For as long as humans have been around, we have been counting things and looking for ways to keep track and represent the things that we count. The Ishango Bone is a great early example of this, but over time our method for counting and tracking numbers has evolved into a number system composed of ten numerals – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 – which we know today as the base 10 system.
Understanding place value helps us determine the value of a numeral based on its position within a number, and since our number system is based on the idea of 10, to fully understand place value, children need to see how the pattern of ten repeats within numbers and how it is used to build numbers.
Children begin with rote counting, 1, 2, 3… From there they get to two digit numbers, 11, 12, 13 and to three digit numbers 100, 101, 102… And so to a child, the 1 in 1, 10 and 100 often means the same thing. However, in place value, a 1 is one, a 10 is 1 group of ten, 100, is ten tens or 1 group of 100.
This concept can be quite difficult to grasp, but base ten blocks can help children visualise place value a little better. The cubes represent one unit, strips represent ten units, flats represent 100 units and blocks represent 1,000 units. Children can easily see that 10 cubes fit into a 10 strip, 10 strips fit into the 100 flat and 10 100 flats fit into the 1000 block. Another way to understand the base 10 system is through the use of our fingers. We start with ones, being our fingers, so our counting units so to speak. Then we go to tens, being sets of fingers. Then we go to ten sets of sets of fingers, which is 10×10=100, so we go to hundreds. In other words, every time we go one place further to the left, that is, every time we go into a unit that is one times bigger than the previous place’s unit, we multiply by our base of ten.
Confused yet? Because I think I am! It’s easy to see why children struggle with this concept, but it’s a fundamental part of mathematics. Having a sound understanding of place value and our base 10 system are basic concepts that children need to be aware of, otherwise future learning will be compromised. That’s why it’s important to provide children with multiple perspectives, like the two methods mentioned above, to help highlight that there is more than one way to approach any given problem.
References
Bellos, A. and Riley, A. (2011) Alex’s Adventures in Numberland. London: Bloomsbury Publishing PLC.
‘Definitions of Base 10’ available at: http://math.about.com/od/glossaryofterms/g/Definition-Of-Base-10.htm
