When I think of the hat tile I think of this shirt. #hatTile #iTeachMath #tessellation #aperiodicTiling

I have two books by an author, Keh-Gong Shih, pub in 1996 that are just brilliant! But they are definitely lost. The first is PIctorial Mathematics: Patterns. It is fabulous! full of images like this. He created his own software called Mathgraf which is used to generate the images. #mathart #mtbos

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

#ElemMathChat A6. I am always taking mental notes for next time and often pivoting mid-lesson because you never know what your kids know until they start talking! I usually do a mental run through right after a lesson planning for next time based on what I learned.

#ElemMathChat A5. I think some activities naturally increase the importance of listening and building on each others’ observations. Also sometimes regular bridge questions like “Does anybody have an answer different from Julian’s” can be helpful in setting a tone of listening to other students.

#ElemMathChat A4. I always try to vary group size for discussions from pair-share to tables to whole class depending on what is going on and at what point in a lesson. And give one on one time to students who have trouble opening up or pair them up with a good patient listener.

#ElemMathChat A3. I find most students are pretty happy to explain their reasoning, but one strategy if they aren’t is asking a slightly different question and how their answer would change.

#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:

#elemMathChat A1. I usually try to model by verbalizing my own mathematical thinking and that I make mistakes. Also I try to open with very low floor and often totally obvious things for students to talk about to open them up and give them confidence before moving to more complex things.

#elemMathChat A0 I am Alex Romero, from Albuquerque, NM but live in Los Angeles, CA. I am a teacher, artist, and co-founder of Tile Farm (math education app). Today I woke up super early and got to enjoy a beautiful morning with a nice cup of coffee, the rising sun, and fresh November air.

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

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

Join us for #ElemMathChat on Thu, Nov 6 at 8pm CST / 9pm EST / 6pm PST! Topic: Facilitating Meaningful Mathematical Discourse Leader: Latrenda Knighten @latrendak.bsky.social Share ways to get students talking and thinking deeply about math!

For those who were asking...

Symmetric Sweetness: #iTeachMath #Halloween #CandyCorn #Symmetry

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

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

Blasphemous use of chemistry notation

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

A6 #ElemMathChat I find when I let kids freely build in Tile Farm Studio they naturally just start asking questions about geometric vocabulary out of necessity to describe what they are doing/trying to do. I was teaching a class yesterday afternoon where so many words came up in a natural context.

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:

A4 #ElemMathChat While equilateral triangles are beautiful and elegant and common, I think it’s important to present triangles in as many shapes and forms as possible. I think it’s also important to present non-triangles when teaching what triangles are. And to count sides, even if it is obvious.

A3 #ElemMathChat To understand all squares are rectangles but not necessarily vice versa, I think it’s important to establish what a rectangle is and isn’t, and all the variations of what it can be, then land on how a square is just a special type of rectangle where all of the sides are equal.

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:

A1 #ElemMathChat I see geometry in the structure of letters and numbers. I see it in every single piece of furniture in the room I’m in. I see it in all of the art I make. I see it looking out at the horizon at all of the buildings in downtown Los Angeles. And of course in my shoes I designed :)

A0 #ElemMathChat Hello, excited to be here. I am a teacher, artist, and co-created of Tile Farm, a math education app with a heavy geometry slant. As a student, I hardly remember any geometry in school outside of 9th grade. Luckily I got a heavy dose of it at home from my geometry loving father.

One of the most fun aspects of last week at #NCTMATL25 was everybody’s enthusiasm for our sneakers designed in Tile Farm Studio. For all of you who signed up for our newsletter, we will be selecting a lucky winner this week to get their own pair! Who knew math could be so fun!?!? #mathmadebeautiful

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

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!

@tilefarmer.bsky.social it was so wonderful meeting you IRL! You are an amazing person!

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

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

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

🎨✨ Math meets art! Join us for #ElemMathChat 📅 Thurs, 10/9 🕗 8pm CST | 9pm EST 👩‍🏫 Host: Dee Crescitelli @dcrescitelli.bsky.social Topic: Math in Art (Beautiful Math) Let’s talk patterns, symmetry, and the beauty of math in creativity. #MathEd #ITeachMath #MTBoS #ElemMathChat

I’ll be giving a 5 minute warmup talk for this event tomorrow talking about “subtractagons”. Hope to see you there!

A8 I think classrooms where math belonged to everyone would be less focused on comparison and more focused on growth. They would feel more like an art or music class where the joy is more in doing the craft rather than worrying about who is doing it best. #ElemMathChat

A7 I wish there were more metrics we tracked than just standardized tests. If we view meaningful math as a human right, we would also be measuring joy, excitement, growth, and if students every used math in ways to build things, or to solve problems that were meaningful to them. #ElemMathChat

A6 I think open ended math talks like “Notice & Wonder” are a great way affirm math as a human right for all students, especially those who have been historically marginalized or excluded. Allowing students to bring their own words and experiences to math is inviting and empowering. #ElemMathChat

A5 I think there are ways to make math exciting and rich at every level. A big fault in a lot of classrooms/curricula is to leave the exciting things in math until after somebody has mastered something. Letting all students have exciting math experiences promotes a sense of belonging. #ElemMathChat

A4 If math is a human right, it is educators’ responsibility to find a way to connect with and reach all students at an appropriate level. It is definitely sad to see any population of students left behind in any subject. #ElemMathChat

A3 I would define meaningful mathematics as using math confidently to describe something, build something, or solve a problem. I would also say experiencing joy while doing or experiencing math is very meaningful too. #ElemMathChat

A2 The phrase “math as a human right” make me initially think of having a baseline knowledge that allows you to navigate the world fluently understanding math you encounter. But also experiencing the joy of using math to solve even small problems and witnessing the beauty of math. #ElemMathChat

A1 I value my students having fun, and feeling a sense of accomplishment and growth. I think my students with disabilities value the same things, but also I think being heard and catered to and not left behind. #ElemMathChat

A0 Excited to be here! I am from NM originally but in Los Angeles now, I am a teacher, artist, and co-founder of the math education app Tile Farm, and have gone for some great bike rides this week. #ElemMathChat

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**overheard at Starbucks** Customer: “What’s the wifi password?” Barista: “1-3-5-7-9. All the odd numbers.” C: “That’s a lot of numbers to remember.” B: “It’s a pattern. Once you see it, it makes sense. But until then, it’s just a bunch of numbers.” Friggin’ profound advice re: math education.

Double take font. Penrose Geometric font based on Penrose triangle. www.myfonts.com/collections/...

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

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

A post for the 10th annual World #Tessellation Day: mathhombre.blogspot.com/2025/06/worl... my favorite kind of #mathart.