through various shows, the people around him change to match what he’s watching. I would have written off this commercial as another hyperconsumerism attempt to valorize solipsism (or perhaps egocentrism) (“Entertainment your way” goes the tagline) except for one small scene.
Watch the ad and see if you spot it as well.

All the action/references is/are cued off the main character except one. Briefly at 0:25, our view shifts to another screen, a family watching Sesame Street. The jarring part for me was the choice of audio to reference: “Who are the people in your neighborhood?.”

Now, Slashfilm1 and Adweek both wrote articles about the ad and specifically mention the Big Bird scene, but only as another example of the exciting range of references. I couldn’t find any article who read the commercial the way I did, so I decided to write this one.

From Adweek:

“We wanted to use shows and movies across the entertainment spectrum, from modern to classic, to really give the viewer the sense that everything is at your fingertips,” says BBDO New York executive creative director Steven Fogel. “At the same time, it was important that the music be very recognizable and iconic, and that each piece work well as a part of the music track.”

The commercial could have used any of dozens of memorable Sesame Street songs, but it chose those words and used the most distinct visual cut to someone else’s real-world perspective. To me that was jarring. Here’s a brief scene within a story that says everyone around you is just scenery for your choices, and it asks you to think about your neighbors. I don’t think it was the express intent of the ad and ad writers as a whole, but I have to believe that someone was trying to cleverly subvert the solipsistic overtones of the commercial.

Who are the people in your neighborhood?

I much prefer the way AT&T handles the intertextual2 references in their “Quotes” and “Quotes 2” ads. They are still trying to sell the same product/service, but they center human interaction and media as a shared experience.

Footnotes:
1. Slashfilm features this ironic opener before gushing over the ad’s use of so many references.
“Not many people pay attention to commercials on TV anymore, mostly because we’re either streaming content with limited to no commercials, or we’re just watching stuff on our DVR that just allows us to fast forward through them.”
I consider it ironic because of the self-absorbtion of the main character who has ‘everything at [his] fingertips.’

2. For a thoughtful consideration of cheap versus rich references: check out this video. And for an example of what I estimate as a pretty cheap use of intertextuality, see this. After seeing this, I partially wondered if an algorithm wrote the screenplay after crawling the internet for positive media responses.


Oct 20 2016

Layered Stencil Portrait How-to

stencil-4

I thought I’d put together a quick how-to of my other big project this summer: Spray painted portraits.

I start with a photograph. I want it to have good lighting, natural, solid, but not overwhelming contrast, and some interesting feature. Sometimes the face is interesting enough.

In a photo-editing program called GIMP, I cut out the background and desaturated the image. Then I made four or five versions of the picture with varying brightness and contrast. Then I reduced the number of distinct colors (Image –> Mode –> Indexed) to 4. For my portraits this became the white, light, dark, and black colors. If attempting a different finished look, one might toy around with other approaches. This approach gave the right amount of detail for the look I wanted.

Once I got the look I wanted, I got the layers ready to print. For this I made 4 copies of the image and re-colored them for stenciling. For each layer the featured color was re-colored dark grey and any color darker than that was colored light grey. The colors lighter than the featured color for that layer were removed.(In the video I switched and made the featured color lighter and the others darker). I have also made all the colors the same and removed one shade at a time. The video below shows a quick and sloppy version of the steps above. It was for illustrating the process; I take more care when making a real stencil.

Then, for a multi-piece set (since I was putting 6 pictures on the wall together), I moved the layers into Powerpoint to lay each face on top of the other to resize them to look uniform.

I then added my signature initials, which functioned as a position marker (something that would be the same on each layer to help align them.

I then used the poster printing program Rasterbator to turn the pictures into multi-page pdfs, which were then printed, cut, and carefully taped together to give the right sized image for stenciling.

stencil-2

Next I traced each image to remove any islands and make it a true stencil. I then taped each onto a posterboard and cut them out with an exacto knife. If I encountered placed that really needed to be islands, then I would cut the shape out of painters’ tape and place that on the canvas (see Olivia’s portrait in the video).

