This is my third Instructable on the topic of BLOKL which I think really does the math on a math manipulative. A set of building blocks that can be played with freely or used to make math puzzles -

Affordable
Colorful
Adaptable
Big

Let's build some big blocks!

Step 1: Here's What You Need

Parts List

1. Three Inch Cube Boxes (gloss finish) - lots of places to get these but I think these are great you get 100 for about $20:
https://www.amazon.com/gp/product/B07CV8327F
If you want to get something else try it first with the washable crayons. The key to this working well is the gloss finish that makes them colorable, cleanable and "re-tape-able".

2. Hot Glue Gun - maybe you have one already? If not even the little low temperature ones will work for this.

3. Scotch® Wall-Safe Tape - CVS, Target, Amazon. This is great stuff, sticks well and comes of smooth surfaces with out tearing.

4. Crayola Ultra Clean Washable Crayons - there are other washable crayons but Crayola has the most consistent color quality in my humble opinion

Step 2: You Can Color These Blocks!

Try this out. Using the washable crayola crayons draw and color some patterns

Step 3: And They Clean Up With a Damp Paper Towel

Now dampen a paper towel and wipe off the color. It may take a couple passes and a final drying step but they clean off nicely. A 3D reusable pallet

Step 4: Let's Fold Up Some Boxes

These steps show some details in box folding.

Step 5: What Will You Create?

Now you have some boxes and it is time to build. The cubes will stack pretty well but are so light weight that they tip easily. Enter Scotch Brand Wall Tape!

I made a poodle. It can be dropped to the floor and stay in one piece. This is could also be a good way to build forms to then paper mache. A little blocky but hey - Minecraft IRL.

I removed the tape strips turning it back into single cubes and made a BLOKL version of the SOMA cube puzzle with them. The instructions for this are up next.

Step 6: The SOMA Cube Puzzle

The SOMA cube is not the only puzzle you can make there is also Pentominoes and Tetrominoes

Findout more about the SOMA Cube's history here:

Thorleif's SOMA page - https://www.fam-bundgaard.dk/SOMA/SOMA.HTM

Wikipedia - https://www.fam-bundgaard.dk/SOMA/SOMA.HTM

Step 7: Red Vee

In addition to boxes and a glue gun you will need colored stickers. Part of what makes BLOKL different from SOMA is that the pieces are color coded for easy recording and tracking of cube solutions.

I like these -

Red, Blue, Green, Yellow, Purple, Orange, Brown and Pink - 2" inch Round Sticker 192 pack
https://www.amazon.com/gp/product/B01KJ0E12I/

Red Vee -

1. Fold up three boxes
2. Hot glue them to form a "V" like the completed one shown in the pic
3. Add the red stickers

Step 8: Green EL

Greene eL -

1. Fold up four boxes
2. Hot glue them to form a "L" like the completed one shown in the pic
3. Add the green stickers

Step 9: Blue Zee

Blue Zee -

1. Fold up four boxes
2. Hot glue them to form a "Z" like the completed one shown in the pic
3. Add the blue stickers

Step 10: Caramel Tee

Caramel Tee -

1. Fold up four boxes
2. Hot glue them to form a "T" like the completed one shown in the pic
3. Add the caramel stickers

I used the name caramel for the color brown for a reason. For BLOKL to be BLOKL each piece must have a unique color that can be abbreviated by a single letter that is the first letter of piece color.

I already used "B" for blue. Caramel is fun to say and the stickers are pretty close to Pantone Caramel Cafe':
https://www.pantone.com/color-finder/18-1148-TPX

Step 11: Yellow Dexter

Yellow Dexter -

1. Fold up four boxes
2. BEFORE you hot glue them together, position them to form the right handed chiral shape like the completed one shown in the pic. It is called Dexter because that is the Latin word for "right".

To make sure it is correct -
3. Put your right hand down with your thumb sticking up next to your stack of cubes
4. Your thumb should line up with the two cubes sticking up from the table
5. You fingers should be able to curve around the the three cubes on the table top.(if you have very large hands at any rate.)

6. Add the yellow stickers

The yellow Dexter piece is an analogy of the aroma of lemon produced by the molecule limonene. Right handed is lemon and left handed is orange

Mirror Molecules - Smell the Difference
https://americanhistory.si.edu/molecule/04exp.htm

Step 12: Orange Sinister

Orange Sinister -

1. Fold up four boxes
2. BEFORE you hot glue them together, position them to form the right handed chiral shape like the completed one shown in the pic. It is called Sinister because that is the Latin word for "left". To make sure it is correct -
3. Put your left hand down with your thumb sticking up next to your stack of cubes
4. Your thumb should line up with the two cubes sticking up from the table
5. You fingers should be able to curve around the the three cubes on the table top.(if you have very large hands at any rate.)
6. Add the orange stickers

The orange Sinister piece is an analogy of the aroma of orange produced by the molecule limonene. Right handed is lemon and left handed is orange

Mirror Molecules - Smell the Difference
https://americanhistory.si.edu/molecule/04exp.htm

Step 13: Violet Crystal

Violet Crystal -

1. Fold up four boxes
2. Hot glue them to form the Crystal like the completed one shown in the pic
3. Add the violet stickers

Step 14: Solution Insights 1 - the Klein Four Group

There are 240 unique solutions to the SOMA cube puzzle. Try the one shown above, it is actually four unique very closely related solutions. By flipping and twisting the orange and yellow pieces joined together to make a "double Zee" on top of a highly symmetrical base made from the caramel, violet and blue pieces four solutions can be found. The green piece will always drop in after correctly placing the "double Zee" to form a cube.

Step 15: Solution Insights 2 - the Diamond Mine

The Diamond Mine is twelve very closely related solutions. The orange and red pieces can be arranged in three unique ways to form a little cube with a missing corner. The diamond is a cubic crystal hence the name "Diamond Mine"

That's three solutions. There are three more solutions by flipping and twisting the blue and green pair once for each of the red and orange combinations.

To get to twelve you swap the yellow and orange pieces. It won't be as symmetrical as the previous six but the yellow and red now also form a little cube with a missing corner. Same process as above for another six solutions. The "little cube with a missing corner" pattern shows up in more solutions as well. As does flipping and twisting the blue and green combo.

Step 16: Record Your Solutions

How to keep track of solutions? Print out a few (or more I have found 176 solutions so far) of the cube grid. Each dot has a number from 1 to 27 representing the a cubelet of the 3x3x3 cube. The is also and E for edge, V for Vertex, F for Face and C for center in each dot. This comes in handy for further math adventures that start with arithmetic and geometry and extend to concepts in graph and group theory and computer science.

I have two short(ish) YouTube videos that discuss finding, recording and categorizing solutions here:

SOMA Cube Solution Methods 1