iiinova — where your digital self keeps evolving

Dan Finkel @mathforlove.bsky.social · 06/10/2026

In a recent visit to some friends, I noticed that their 7-year-old son was playing with 21st Century Pattern Blocks. His mom sent me this photo today.

2203

Dan Finkel @mathforlove.bsky.social · 23/07/2026

Side project update! I'm having a ridiculously good time working with my brothers on a new board game, Battle of the Species. We'll be Kickstarting it soon! My older brother had the brilliant idea to have our artist make cards featuring us. I quite like how mine turned out!

Playing card from the Game Battle of the Species, featuring one of the creators, Dan.

220

Dan Finkel @mathforlove.bsky.social · 06/05/2026

Anyone passing through Times Square see this awesome display from @mathhappens.bsky.social? Pretty cool to see 21st Century Pattern Blocks up there 😀 #iteachmath

A billboard for Math Happens in Times Square

0100

Dan Finkel @mathforlove.bsky.social · 12/03/2026

Just posted a new guest blog post from a parent using our curriculum as she homeschools her 3rd grade son. It's a lovely read, and more testimony on the power of the play-based approach. mathforlove.com/2026/03/a-ma...

A boy holds a white board in front of his face containing the record of a logic game he just completed. A dog is in the background.

162

Dan Finkel @mathforlove.bsky.social · 14/01/2026

If you're a teacher or educator in the state of #Maine who works to teach or support math for 3rd - 5th graders, you can sign up for a series of virtual workshops I'll be leading to support Numeracy. #iteachmath Learn more and apply - registration closes Friday! forms.office.com/g/4HXtFY8tST

Poster promoting workshop series on Unlocking Numeracy

030

Dan Finkel @mathforlove.bsky.social · 01/01/2026

She created some of the original dice images I've used for #unitchats for many years. She also made this gorgeous image that we used (with her permission) as the cover of one of our curriculum books.

Cover of a math textbook, featuring star polygons made of string.

051

Dan Finkel @mathforlove.bsky.social · 24/09/2025

Proofing #SubtractionbyHeart! The new cards are looking lovely :-) We should have these out by early 2026! #iteachmath #mtbos

A box of flash cards called Subtraction by Heart

171

Dan Finkel @mathforlove.bsky.social · 17/09/2025

I either need ones on the first die to make 2, or 2s on the second die. In the first case, that's going to force die 2 to consider of odd numbers, and die 1 to contain three blank sides and three ones. Forgot to check the total. But I'm okay - it's 21 dots totay!

110

Dan Finkel @mathforlove.bsky.social · 17/09/2025

There are two other possibilities: a 2 by 3 and 3 by 2 array of ones. Each of these is going to lead to potentially more choices. Though once one die is complete, it forces the numbers on the other die. Let's see - let's go with the first image and see the options.

110

Dan Finkel @mathforlove.bsky.social · 17/09/2025

Yep, the rest of this is forced. Another solution! Still, there's more here.

100

Dan Finkel @mathforlove.bsky.social · 17/09/2025

Interestingly, I could also have the second die consist entirely of ones, and get a 6 by 1 array instead. Wait a minute... I see where this is going. This is going to force Die 1 to lose one face from every side. I'll put the 1 in on die 1, and I'll get all six 2s. And so on.

100

Dan Finkel @mathforlove.bsky.social · 17/09/2025

Interestingly, those six spots are going to need to be arranged in a rectangular shape, since they're determined by the column and row numbers. So I could have a 1 by 6 rectangle of ones, which could only happen if the first die was blank. That'll be my trivial solution again.

110

Dan Finkel @mathforlove.bsky.social · 17/09/2025

I forgot to fill in what the total roll is. 0 + 1 = 1. I'll fill that in. Now there are 36 possible rolls (corresponding to the 36 empty squares in the table). I need 6 of them to be ones, 6 to be twos, and so on, up to 6 sixes. So what are the options for having 6 ones?

Table of dice values with one entry filled in with a 1

100

Dan Finkel @mathforlove.bsky.social · 17/09/2025

Let's think about this. To get a one, I need a 1 on one die, and a 0 on the other. (No half dots.) Also, I can't have a 0 on both dice, because then 0 could be an outcome. So without loss of generality, I can assume my table looks like this.

Table of dice rolls, with a 0 filled in as an option for die 1, and a 1 filled in as an option for die 2

100

Dan Finkel @mathforlove.bsky.social · 17/09/2025

Normally I'd use pen and paper, but I think it'll be easier to take screenshots of a computer visualizations, so I'll do that for the purposes of speed in posting. Unless I get stuck, in which case I'll need to move to pen and paper to let my brain roam a little more.

A an empty table of possible dice rolls, still to be filled out.

110

Dan Finkel @mathforlove.bsky.social · 12/03/2025

This image, featuring the purple concave hexagons, blue rhombuses, and gray darts, is one of my favorites.

Two hexagons made from different 21st Century pattern blocks, in different ways.

010

Dan Finkel @mathforlove.bsky.social · 12/03/2025

The 21st Century Pattern Blocks allow for even more opportunities for these kinds of provocations! We were just playing around with them in a teacher session recently. Having blocks that can't be made from the base green triangle makes this kind of argument really appealing.

Four rhombuses and 4 right triangles combining to make the same larger rhombus

120

Dan Finkel @mathforlove.bsky.social · 06/02/2025

Newsletter: The Power of Openers mailchi.mp/mathforlove/...

Still from a workshop on openers in the classroom.

Can you solve the Giant Cat Army Riddle?

Dan Finkel: The Power of Openers in the Classroom. A still from a Teacher Talk video.

Calculator with 0, 1, 2, and decimal point buttons broken. Goal is to make the calculator readout equal 21.

050