If you talk to almost any elementary teacher about math, place value will come up as a topic. Place value refers to our number system. We have ten digits: 0,1,2,3,4,5,6,7,8,9, and indicate the value of those digits with their placement in a number. The 9 digit in 2,974, for instance, is worth 900. Undoubtedly, the reason we have ten digits in our counting system is that we have ten digits (otherwise known as fingers) on our hands.
The problem with place value is that it is hard for young children to understand such an abstract concept. They can often tell you that the 9 is worth 900, but they don't have any idea of what 900 means and they don't really understand that place value is a thing.
To counter this, this year we have done some counting in other bases. This is Drago:
Drago teaches math to dragons and speaks with a terrible Russian accent. He has three digits on each hand and he has a problem. In his number system, he uses tally marks:
Drago finds that math with tally marks takes a long time and is very awkward. The children taught Drago to count like this: 1, 2, 3, 4, 5, 10. Like us, the last digit on his hand has a value of ten. Mathematicians would say that Drago counts in base 6.
Jake
Sir Sloth-a-lot
Parrot (as yet unnamed)
The problem with place value is that it is hard for young children to understand such an abstract concept. They can often tell you that the 9 is worth 900, but they don't have any idea of what 900 means and they don't really understand that place value is a thing.
To counter this, this year we have done some counting in other bases. This is Drago:
Drago teaches math to dragons and speaks with a terrible Russian accent. He has three digits on each hand and he has a problem. In his number system, he uses tally marks:
Drago finds that math with tally marks takes a long time and is very awkward. The children taught Drago to count like this: 1, 2, 3, 4, 5, 10. Like us, the last digit on his hand has a value of ten. Mathematicians would say that Drago counts in base 6.
Drago continues counting like this:
1,2,3,4,5,10,11,12,13,14,15,20,21,22,23,24,25,30... but when does he get to 100. I'll leave that for you to think about, but feel free to check in with me or leave a comment if you think you have it right or just plain get stuck.
In base ten, we use place value blocks to help us understand what is happening when we "operate" on numbers. They look like this:
Drago wanted to take some place value blocks back to his students, but of course, they had to be in base six. The children drew them like this (not all attempted the thousands block):
The results were, quite frankly, thrilling. Every single child could count in base six and almost all of them could independently draw ones, tens, and hundreds blocks.
The next day, the children met some new characters. We used their digits to count too and made more blocks in their bases.
JakeSir Sloth-a-lotParrot (as yet unnamed)
Some children, by the end of the second day, were even attempting to add in different bases. WOW!
Next week, we will return to looking at base 10 and it is my hope, that the children will begin to appreciate our counting system in a new way and will be more open to seeing the patterns and inherent beauty in our number system.
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