Jake Stencil

Once the real stencils were made I laid the light one first on the canvas, weighted it down so the paint wouldn’t sneak under the edges, and sprayed the first color. Always test your paint to make sure it sprays smooth. I then peeled off the stencil, let the paint dry and then lined up the next color. Same process as the first for the second and third.

And that was it.

stencil-3


Sep 12 2016

World Map

world map

First Coat Complete


One big project I (with the help of many others) finished up the summer with (that I’m still putting ‘final’ touches on) is an approximately 20′ by 36′ geo-political map of the world. When Tiffany talked to me about the idea, I thought it was great. Our school hosts students and families from all over the world. The concept of a huge map to play on and talk about seemed like a great fit.

For me, it seemed like an issue of respect. In our political climate, the map to me seemed like an act of hospitality. Shorewood is glad to be an international community. That being said, representation and quality were very important to me.

 

world-stencil

Stencil

In terms of quality, I wanted each country’s painting to express care. I wanted it to look good from a distance, when taking the whole map in at once, and up close, when investigating a single country.

A political map has plenty of issues of representation to deal with. The stencil we used projected the globe in a way that I think is good quality but it neglected many of the island nations. This is understandable given the style of the stencil; but given the scale of the map, I thought we could do better. I tried as well as I could to represent all the landmasses size would allow. Islanders are important to our community too.

world-dots

The Dotted Line

The stencil was also a bit outdated, so some newer sovereign states had to be added by hand. Also, plenty of political borders around the world are disputed. Therefore, every map is a political statement. I tried to deal with this as respectfully as I knew how.

Perhaps a borderless map would have been more ideal(istic), but internationality is an important aspect of the school.

world-lines

Country Outlines

Overall, I’m pleased with the project (Except I noticed yesterday that Jordan looks wonky). I still have some touchups to work on, but it is useably complete.

It has been very fulfilling to see how many families have walked over the map, talking about various places.

Thanks, SHES PTO, for making the project happen. Thanks to all who helped paint as well.

Nearly Finished, in Panorama


Aug 9 2016

Zombie Run (17 minute puzzle)

[zombies courtesy of competitor.com via Deadtoorights.blogspot.com]

 

I am always sometimes trying to find activities for all four kids to participate in together, with their varied abilities.

There is an old transport puzzle that I caught a video about a while back sometimes called the Bridge and Torch Puzzle. It is usually a mental puzzle, but given the four characters in it, I thought we could act it out.

I showed the kids the first part (up to 2:00) of the animated video below to explain the premise and rules of the activity.

Then we biked to a walking/biking bridge not too far from our house.

Screen Shot 2016-06-03 at 8.29.57 AM

Then, because my kids wouldn’t take 1,2,5, and 10 minutes, respectively, to cross the bridge, I timed each one running across. To get a better sense of your runners’ speeds, you might want them to run a round trip and cut the times in half (to account for transitions). This activity is best if your 4 runners have clearly different running abilities (our 3, 5, 7, and 8 year old crew was great for this).

To calculate the goal time: add the fastest and slowest times and then add 3 times the second fastest (these are one-direction times). You might give a little bit of wiggle room time, but not so much that a different (less-than optimal) running arrangement would succeed.

Their first try was a very common wrong attempt, but then we talked through where they could make up time. The second attempt was a better arrangement and saved them more time.

Watch the 2nd half (after 2:00) of the animated video for the solution, if you want.

Here are our runs:

First Attempt:

Second Attempt:


Feb 16 2016

Reading Nook Book Art

Book Collage

Inspiration

With Tiffany working full-time I decided to move her desk upstairs and transform that space into a reading nook. Surfing the web for reading related art projects, I found this amazing piece by Ekaterina Panikanova.

