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Alex Romero @tilefarmer.bsky.social · 22/08/2026

How many little triangles? Do you know the trick?

A triangle made out of many little triangles.

Alex Romero @tilefarmer.bsky.social · 05/06/2026

Okay, maybe I’ll just let you take it then :) On a related note, can you tell what this says? Your conference attendees might like it.

An image with Crimson and white squares on top and red and black triangles on bottom, in clusters that have 19, 15, 15, 14, 5, and 18 squares, and 3, 15, 23, 2, 15, and 25 triangles

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Alex Romero @tilefarmer.bsky.social · 25/05/2026

And some good follow up questions, how does this compare to when Caltech did it? Who had to buy more black and white tarps? What if you did it with your own school’s name?

The Hollywood sign changed to say Caltech

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Alex Romero @tilefarmer.bsky.social · 25/04/2026

If you’re in Los Angeles, come to this event at Exposition Park tomorrow, fun for people of all ages! We’ll have a Tile Farm booth and I will be on an Early STEM learning panel at 1:15.

An image with a kid doing science experiments and info about city of stem festival at exposition park on April 26 from 9-5 in Los Angeles

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Alex Romero @tilefarmer.bsky.social · 03/04/2026

#ElemMathChat Q7 “Last Tile Standing” is another one of my favorites (for Tile Farm’s version go to tiletalk.tilefarm.com). I’ve chosen one of the 24 patterns above, can you think of yes/no questions that could help eliminate options? Ask and I’ll answer yes/no. Can comment below if easier.

Twenty four clusters of tiles that look like 3D clusters of cubes, each with a differing number of cubes.

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Alex Romero @tilefarmer.bsky.social · 03/04/2026

#ElemMathChat Q6 “How Many?” is another great question asking activity (shout out @triangleman.bsky.social ) (for Tile Farm’s version go to tiletalk.tilefarm.com). What “how many” style questions can you ask about the above pattern? Can you think of one you can’t answer?

A blue and white pattern seemingly made out of hundreds of hexagons colored somewhat randomly but with a certain pattern.

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Alex Romero @tilefarmer.bsky.social · 03/04/2026

#ElemMathChat Q5 “Notice And Wonder” is an obviously great question asking activity (shout out @mfannie.bsky.social ). Can you ask some questions about things you wonder about the above pattern? (Made in Tile Farm Studio)

A thirty sided polygon made out of thousands of isosceles triangles.

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Alex Romero @tilefarmer.bsky.social · 09/03/2026

I see an octagon inside there.

A red hexagon with an x inside of it, where the x has been converted into an octagon that says stop on it.

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Alex Romero @tilefarmer.bsky.social · 25/02/2026

My dad continuing his study of knot theory in #tileFarmStudio at a laundromat in Berkeley, CA.

Man in a laundromat looking at pictures of digital knots on a tablet.

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Alex Romero @tilefarmer.bsky.social · 14/02/2026

Here’s a special Valentine’s Day crypto tiles puzzle. Can you tell what it says?

Four groups of little hearts with 12, 15, 22, and 5 in each group.

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Alex Romero @tilefarmer.bsky.social · 11/02/2026

If you are at #NCTMIndy26 come to one of my talks! Tile Talk: A Daily Math Routine to Build Number Sense Thursday, Feb 12, 2026 | 11:30 AM (JW Ballroom 1) Secret Codes and Creative Thinking Bridging Math and Literacy with Typography and Cryptography Thursday, Feb 12, 2026 | 2:30 PM (Room 309-3)

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Alex Romero @tilefarmer.bsky.social · 13/01/2026

I saw this at the Huntington gardens and thought, wait, I know the ratio of the area of the hexagon to the octagon, but then I realized it is different than your pattern! Can you tell what it is here?

A cobbled tiling pattern with octagons, hexagons and squares

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Alex Romero @tilefarmer.bsky.social · 12/12/2025

And of note, this is also closely related to my phone case which I also designed in Tile Farm Studio: #mathArt #tessellation

A phone case with a tessellation that consists of repeated hexagons made out of 3 rhombi, and each rhombus has a simple smiling face on it

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Alex Romero @tilefarmer.bsky.social · 12/12/2025

Here’s something fun I made in Tile Farm Studio while watching @isohedral.ca talk about spiral tilings during the #illustratingMath seminar this morning.

A spiral tiling with hexagons shaded to look like boxes with smiley faces on them. Concentric rings of hexagons spiral in towards infinity.

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Alex Romero @tilefarmer.bsky.social · 18/11/2025

How many tiles do you see? How many hexagons do you see? How many dots do you see? How many colors do you see? What other “how many” questions can you think of? Check my link in bio for free daily visual “how many” prompts like these in Tile Talk. #iTeachMath #MTBoS #mathsToday

An image with a sunset palette showing an array of polygons including 5 triangles, 15 dotted squares, 5 pentagons, 5 regular hexagons, 5 irregular hexagons, and 5 heptagons. The dotted squares have 5, 5, and 1 dots on them, in 5 groups.

