## Wednesday, October 26, 2011

### A Perfect Ten

Don't you love tests where you ask a question which you believe everyone will get correct, and then find out it just isn't so?  I gave my PreAlgebra college students a pretest to see what they knew and didn't know.  One of the first questions was:  Why is our number system called Base Ten?  This is an extremely important concept as it reveals what they know about place value.  Below are some of the answers I received.

1)  It is called Base Ten because we have ten fingers.  (Yikes! If that is so, should we include our toes as well?)

2)  It is called Base Ten because I think you multiply by ten when you move past the decimal sign.  (Well, sort of.  You do multiply by ten when you move to the left of the decimal sign, going from the ones place, to the tens place, to the hundreds place, etc.)

3)  I think it is called Base Ten because it's something we use everyday.  (Really????)

Enough!  It is called Base Ten because we use ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to write all of the other numbers.  Each digit can have one of ten values: any number from 0 through 9. When the value reaches 9, just before 10, it starts over at zero again.  (Notice the pattern below.)

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, etc.

In addition, each place is worth ten times more than the last. Ten is worth ten times more than 1, and 1,000 is ten times more than 100. The pattern continues infinitely both ways on a number line.

The decimal point allows for the place value to continue in a consistent pattern with numbers smaller than one. As we move to the right of the decimal point, each place is divided by ten to get to the next place value.  One hundredth is one tenth divided by ten, and one thousandth is one hundredth divided by ten.  The pattern goes on infinitely.
100's, 10's, 1's . 0.1, 0.01, 0.001, 0.0001, 0.00001, etc.
Since all mathematics is based on patterns, this shouldn’t be a new revelation. Perhaps on the posttest, my students will omit the fingers and instead rely on patterns to answer the questions!

For more information about teaching place value, refer to the September 7th posting entitled: There’s A Place for Us.

Barbara said...

I'm going to ask my 7th grader when he comes home from soccer practice and see what he says! Thanks for helping kids get back to the BASICS!

Barbara

Kim said...

I am so excited to have discovered your blog!
And I can't wait to teach digital roots next week.
I just perused several different posts and got lots of ideas... Thanks! I'll be back!

Kim