A slide titled Target Answer Challenge. A green banner in the center reads Design two different math problems where the answer is 2x plus 1. Below the banner are two colored boxes. On the left is a red box titled Linear Relations with the instruction Design a problem where the goal is to determine the equation of a line. Underneath it says Think about: Constructing a problem using two coordinate points, or using a point and a given parallel or perpendicular line. On the right is a blue box titled Differential Calculus with the instruction Design a problem where the goal is to determine the derivative of a function. Underneath it says Think about: Finding the first derivative of a second-degree polynomial, or the second derivative of a third-degree polynomial.

A problem to start calculus class on Monday. We're not to integration yet, but I want to start nudging student thinking in that direction. Plus a bit of retrieval practice and creative thinking/problem solving. #ITeachMath

working with students on problems of the nature:

How many ways can you distribute 10 cookies among 3 people if the max # per person is m?

For e.g. m = 4, you can ignore m and make the full list of all distributions. Then naively cross off every entry each time it contains an entry ≥ 5.

But, then+

This is so cool! Given only the "exponential minus log" function, elm(x,y)=exp(x)-ln(y), and the constant 1, you can perform +, -, x, ÷, exp, ln, trig, powers, roots, etc. You can also obtain e and π! See arxiv.org/pdf/2603.21852 and arxiv.org/src/2603.218...

Congrats! This is a great session idea. I wish I could go!

I've confirmed to speak at the NCTM Annual in Denver 🗣️🎤

Here is the abstract:
🪑: www.aievolution.com/ntm2601/Abst...

Deets:
#NCTMDEN26 Annual Meeting, October 28-31 in Denver!
www.nctm.org/denver2026/

See you there???
#iTeachMath ♾️ #MathSky 🧮

Oooh yes. For what the kid was working on it didn’t matter but I like the challenge of fixing it!!!

Ooooh lovely! They weren’t working on desmos so they I’m sure were thinking of straight up algebraic stuff - this was part of an equation they were trying to build up.

I’ve definitely done this before!!!

I had a student who essentially needed something to yield 0 when positive and to yield 1 (or -1) when negative. They came up with this idea 💡 which was oh so lovely. #mtbos

I love creativity and out of the box thinking.

Oh yes! Not a full class but just 6 days between semesters.

"A 'Crack the Code' puzzle for Week 6. Five three-digit number clues are given: 342 (one number correct and well placed), 273 (nothing is correct), 165 (one number correct but wrongly placed), 853 (one number correct and well placed), and 264 (two numbers correct but wrongly placed). Three blank boxes at the bottom await the solution."

A 'Which One Doesn't Belong?' activity showing four coordinate plane graphs. Top left: a black cubic function with a blue tangent line at a point near the origin. Top right: a black circle with a blue tangent line touching it. Bottom left: a black parabola opening upward with a blue tangent line at a point on the left side. Bottom right: a black cubic with a blue secant line. Students are asked to find a reason why each graph does not belong.

A warm-up asking students to find dy/dx for four similar-looking trigonometric functions: y = sin(2x), y = sin(x²), y = sin²(x), and y = 2 sin(π/2).

Every day in Calculus, there's a warm-up on the board as students walk in. Gets them thinking and sets the tone before we even start. A few from this week: Crack the Code, Which One Doesn't Belong?, and four trig derivatives. Low stakes, high engagement. #ITeachMath #MathsToday

(I got my masters degree in history of science so it was up my alley.)

I did! And I even read it with students. I too thought it was great. The thing about his work is that it is “real” history of math (like part of the academic history world), so it’s more dense than a lot of popular math books. i wonder if thats why others might not have liked it???

I probably won’t be able to read this book (Proof: How the World Became Geometrical) for a while. But I thought the two other books by the author were great. And what a lovely cover! #mtbos

These are great questions for students to be asking as they approach a challenging math question.

Four napkin rings of various radii

The four napkin rings are the same height

At Gathering 4 Gardner, @cardcolm.bsky.social suggested I try the following 3D-printing project.

Recall the "napkin ring problem": Take a sphere of radius r and drill out a hole along a diameter so the remaining shape has height h. Then the volume, V = πh³/6, does not depend on R.

He thought that

A 3D-printed sphere sliced into equal-height pieces.

Another 3D-printing suggestion from @cardcolm.bsky.social:

Archimedes proved that if you slice a sphere of radius r with two planes a distance h apart, the surface area is 2πrh—the same as a cylinder of the same radius and height. So, it doesn't depend on where the slicing occurs.
1/2

I used to pride myself on writing questions that assessed what we had talked about, but in new & different ways.

They'd get plenty of "the standard" questions, but I'd regularly mix in extension problems to see how they can apply their understanding.

This was a favorite

#mtbos
#iteachmath

I feel similarly!

Small Rhombicosidodecahedron if u even care.

I know it can be made with a single (incredibly long) modelling balloon because every vertex only has four lines coming from it, so it has an ✨Eulerian path✨

G4G16 Gift Exchange The gift I made for Gathering 4 Gardner in 2026, together with files so you can make more at home.

I wrote a blog post about my G4G16 gift. If you want a copy of your own, download and print the files!

Golly I love living in NYC. I got a ticket for this at noon today.

I was filled with childlike wonder for 5 minutes of paper planes swirling down from an oculus…

thewangcontemporary.org/events/20000...

Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart

Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart

Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart

Three knight's tours of a 32x32 chessboard. Each contains the set of edges (knight's moves) shown in the top left. Each is a single unicursal path that can be traced without lifting one's writing implement from the paper. #mathart

Two knight's tour (32x32 and 64x64). Two terms of an infinite sequence of tours.

Built a “3D” sphere (SVG) to show RYB transformations.
Over-iterated in @codepen.io

10% optimization, 90% procrastination.

codepen.io/meodai/full/...

A few more experiments! Nothing new but these look nicer than my last set I think!

#mathart #mtbos

This is so gorgeous!!! And looks like so much fun! 🤩 I must try this at my school!