## Posts tagged ‘fun’

### Think of a Number

I love to create math games almost as much as I love to play them.

My favorite professional project was leading the development of Calculation Nation. And my favorite game on the site is neXtu, though other games on the site may promote more sophisticated mathematical thinking.

I have many reasons to love my wife, not least of which is her creation of the game Dollar Nim. While I can’t take credit for the rules, I will take credit for its analysis and its popularization. (What do you call a wife who makes up a game that gets you a publication credit? A **keeper**!)

Recently, I’ve been frustrated by the lack of games for teaching algebra. I’ll give props to the good folks at Dragonbox, which uses a game environment to teach algebra. But I’m not yet convinced that it leads to deep algebraic understanding; even they admit “to transfer to pencil and paper, children must be explained how to rewrite equations line by line.” They also claim that “in-house preliminary tests indicate a very high level of transfer to pencil and paper,” but that’s the fox watching the henhouse.

So I’ve been thinking about games I can play with my sons that will allow them to engage in algebraic thinking. But I don’t want them to know they’re engaging in algebraic thinking. I have two criteria for all math games:

- The game mechanics depend on mathematics. The math is not tangential to the game; it
**is**the game. - Kids don’t realize (or at least they don’t care) that it’s a math game, because it’s fun.

It pains me to write that second criterion, because math **is** fun. But I know not everyone shares that opinion. So I do my best to disguise any math learning in the game and then, when they least expect it — BOOM! — I drop the bomb and show them what they’ve learned.

So here’s a game I recently devised.

- Player A chooses a number.
- Player B chooses two operations for Player A to perform on the number.
- Player A performs those operations and then tells the result to Player B.
- Player B then tries to identify Player A’s number.

These rules leave something to be desired, since Player B could simply ask A to “multiply by 1” and then “add 0,” in which case finding A’s number would involve no work whatsoever. To be a stickler, an additional rule could impose that either addition or subtraction can be used exactly once and that no operation can involve either 0 or 1. In a middle school classroom, I suppose I would state such a rule explicitly; for playing this game with my seven-year-old sons, I opted not to.

We played this game three times on the car ride to school yesterday. One game went like this:

- I thought of a number (14).
- Eli asked me to add 3 to my number.
- Alex asked me to multiply by 3.
- I told them the result: 51.

Eli then guessed that my number was 16. He had subtracted 3, then divided by 3.

“No!” said Alex. “You added 3 first, so you need to subtract 9.”

“Why 9?” Eli asked. “Daddy only added 3.”

“But he multiplied by 3, so if you subtract first, you have to subtract 3 × 3.”

Eli then realized that my number was 14.

He thought for a second. “Oh,” he said. “I should have divided by 3 **first**, then subtracted.”

Wow, I thought. This is going even better than I hoped.

Though they didn’t use the proper terminology, the boys had a great discussion about “undoing” operations by performing inverse operations in reverse order. In 10 minutes, they taught themselves how to solve a two-step equation:

3*x* + 3 = 51

Grace Kelemanik once said that she knew she was being effective when she didn’t have to say a word. She’d watch from the back of the room as students carried the conversation and guided one another to correct mathematical thinking.

I will never claim to be half the educator that Grace Kelemanik is. But yesterday morning, I was pretty darn effective.

**I’d love to hear about math games you’ve played with kids, whether you invented them or not.**

### XXX Rated

Today is 10/10/10, which Julius Caesar and others might have written as X/X/X. In honor of the date, today’s post contains some XXX‑rated jokes. (Okay, not really. There is no pornography. But today’s jokes are slightly off‑color and probably not appropriate for the classroom. Then again, I know a high school teacher who used the following mnemonic to help students remember SOHCAHTOA: Sex Over Hot Coals Adds Heat To Ordinary Affection. So perhaps I don’t really know what is and isn’t classroom inappropriate.)

But before we get to the jokes, a math problem for you containing three 10’s. When the following expression is written in standard form, how many digits does it contain?

10^{1010}

(By the way, for all you code geeks, that expression was done with straight HTML. No MathML required! It simply uses nested <sup> tags.)

Okay, to the jokes…

How is sex like a fraction? It’s improper when the larger one is on top.

What is the square root of 69? Eight something.

What is 6.9? A good time interrupted by a period.

I was hanging out in an Internet cafe when my server went down on me.

Calculus teachers do it to the limit.

Statisticians probably do it.

Combinatorialists do it discretely.

Algebraists do it in groups.

No post about dirty math jokes would be complete without…

Speaking of integrals, here’s a half-assed integral:

And a slightly longer one…

The math professor explained to her students that there would be no acceptable excuse for missing the final exam. “Unless you or a loved one dies, I expect you to be here,” she told them. “No other excuse will suffice.”

“What about sexual exhaustion?” asked the class clown, which made several of the other students snicker.

“Sorry, Johnny,” the professor said. “You’ll just have to write with your other hand.”

Finally, I’ll leave you with my favorite dirty math problem, which I love mainly because of its subtlety:

A mother is 21 years older than her son. In 6 years, she will be 5 times as old as her son. Where is the father?

### Martin Gardner

When I was an undergraduate at Penn State, I used to go to Pattee Library to do research or to study. Invariably, though, I’d find myself perusing the shelves corresponding to the 510’s of the Dewey Decimal system, locate a book with an intriguing title… and several hours later, I’d surface from the stacks. Nine out of 10 times, the book that would occupy my time would have been written by Martin Gardner.

It was through one of those books that I learned how to make a tetra-tetra-flexagon, and in another I read about the numerologist Dr. Irving Joshua Matrix. It was also in one of these books, Wheels, Life and Other Mathematical Amusements, that I learned my favorite problem, which became my favorite problem because it was the first true problem that I had ever solved entirely on my own. (By “true problem,” I mean that when I first looked at it, I had no idea how to proceed; it was not just an exercise, and it was going to take something beyond what I had learned in my math classes.) If you’re a math nut or a Martin Gardner fan, you’ve likely seen it before, but I offer it here for those who haven’t:

On Monday, Jonathan deposited

xdollars in the bank. On Tuesday, he depositedydollars. Each day thereafter, he deposited an amount equal to the sum of the previous two days’ deposits. On the following Thursday (that is, a week-and-a-half after his first deposit), he made a deposit of exactly $1,000. How much did he deposit each day?

(My apologies for paraphrasing. That may not be the exact wording that Gardner used, but you get the idea.)

I finished solving that problem at a very late hour. It was dark outside Pattee Library, and though I should have been tired, I was as awake and alive as I have ever been. I looked at the solution on my paper, and I remember thinking to myself, “Wow! That was fun!” And a second later, I was disheartened to realize that I was a sophomore in college, yet no one had previously shown me how much fun math could be.

That problem sparked my love affair with math, and it greatly influenced my philosophy about teaching.

Martin Gardner passed away on Sunday, May 22. My heart grew heavy when I heard the news, but my spirits were buoyed when I thought about his great life and the tremendous impact he had. It’s hard to estimate how many people he affected during his 25 years of writing the “Mathematical Games” column in *Scientific American* or with his 70 books.

But I know he affected at least one, and deeply.

Thank you, Mr. Gardner, and may you rest in peace.