Imagine a world in which every whole number had its own symbol: a symbol for 1, 2, 3..., along with a symbol for 87, 135, and 62 million (to name a few). We would hardly be able to count, let alone perform arithmetic or any of the mathematics that we have today.
As far back as we know, humans have always recognized that numbers need some kind of pattern to make sense of them and do math with them. However, for many centuries, those patterns still used new symbols for 1, 10, 100, 1000, and increasing powers of 10, along with whatever symbols they used for the individual numbers 1, 2, 3, 4, and so on. Different number systems represented these numbers in different ways, but the real breakthrough was the invention of the number zero, which allows us to represent all whole numbers with just a few symbols. Today, we can represent every number with only 10 digits in total: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For example, we can represent the large number 61,432 with the symbols 6, 1, 4, 3, and 2 because of the place-value system.
What Is Place Value in Math?
Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value. The number 42,316 is different from 61,432 because the digits are in different positions. In the standard system, called the base ten number system (or decimal system), each place represents ten times the value of the place to its right. You can think of this as making groups of ten of the smaller unit and combining them to make a new unit.
Ten ones make up one of the next larger unit, tens. Ten of those units make up one of the next larger unit, hundreds. This pattern continues for greater values (ten hundreds = one thousand, ten thousands = one ten thousand, etc.), and lesser, decimal values (ten tenths = one one, ten hundredths = one tenth, etc.). In Grades 2 and up, your students will be focusing on mastering place value for ones, tens, and hundreds. In this article, we provide two lessons for introducing and developing the concept of the base ten number system.
Be the first to read the latest from Shaped.