You say 1. The box says 2.

You say 2. The box says 5.

You say 3. What will the box say?

For the sake of this contest, let's call what's going on here **a mathematical mystery box**. This one is numerical, but that isn't important. It could have been geometric, graphical, verbal, etc.

What's important is …

The box contains an unknown mathematical relationship.

You can throw your thoughts at the box.

You get to see how the box transforms those thoughts.

You're invited to speculate about the relationship in the box.

At Desmos Classroom, our free Activity Builder offers a fantastic environment for creating mathematical mystery boxes. You can set up different components—tables, equations, graphs, animations, etc—tuck the relationship behind the scenes (in the box if you will) and let students play with it.

Check mine out! Here's how I made it.

The key parts are, first, a math component where students can type a number. I have named that number input `number_input`

using the same care with which I named my beloved children, `child_1`

and `child_2`

.

Then, in a note component farther down, I added the following “Computation Layer” code:

```
mystery_box = simpleFunction("a^{2}+1", "a") #1
num_in = number_input.numericValue #2
num_out = mystery_box.evaluateAt(num_in) #3
content: "`${num_out}` #4
Do you know what's going on in the mystery box?"
hidden: not(number_input.submitted) #5
```

What each line does:

Creates the mystery function, which we'll use later.

Grabs the number from the number input.

Uses the mystery function on the number.

Determines what people will see in the note.

Razzle dazzle (by my standards) so people won't see the note until they submit a number.

That's it!

**Why don't you create and send in your own mathematical mystery box using Activity Builder sometime between now and July 15, 2022, 11:59PM Pacific?**

*Rules*: Make it one screen only.

*Submission*: Send the link into the comments here or get it to me via DM at Twitter or dmeyer@amplify.com. I'll collect them all into one activity and share.

*Prize*: Everyone's submission will receive some appreciative and constructive words from me or our Graphing / Computation Layer teams here. I'll select a few random submissions to get some free Desmos Classroom gear.

If you have an idea you like but don't know how to work the technology, then let us know in the comments. If you know how to work the technology but don't have an idea you like, let us know in the comments as well. We'll figure out how to make some matches.

**Also, a bunch of us at Desmos Classroom are offering a two-week long course called Design With Desmos which will cover all of these skills and more.** There are only 12 more slots as I'm posting this.

And if you are simply doing your absolute best just to pick yourself up off the ground after the last school year then [salutes weirdly] please accept best wishes from all of us here at Mathworlds and our highest hope to see you back in the fall. 💙

Here's mine:

https://teacher.desmos.com/activitybuilder/custom/62b858934b545ec2e57ac5e2

Mine has a cooking theme: https://teacher.desmos.com/activitybuilder/custom/62bf331fc4848d052acb4066