Base-Ten What Now?

Last week, my teacher introduced my fellow classmates and me to classmates a little something called "bases". She told us that we have been doing base ten our entire lives and to not worry. What did I do? I worried. I had no idea what she was talking about, I was thinking "OK, so we are going to multiply numbers by 10". Nope. Wrong. Let me explain. First, you have to start out by understanding number systems. Our number system relies on 10 digits-0,1,2,3,4,5,6,7,8,9. The written symbols for these digits, like 3 or 4, are numerals. A numeration system, is a collection of properties and symbols agreed upon to represent numbers systematically. The numeration system that we use today, relies on two properties: All numerals are constructed from the 10 digits;  Place values are based on powers of ten, the number of digits in the number base of the system. Confused yet? Ya I was too, but let me break it down.

Place value assigns a value to the digit depending on its placement in a numeral. For example: 

So, to find the value of a digit in a whole number,we multiply the place value of the digit by its face value. For example in the numeral 3647, the 3 has place value"thousands", the 6 has a place value"hundreds", the 4 has a place value "tens" and the 7 has a place value "units". The easiest way I've come to figure this out, is to use base-ten blocks. With base-ten blocks, a student can get a better understanding of place value and adding and subtracting multi-digit numbers. A set of base-ten blocks, consists of units(one), longs(tens), flats(hundreds), and so on and so forth.

Once I figured out what place value and digits were, it was really pretty simple to work out the rest. we are still working on bases in class. I understand whats going on, and I hope that after this you do too!