Eight days a week we turn it up to 11

Today, to finish our week of talking about exploring time in math lessons, I come to the concept of exaggerating to the point of hyperbolic excess. More than once. And so on. Ditto.

Here are some examples of what I mean:

• eight days a week (Beatles song and a movie)
• turn it up to eleven (Spinal Tap movie)
• 110 percent effort

Talking like this really isn't math but it's human nature. 

How do kids know the difference? How do they learn when we are being serious and when we are kidding around in our use of numbers? I'm not an expert on youthful liars but I understand they can be pretty good by the age of 4-5. Some kids might be lying by the age of 3. How do we know? Because they tell outrageous fibs without knowing how adults judge the difference between truth and lies.

Of course that's a whole subject in itself. Let's stick to the numbers. How does anyone know if numbers are accurate?

We have a few tests and questions we can ask ourselves:

• is the number consistent (does it appear the same way each time we see it)
• does a number fit a pattern (use a check digit, or have the right number of digits, etc.)
• is the number from a reliable source (person, program, machine)
• is the number intended to be an estimate
• is the number precise (to a reasonable number of decimal places)
• is there a stated degree of precision (is it meant to be accurate)
• has the number been rounded (from another value)
• is the number arbitrary or actual (on a scale of 1-5 how do you feel? vs here are 3 rocks)
• is the number a repeating fraction (.66666) with no end?
• is the number irrational and not repeating or finite (π = 3.141592 ...)

Mathematicians use a term "confidence" or "confidence interval" to express how well they believe a given number represents the real number.  I've extracted a nice formula from Wolfram Mathworld to clearly explain this subject of confidence interval.

Here it is:

I'm betting you'll look at this and think "They don't learn that in Excel Math!" You're 110% spot-on.