**Answers – 50 cents**

**Answers, requiring thought – $100**

———————————————-

My favorite joke:

The military had purchased a piece of machinery for a cost of $100 million. There was just one problem. It had quit working. After trying everything they could possibly think of without success, they called in a consultant, Dr. Amazing.

Dr. Amazing walked up to the machine, hit it three times with a hammer, and what do you know, it sprung to life! Everyone present applauded and exclaimed how amazing it truly was.

The next week, they received a bill from the good doctor for $1 million. The chief financial officer was outraged.

That’s outrageous! A million dollars for three taps with a hammer? I’m not paying this until you send me an itemized bill to justify this fee!

The next day, he received the following:

==============================

*Itemized Bill for Machinery Repair*

Tap with hammer: 3 @ $1 = $3

Knowing where to tap: $999,997

==========================

My point is that what is often most important to know is when, where or why to do something, rather than how, how fast.

Take math, for example.

How many times in your life has someone run up to you and said,

Quick! What’s 8 x 7? This lady is falling from the sky here and will die if you don’t get the right number fast!

I have used math to make my living for all of my adult life. I’ve been an industrial engineer computing the time it takes to build an airplane, a programmer calculating the best predictors of failure, whether it be a part in a machine or a student in school.

There is a need for “math fluency”, that is, the ability to rapidly and accurately access basic math facts. It makes it easier to solve math problems. Yes, you can use a calculator but I know 8 x7 = 56 instantly. I don’t need to type it into a calculator and that lets me focus on what is important.

What IS important? Let me give you an industrial engineering example –

The factory has been making 40 widgets a month, working an 8-hour shift, 5 days a week, for the past 6 months. The total number of widgets due to the customer at the end of an 18 month contract is 900.

So … we are 60 widgets short now and unless we go on to overtime we are going to be 180 widgets short at the end.

There are multiple solutions for this problem, but it IS a real problem. My point is that the important part here wasn’t figuring out 40 x 6 as fast as possible but rather seeing that 900 in 18 months means we needed to average 50 per month, which we did not. It also means realizing that we need to work more than a 40-hour shift. It’s important to realize that you could increase the number of hours per day, days per week or both. You need to understand that increasing the output to 50 per month will not completely solve the problem, because you are behind by 60 widgets. You should also realize that you don’t have to increase the number of hours at a constant rate. You can increase the hours to 60 per week to get back on track, and then after 6 months go to 50 hours per week. In fact, that is exactly what we did.

This was an actual occurrence, and, in fact, going into his office and pointing this out is how I met my late husband. I even learned a programming language to do computer graphics, which was cutting edge 30+ years ago. I thought I was very smart. He thought I was an insufferable know-it-all, but also right, and put the factory on overtime. (I guess he changed his mind, because we were married a few years later.)

Now, none of this is calculus, and if you sat down and thought about, you could no doubt have figured this all out by yourself easily enough.

IF YOU SAT DOWN AND THOUGHT ABOUT IT is the key phrase in that sentence.

That is what we are doing in our games, teaching students to stop and think about the problems. We start with easy ones and get progressively more complicated.

Complicated is good because it’s like real life.

Buy Spirit Lake: The Game here . Fish Lake will be available soon.