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Alex Romero @tilefarmer.bsky.social · 11/11/2025

Spent some time this evening relaxing playing in Tile Farm Studio and like this creation made out of 900 rhombi. Can you see factors of 900 in it? #tilefarm #mathart #rhombi

900 rhombi arranged to have 3 fold symmetry with blue-purple gradients.

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Alex Romero @tilefarmer.bsky.social · 07/11/2025

#elemMathChat A2. As a Tile Farmer, I love making visual problems in Tile Farm Studio (or using ones in Tile Talk) and using those to get students to talk about math strategies. I think visual problems almost always lend to diverse strategies which makes for great conversations about math. Example:

A hexagon with 7 dots surrounded by 6 1 dotted squares, 6 2 dotted squares and 12 triangles.

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Alex Romero @tilefarmer.bsky.social · 05/11/2025

Happy “Key” day! Is it just a coincidence that today’s level 1 Crypto Tiles puzzle is both a word and a representation of today’s date (11/5/25)? When is the next time the date will form a real word? From tiletalk.tilefarm.com #iTeachMath #hexagon #cryptography #EduSky #mathEducation

Three clusters of three hexagons with 11, 5, and 25 dots in the respective clusters left to right

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Alex Romero @tilefarmer.bsky.social · 04/11/2025

Not only is this the level 1 Crypto Tiles puzzle on tiletalk.tilefarm.com but it’s also what you should go do today! Hint: the number of tiles in each cluster corresponds to a letter in the alphabet. #iTeachMath #cryptography

Four triangles made out of triangles, trapezoids, and rhombi with 22, 15, 20, and 5 tiles in the respective shapes.

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Alex Romero @tilefarmer.bsky.social · 31/10/2025

Some spooky Crypto Tiles puzzles coming to you tomorrow at tiletalk.tilefarm.com #iTeachMath #cryptography

Three columns of squares with 2, 15, and 15 dots respectively

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Alex Romero @tilefarmer.bsky.social · 28/10/2025

We have some fun Halloween themed patterns you can collect in Tile Farm Harvest this week. Here is one built in Tile Farm Studio by a 2nd grader from Albuquerque, NM. It’s a beautiful design, but also has a lot of underlying math in it. #TileFarm #iTeachMath #PixelArt #Halloween #Frankenstein

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Alex Romero @tilefarmer.bsky.social · 26/10/2025

Blasphemous use of chemistry notation

A sign using periodic table symbols mislabeled such as Na being copper

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Alex Romero @tilefarmer.bsky.social · 24/10/2025

Did any of my Canadian friends, fellow Angelenos, or baseball fans catch the World Series themed puzzles in CryptoTiles today? These are a part of a new free math talk resource we have called Tile Talk that you can find here: tiletalk.tilefarm.com #iTeachMath #cryptography

A sequence of checkerboard square patterns with 4, 15, 4, 7, 5, 18, and 19 squares in order.

A set of 4xN arrays with differing numbers of dots corresponding to letters in the alphabet.

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Alex Romero @tilefarmer.bsky.social · 24/10/2025

Yes, that’s a fantastic idea! So many different ways I could see it working. I happen to have a snub squares tiling I am making on my floor with painters tape and just had a fun little dance on it:

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Alex Romero @tilefarmer.bsky.social · 24/10/2025

A5 #ElemMathChat I think composing shapes out of smaller shapes, or counting shapes in complex composite shapes are great things to get kids flexing their knowledge. Here’s a fun little thing with a lot of geometry vocabulary to talk about that I just whipped up in Tile Farm Studio:

A complex tiling with many different types of triangles, quadrilaterals, pentagons, and hexagons.

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Alex Romero @tilefarmer.bsky.social · 24/10/2025

A2 #ElemMathChat So much to squares! They describe special numbers, they are ubiquitously used in art, architecture, and design, they are the basis of how we measure so many things like houses or tire pressure, they have a dance named after them, and can even illustrate subtraction of fractions:

A square made out of isosceles triangles that get smaller and smaller as they go inwards.

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Alex Romero @tilefarmer.bsky.social · 18/10/2025

Team Tile Farm just competed in the 4x400m relay at the math education Olympics. #NCTMATL25

Four people in front of the Olympic rings in Atlanta

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Alex Romero @tilefarmer.bsky.social · 17/10/2025

My brother solving a CryptoTiles puzzle at #nctmatl25. Come by the Tile Farm booth in the exhibit hall tomorrow to try it out. It’s part of a fun new free resource we have called Tile Talk!

