Here is a problem that opens "Math Recess"...

When I go into classrooms, the Birthday Puzzle, is one of the first ones I open with--for many reasons. Who isn't going to be intrigued by how a "stranger" is correctly guessing everyone's birthdays by some "box-pointing"...

I show the image below on a screen. I then ask students to find their birthday date--day only(ie, 07, 23, 29, etc) on as many cards they can. Once they have done that, I ask them to tell me which ones they found their birthday on. In about a few seconds, I tell them their birthday...

I do this in rapid fire succession, not even blinking to capture the astonishment/disbelief on the faces of the students.

The natural question comes up--HOW are you doing this?

I ask..."Do you REALLY want to know"?

Because the response is organic and overwhelming, I don't just give them the superficial answer of looking at the top left binary numbers. I tell them how this works, and for them to construct their own cards!

This also creates a rabbit hole into Base 2, and other great Base 2 problems, which in turn creates further rabbit holes of playing in different bases...

And so on...

We want to create the "So On's"...:)