Considerations

I can’t draw or paint nearly at the level I would want for this project, so I needed a printable workaround. I also did not want to have to deal with the weight of real books hanging on the wall. With those things in mind I did the following:

Digital Process

Scans

I went to a couple campus libraries and perused the shelves for what I considered interesting books to function as the background to the picture. Had I not rushed from idea to creation, I might have given more thought and care to the book selection, but I wanted to make it sooner than later.

I used a flatbed scanner at my university on a higher quality, color setting. You don’t want to use black & white, as much of the real book detail/texture is lost. I scanned quite a few more than actually got used. Again I might have better selected out of my scans but I was antsy to make it. (I am also a PhD student)

Focal picture

I suppose the image could have been of anything, but I liked the idea of the picture in the reading nook being of them reading. I got the younger girls out of their skeleton costumes, tied Aly’s hair back, and posed them with books they actually like to read. They were actually really great about the photo shoot. I took several different poses but felt like the final selection fit the shape of the space the best.

DSC_2324 DSC_2331 2 DSC_2319 2

You can view the video for more explanation of the digital processing after the scans and focal picture are completed. I apologize that its quality is terrible; my computer was not interested in cooperating. (you could probably watch in 1.5x or 2x speed)

 

Since I’m a really high-end graphic designer/photographer (/sarcasm), I did all my editing in PowerPoint. I removed the background, adjusting as needed. Then I went with a sepia color system (for the background books as well), increasing the brightness quite a bit on the photo. Of course, you are welcome to adjust the colors to your tastes as well.

I then imported scans pages, resizing and laying them over the picture. I wanted a more gestalt feel to mine (more empty spaces) compared to Ekaterina’s (though I wanted the kids’ faces to be mostly clear). The sizing of the page scans is an important part. I needed my horizontal distance to total very close to 50 inches. I also wanted each of my scans to print on an 8.5 x 11 sheet of paper. This constrained the layout of the books. One could make bigger books but this would complicate the resize.

Once the books were appropriately sized, I brought the focal picture in front of the books and gave it a 50% transparency. I then calculated the scaling factor from the largest book page to the printable size to prepare print-ready pages. [This section is clearer while viewing the video, I think]

To make print-ready pages, I duplicated the slide and removed all but one of the book pages. I then cropped the focal image to the edges of the remaining book. I then grouped the images and resized, using the factor I had previously calculated. I then repeated that process for the remaining 11 books.

Physical Process

Print pages

I printed in color, using a decent but not fantastic printer at the university (certainly not photo quality). I had to export as a pdf, if I remember correctly, so that the transparency would be recognized and print properly. So, before printing, make sure your prints are rendering the transparency (if you want it; I personally prefer it).

Cardboard “Cover”

DSC_2467

For the book’s cover, I laid each print on some roughly 1/8 inch corrugated cardboard and cut around, leaving a hardback book-sized margin.

 

Extra pages

DSC_2469

To give the piece a more authentic feel I added additional pages behind the prints. This helped bulk out the ‘book’ and give it some curvature. I did this by laying the prints on a phonebook and cutting around them several layers deep with a utility knife. I then gave them all a soft fold together (the scans I had gave the illusion of a fold some already).

 

Assemblage

DSC_2466

With all the pages stacked together I ran a short bead of hot glue along the edge and then flattened the glue into the pages, so they would stick together without the glue showing. I just repeated this as much as needed to get all the pieces to stick together. I then glued it to the cardboard, trying to flex the pages a bit to give it a more book-like shape.

Lastly, I laid them out, and then starting at one side, leveling, I nailed each into position, minding the alignment of the images and the needed gaps.

DSC_2396


Jan 18 2016

Customized Chinese Checkers

 

cc-board full close

This project was a pretty quick one. Since we have six people in our household, I wanted to personalize a six-person game. The first to pop into my head was the classic Chinese checkers. I had originally planned to have each of us make marbles out of polymer clay colored to each one’s liking. Maybe we’ll do that another time. We went with our pictures instead this time.

