Base Blocks are Amazing!

     In our numeric system, we use base ten to count and as our written representation of numbers, however not all cultures use this system. People can count in base four, base two, base five, base twelve, ect. but a great was of representing, teaching, and visualizing these alternative systems, and our own base ten system, is with base blocks. Base blocks are a manipulate used to organize units to create a whole number and can be used in a variety of base blacks. They consist of at least three different types of blocks, a unit, a rod, and a flat. In base ten which we are most familiar with, a unit represents one, a rod represents 10, and a flat represents a hundred. For example, this picture shows the numbers 77 and 145 in base ten blocks:

Base ten seems pretty simple to us as people using the system everyday, maybe without knowing it, but to break it down, lets look at the number 145. In this case lets start out imagining 145 single units, the smallest squares, which each represent one. Now if we simply had a bunch of units sitting there together it would take a while to count them all up to figure out how many we have total, so instead we will group them into sets of 10  (base 10, get it?). Now we have 14 sets of ten (rods) and 5 remaining units. Since we are using base ten, can we make any more groups of ten? Yes! We can make one group of ten out of our rods to make one group of what would be 100 individual units (a flat). When you lay our 1 flat, 4 remaining rods, and 5 remaining units together, you still have 145 units in separate groups, and them we can write it out as 145, where the 1 represents the number of flats, the 4 represents the number of rods, and the five represents the number of units. 1-4-5.

     When each step to our base ten system is explained, it sounds pretty complicated, but once you have the system down, you can do the same thing in any base! For example, lets try base four using the same number. if we have 145 single units, how many groups of four can we put them into? We can make them into 36 rods, with one unit remaining. Ok, now how many groups of 4 can we put those 36 rods into? 9! So now we have 9 flats, 0 rods, and one unit. In this case we are going to need a block that is bigger than a flat, so we have our cubes. Now how many groups of 4 can we group our flats into? 2, with one flat remaining. So our final base blocks are going to be 2 cubes, 1 flat, 0 rods, and 1 unit. So if we were to describe the number we like to call 145 in base four instead of base ten it would be 2101!

     Switching bases can be pretty confusing at first, but I found this great online tool, Base Blocks, where you can have virtual base blocks of any number and it will even give you problems to practice on!