A guy looking at a big screen with a geometrical cryptographic message

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Alex Romero @tilefarmer.bsky.social · 15/10/2025

My dad is doing some serious math on his complimentary NCSM post it notes he got at the conference. He went through the whole pack, here are some highlights: #NCSM2025 #NCTM2025 #iTeachMath

Post it notes with math equations written on them

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Alex Romero @tilefarmer.bsky.social · 15/10/2025

If you are in Atlanta for NCTM come by the Tile Farm booth! We are debuting our new math talk activity “Tile Talk” which is free and includes a really fun activity called CryptoTiles. Here is a simple kindergarten level CryptoTiles puzzle that says “Atlanta”. #NCTM #NCTM2025

A cryptographic font where the number of dots in a column corresponds to the letter in the alphabet.

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Alex Romero @tilefarmer.bsky.social · 12/10/2025

Just arrived in Atlanta with these new shoes that I designed using Tile Farm studio. The tessellation on them is related to the truncated squares Archimedean tiling. If you come by the Tile Farm booth at @nctm.org this week I’ll show you how I made them! #NCTM #NCSM2025 #iTeachMath #Tessellation

Pair of shoes with a swirling tessellation pattern.

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Alex Romero @tilefarmer.bsky.social · 25/06/2025

I arguably spent too much time this morning trying to make a hat tile bucket of popcorn in Tile Farm Studio. #iTeachMath #tessellation #tileFarm #hatTile

A bucket op popcorn where the popcorn kernels are based off of the hat tile aperiodic tiling.

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Alex Romero @tilefarmer.bsky.social · 24/06/2025

#mathPhoto25 #angles Always loved all of the angles in baseball fields and their grass.

A picture of a baseball field with lots of striped lines in the grass.

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Alex Romero @tilefarmer.bsky.social · 18/06/2025

I saw 2, 3, 4, 5 like this, and I have my early triangular numbers memorized so I know it is 15-1 =14.

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Alex Romero @tilefarmer.bsky.social · 17/06/2025

Here’s a few I made in Tile Farm, the first one with faces I designed for my phone case, the second is a favorite pattern from the Alhambra that is just soooo satisfying, the third is something I « invented » earlier this year that can be generalized to all Archimedean tilings.

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Alex Romero @tilefarmer.bsky.social · 15/06/2025

#MathPhoto25 #Symmetry Here’s a pair of shoes I designed in Tile Farm Studio. The underlying pattern relates to the subtraction of fractions, geometric series, and the Euclidean Algorithm, and is a highly symmetric 42 sided polygon, but I colored it asymmetrically. #iTeachMath #TileFarm

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Alex Romero @tilefarmer.bsky.social · 10/06/2025

A #square geometric pattern on the side of a barn in Western Pennsylvania. I recently learned this is a “Pennsylvania Dutch Barn Star”, and they have been a fairly important part of Pennsylvania Dutch culture for centuries. #MathPhoto25

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Alex Romero @tilefarmer.bsky.social · 08/06/2025

Made a Dodgers jersey using a simple cryptographic font (a=1 square, b=2 squares etc.). Designed in Tile Farm Studio, then used a cricut machine to cut the design with iron on vinyl. #iTeachMath #cryptography #TileFarm #Cricut #Dodgers #MookieBetts

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Alex Romero @tilefarmer.bsky.social · 18/05/2025

Working on a 50 states art collection that I’m curating from patterns made in Tile Farm studio. Students will be able to collect these. Can you tell what state this is for? If US based, what image or symbol would you want for your home state? #iTeachMath #mathArt #geometry #tileFarm

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Alex Romero @tilefarmer.bsky.social · 07/05/2025

Friday is a very special day as it is 5/9/2025 and 5^2 * 9^2 = 2,025. This image is that illustrated visually in Tile Farm Studio. Good question for you or your students: when was the last time the day squared times the month squared equaled the year? #iTeachMath #Math #TileFarm #PerfectSquare

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Alex Romero @tilefarmer.bsky.social · 01/04/2025

Bout time to bust out my shirt for the season

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Alex Romero @tilefarmer.bsky.social · 31/03/2025

#MathArtMarch day 31, “change”. Using the substitutions shown below, how can you get from dodecagon A to dodecagon B? It’s fun to try yourself, but a solution is shown in comments. Credit to my dad for coming up with the concept of “flipping pentagons”. #tilefarm #patternblocks #iteachmath

A diagram with two dodecagons made out of pattern blocks, and substitutions that can be used to transition between them.

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Alex Romero @tilefarmer.bsky.social · 30/03/2025

#MathArtMarch day 30, “game”, here’s some chess pieces I designed and built a few years back. All the pieces are composites of various sizes of square prisms. This started as a one day project and turned into a many months project.

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Alex Romero @tilefarmer.bsky.social · 29/03/2025

#MathArtMarch day 29, “unsolved”. How many different side-length 1 dodecagons can be made from classic pattern blacks? What’s your estimate?

Four dodecagons made out of classic pattern blocks.

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Alex Romero @tilefarmer.bsky.social · 28/03/2025

#MathArtMarch day 28, “quadrilateral”. A favorite dodecagn you can make out of quadrilaterals with basic pattern blocks. #TileFarm #iTeachMath

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