The Pieces

cc-family

First we bought some glass pebbles from the dollar store (the consistency of size and the clarity weren’t great, but the price was). Using powerpoint, I circularly cropped headshots of each of us, sized them to be a bit smaller than the cross section of the pebble, and printed them. I could have gone smaller; the pebble magnifies and the smaller version may look better. If I would have reduced the photo size I might have made a colored ring around the picture to make it stand out. I’m sure a photo-quality printer would have been nice too.

From there I just glued the pictures I had cut out onto the pebbles with white glue.

Especially because we have two girls who look very similar and, at a glance, it wasn’t so easy to recognize the images, I wrapped each with a small rubber hair tie of a favored color. I used a little smear of glue on them as well.

And that was it for the “marbles;” some tedious (60 total pebles) cutting and gluing and such but nothing challenging.

cc-allbeads

The Board

I used this template to make the board. I made the diameter of the circle match the size of the larger pebbles. I used powerpoint and simply created a circle the right size and then resized the template to match. I also cropped the image to just one point of the star.

I then taped it on my cardboard and made shallow cuts with a utility knife for all the circles. I moved the template, overlapping one row to make the next star point. And again for all six points.

cc-finishblank

 

I peeled the top and corrugation layers from the cut circles. I then lined out a hexagon for the top of the board. My top cardboard piece was pretty flimsy, so I glued it to a slightly larger circle, making the corrugation of the layers perpendicular.

And it was done.

We tried to play a six player game with it, but the 2 year old wasn’t interested for too long and eventually siphoned off the five year old and later then six year old. Maybe in a couple more years.


Jan 10 2016

Chess Board Snake Cube

Idea

I had made some puzzles that were predesigned, that is, someone else had already made the arrangement, but with a bit of personal flair. For example, a soma cube with Rubik’s coloring and the modular origami bedlam cube. After making a pentomino chess board and a 3x3x3 snake cube out of paper pulp, I was looking for another puzzle to build. (Here are some other projects I’ve made)

 

rubik colored soma cubemodular origami bedlam cubepentomino chess boardpaper pulp snake cube 3x3x3

I thought about the 4x4x4 snake cube and quickly realized that the 64 cubelets could potentially also make an 8×8 square.

I searched online for anyone who had done it. Finding no one, I set my mind to finding a way or finding that it was impossible.

*****************************************************************************
How could I figure out a snake arrangement that could form a square and a cube?
*****************************************************************************

Huge Possibilities

Calculating the number of different snakes from 64 cubelets was easy enough. There are 3 kinds of cubelets: the ends, the straights, and the turns. There are 2 ends and then each of the 62 remaining could be straight or turn, giving 2^62 (or 4,611,686,018,427,387,904, over four quintillion) different 64-cubelet snakes. Of course most of them wouldn’t make a square or a cube, let alone both. With some research I found that a 4x4x4 had  27,747,833,510,015,886 possible Hamiltonian paths. This counts rotations and reflections as unique, which was not of concern to me, so I was only looking at about one quadrillion possibilities. As for squares, I only had to look through  3,023,313,284 (really only about 378 million discounting rotations and reflections). Once I discovered these numbers, I knew a few things.

I was going to need to write a computer program (and I’m no programmer). I should start with finding paths on the square (it’s the smallest big number). If there wasn’t any overlapping solution, it would be incredible (maybe there’d be an article to write on that).

As with most work, the write-up makes things sound a lot smoother and more orderly than they really were. There was massive wasted effort exploration coming to the conclusions I did. It required a lot of learning split up over a long time (I’m getting a PhD in education policy, not snake cubes).

missing puzzle pieceIt ended up being possible to find a snake arrangement that produced a cube & square. However, in my pursuit to built the first one I found I left unfinished another aspect of the search I would love to figure out: how many solutions are there? I would love to have a complete map of all the snakes that solve both ways and all the different ways each snake solves. It is possible that one snake arrangement might have, for example, four cube solutions (ignoring rotation/reflection) and ten square solutions while another snake has unique solutions for both. Of course, with the carving out I’ll discuss later, another layer of matching is introduced that would make multiple solutions unlikely. But for snake cubes themselves it would be interesting to list the snakes by solutions spaces.

