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"Let us strive to make each moment beautiful."
Saint Francis DeSales
painting by Katie Bergenholtz

Base Six Math

Have you ever thought about using numbers with bases other than 10? 
The concept of place value involves the notion of grouping numbers or amounts of objects.
This is true for all bases.
We played a game in which we grouped by sixes instead of tens, and then used this to establish a more broad concept of place value.

The rule for this game is that no one can use the word six (or whatever number you use as your base.) You use a nonsense word instead. Have them make up the word.
My boys came up with the word googa.
Then we placed counters down and counted to five and then the next counter was called googa.
Each time this counter was reached, we cleared the table and the counting started over.

Once they got used to counting in this way, we started counting on a dry-erase board instead, with a line down the middle. We counted directly on the board with the ones on one side and the googas on the other. We then wrote numerically on the side.
Next we practiced counting forwards and backwards in base 6 using cups and beans.
After we had done this for awhile, we recorded these numbers on paper so that they may be examined for  patterns.
Can you see where he made a mistake, and then tried to erase it?
It is easy to see when you make a mistake when you look at the patterns.
This can also be done with colors, each place value equalling a different color.
It can be done with colored counters, colored squares of paper or on a sheet of large-block graph paper.


5 comments:

  1. My math crazy son would love this

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  2. We had to do a similar activity when I was in college to show us how hard it is for kids to learn math. I thought it was the funnest thing ever.

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  3. The funny part about it is that the boys had no trouble with it and kept rolling all over the place laughing. They had no trouble with the concept of a differing base system.

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  4. I can see where that would be a lot easier for children than adults. I can feel a pain beginning behind my eye, just thinking about it :)

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  5. Oh, I remember doing a "Math Their Way of Thinking" workshop (any Marylin Burns fans out there?) in college where we worked with different bases. That was when I realized I actually understood the WHY and HOW behind multiplication...

    Working with different bases is IMPORTANT for kiddos...wish I had been taught that way as a child!

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