My head is spinning. My #FediFriends are amazing.

Proving something fundamental (like the circumference of the earth!) or teaching dimensional analysis with animals, or graph theory, or simultaneous equations (which their teacher has told them to just guess at), or, well, y'all just have to read the thread. There's some incredibly fun stuff in here.

@DrTCombs
Maybe you can prove something fundamental?

Calculate the circumference of the earth, calculate how fast things accelerate with gravity?something like that?

I would include the gathering of the data, so go out and drop some things and time them. Measure the shadow of a stick and have a family member that is far away do the same, at the same time, to calculate the circumference.

@DrTCombs multiplying and dividing silly things like fractions of cats and dogs might be fun, story problems, a taste of algebra, and is analogous to multiplying units, which helps keep your conversions right since cat/cat = 1... Like 3/4 liters water balloon per dog * 2 dogs per 4 cats... IDK that example needs work

@DrTCombs Eulerian circuits and the 7 bridges of Konigsberg! It's a simple enough problem to describe to smart kids of that age, and demonstrates some fundamental graph theory, which is an entirely different branch of math than most kids ever get exposed to.

@DrTCombs My wife says, "I would do the derivation of e. There's a really cute derivation of e... actually multiple cute derivations of e.

Maybe also derive the pythagorean theorem? There's a geometric proof. If they haven't seen pi by then, they should be introduced to it. They wouldn't understand it fully, but I would show them a youtube video of the harmonics of the riemann zeta function. It's so amazing to see. OOH nonlinear dynamics the butterfly oscillator!"

(And then I cut her off.)

@DrTCombs There's a lot of mathematics to be learnt in the game of Hex. easy and fun to learn for kids of this age. just copy the game board as handouts. https://en.wikipedia.org/wiki/Hex_(board_game)

@DrTCombs

The birthday paradox is fun and easy to explain https://en.m.wikipedia.org/wiki/Birthday_problem

That a US state attempted to legislate a specific value for the number Pi and its possible consequences is also hilarious https://en.m.wikipedia.org/wiki/Indiana_pi_bill and gives itself to quite the discussion.

That a math theorem was proven by a US congressman, James Garfield, over a century ago https://en.m.wikipedia.org/wiki/Garfield's_proof_of_the_Pythagorean_theorem makes for another good discussion: it’s the Pythagoras theorem (and the proof is intuitive and easy to explain by drawing and measuring areas of triangles), and sets a baseline of expectations for the intellectual capabilities of anyone running for office … or it should.

@DrTCombs Coding. That's what I would've wanted to learn 😁

@DrTCombs The Math is Cool (WA school math competition) starts in 4th Grade. You can get the tests here: https://academicsarecool.com/#/samples It also has a speed team competition piece to it, the "Knowledge Bowl" section of the test.

@DrTCombs @albertcardona Personally, I would avoid something heavy in boring arithmetic computation. They’ve likely been doing that for years now and may even see that as the whole of math.

Instead, I would look to introduce some of the more visual or conceptual topics. Graph theory is always a great one that feels fresh and is not so arithmetic focused. It can focus on reasoning about the structure and figuring out fun things about the graphs.

Joel David Hamkins has some great booklets on this that I shared with my kids. You might check out

https://jdh.hamkins.org/math-for-seven-year-olds-graph-coloring-chromatic-numbers-eulerian-paths/

for some inspiration.

Also, this can be a good time to start to introduce some basic logic and reasoning on a more formal level and start to introduce things like fallacies.

Additional possibilities might even include looking at different kinds of numbers and diving into the idea of number in a way that isn’t so calculational but more conceptual. Most kids have some familiarity with “circular numbers” or “clock numbers” (i.e. Z_n or modular arithmetic) and that can be used as a jumping point for discussion about operations in general and the ideas behind what numbers do. Such a topic might usefully touch upon all the controversies of number people have debated over the millennia (the controversy of zero, the controversy of the negative, the controversy of the imaginary, the controversy of the undefinable, …).

Finally, for a little more calculation oriented class, that grade level is a good one to introduce the ideas behind possible worlds and counting possibilities (combinatorics). If brought in with a section on logic, it can even introduce the association between the logical operation on properties (AND / OR) with the arithmetic operations (x / +).

I think at that age, kids start to tire of the focus on computation, and it’s a good time to bring in concepts that can widen their perspective of math.

@DrTCombs my 10 year old suggests algebra 1. He is in 5th grade taking 6th grade math, not sure if it helps your 4th graders.

@DrTCombs Hilbert Hotel and Cantor diagonal argument

@DrTCombs The Beast Academy series goes way deeper—and waaaaaay funnier—than standard elementary math curricula do: https://beastacademy.com/

It really lays the foundation for thinking like a mathematician, not like a computer.

@DrTCombs Donald Saari once taught 3rd-4th graders some social choice theory (there is a very nice write-up of the experience on his website - google it!) I don't think he went all the way to the Arrow (Im)possibility Theorem or to incentive issues, but even the basics are enough to get kids to think about order relations and functions defined on (products of) them.

@DrTCombs They know long division. And they have calculators. So they know about square roots. Teach them long square roots. To prove there is always something else to learn. If they push you, teach them binary arithmetic, including multiplication and division. They’ll see how it is just shifting and addition/subtraction. Then tell them that’s how dumb computers really are. You might making computer scientists of some of them.