I would also be interested to see what percentage of hamiltonian paths for the 8×8 and 4x4x4 make it onto the list. Based on my work so far, I’d say it’s a small percent.

8×8 Hamiltonian Path Creation

So I wanted to find hamiltonian paths for the square. But with billions to work with, how was I to search all paths without missing, repeating, or wasting time?

Here’s a video of the algorithm that I finally landed on for finding hamiltonian paths on the 8×8: (I’m kind of a slow talker, so you might want to watch at 1.5 or 2x)

Basically it adds a square at a time by
Finding the neighbors of the end of the path
removing any options that obviously don’t work
and stepping back when no options exist.
It is a depth-first search, trying to find the longest path before moving to the next.

You can also watch this video for a walkthrough of my code.

Snake Creation

The algorithm made the snakes alongside the square paths. Sometimes different paths used the same snakes.

Cube Checking

After finding a bunch of paths on the 8×8, I needed to see if any of the snakes formed by those paths could also make 4x4x4 cubes. I suppose I could have made the program run each 8×8 as it came along but I didn’t, perhaps the batching saved some computation because I removed repeated snakes (those with different paths but same snake configuration).

Basically it functions much like the 8×8 builder but selects the options based on the cubelet type. It starts with the first snake and the first position. It tries all the options, tracking any full paths produced. Then it proceeds to the next position and so on. Then proceeds to the next snake.

Finding the One

After making a whole bunch of 8×8 paths, I grabbed a few and eventually found a snake that fit the criteria. I double checked it to make sure it worked. Below is one solution in each form (I’m not sure if there are others for this particular snake)

Snake: 3, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 3

8x8 solutioncube solution

Chess Board

It is very common for snake cubes to utilize a checkered pattern. Here I had a snake cube that could form a chess board in its 8×8 form. I thought it would be especially awesome if in its cube form all the chess pieces would fit inside. For this to be worth it to me, I needed the pieces to be appropriately sized relative the board squares and I needed all the faces showing on the cubelets in both forms to be smooth.

Eventually I came up with an arrangement that seems to work. I learned 123D Design so I could construct a virtual prototype and I’m now working on a physical one. After a rough draft I may have to produce a high-quality one.

Snake cube

Snake Cube Chess Board Snake Cube

This relatively simple idea became a consuming project that led me into learning from several fields.

 

Here’s my code

Here’s my design


Jan 4 2016

DIY Find the Differences with Bitstrips

Bitstrips Find the Differences

Ada, who just turned 5, wanted me to make some ‘Find the Differences’ puzzles for her. I decided that Bitstrips would be a great fit for this project.
It’s pretty easy to do.

1. Sign-up for bitstrips and log-in.

2. Create some characters.

family bitstrips

This is pretty straight forward. Here is one basic tutorial. My kids love making all kinds of characters, but I thought having their characters in the image would be more interest keeping.

3. Create ‘Find the Differences’ puzzles

Find the Differences

Create a two panel comic.
Design the first panel using a lot of adjustable objects.
Use the duplicate panel button
Make alterations in the second panel. (You may or may not want to keep track of the changes)
If the want to reuse a comic, you can remix after you save.
It’s that easy.

Here is a basic tutorial video.

We’ve also used Bitstrips to make bookmarks, coloring pages and writing prompts, and seating markers.

seat markers

table settings

arrangements counter


Mar 6 2015

Happy Birthday

Happy Birthday
 
You know I love a surprise party, especially if it’s themed. This year, playing off 32, which is how old Tiffany is turning, I went with a 2^5 theme. In this context that means packing in 5 “party of two” dates in one day.

Thank you to all the people who took care of the kids so we could get out so long.

Date one:
Lunch at Nitty Gritty (the Official Birthday Place)
and a game at I’m Board!

Date two:
Swing by Sonic on the way to Fired Up Pottery

Date three: Strolling to Picnic Point and out onto Lake Mendota for the sunset

Date four: Madison Museum of Contemporary Art

Date five: Dinner downtown and home with no kids

I love you Tiffany


Feb 14 2015

Happy Valentine’s Day

To Tiffany. I love you (nerdily).
Happy V-day

Feel free to copy the following into the wonderful Desmos Calculator:

$\left(\frac{2\sqrt{2}\cos \left(t\right)}{\sin ^2\left(t\right)+1},\frac{2\sqrt{2}\cos \left(t\right)\sin \left(t\right)}{\sin ^2\left(t\right)+1}+1\right)$

$\left(\frac{3}{2}\cos \left(\frac{7}{4}t\right)\cos t,\frac{3}{2}\cos \left(\frac{7}{4}t\right)\sin t-\frac{5}{4}\right)$

$\left(4\sin \left(t\right)^3,3\cos \left(t\right)-\cos \left(2t\right)-\frac{\cos \left(3t\right)}{2}-\frac{\cos \left(4t\right)}{6}\right)$

Domain: (0, 50) is sufficient.


Aug 12 2014

Cardboard Bookshelf

Shelf models
The planets aligned a couple weeks back. My wife was out of town for a couple days, which meant lonely evenings and less concern for tidiness: a great combination for a large craft project. This coincided with move-in/out weekend at my apartment complex, which equated to substantial amounts of cardboard in the recycling bin, which I gladly rescued.
We have been needing a solution for the toys that find themselves downstairs. Upstairs we still use the Tetris shelves I made a couple houses ago. They are still holding up.
I’ve been on a bit of a cardboard kick lately [see some previous posts].
I figured the cubbie-hole style would allow the cardboard to hold more weight than trying long shelves. The holes needed to hold toys so I made them 14-inch cubes (theoretically; more on that below). I estimated that 4 corrugations thick would be about 5/8 inches and would be sufficiently strong. You can see from the sketch the form of the six internal interlocking pieces and the four external pieces.
Shelf sketch
I wanted to alternate the locking because I thought it would be sturdier, but I didn’t anticipate how difficult (but clearly not impossible) piecing together would be.
Most of my pieces ended up a bit fatter than 5/8 because I found most the large boxes used doubled corrugation. Therefore I ran the doubles on the outside with matching direction and used a single in the middle with opposite corrugation direction. I think the design would hold the pieces together with no glue, but gluing makes cutting much easier. I used hot glue, but I wouldn’t recommend it. Some white or wood glue would be better, I think, but I didn’t have it on hand (plus, it dries more slowly). To keep the shelves square I needed to fix in two bracing pieces 14×14 inches with 5/8×2 inch tabs, as shown in sketch. I ended up just finding some very stiff cardboard and going with a single layer (same for the front pieces (though the front is not so stiff)). The back pieces I glued in. I added some glue to the external boards as well. I think longer connectors would have helped and could be trimmer later if need be.
Finished Unfilled Shelves

back brace connectionback brace

end connectioncorner connection

alternating interlocking boards
The personalized covers were fun but can be a bit tricky to put on. I wanted covers so the kids could have some autonomy in storing their junk (they collect a lot of junk) without Tiffany and I needing to look at it. Because my boards were thicker than 5/8, I cut the front squares 13 7/8 so they would fit better and notched the boards ¼. The big kids chose their fonts from a list of stencil fonts and told me the color they desired (I had to mix the Princess Else-inspired light blue).
Finished Fill with covers
Plus, if you happen to have six covers, you can show how two consecutive triangular numbers add to a square number.


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