Counting with marbles...
Our first un-automate adventure is a fun, clever alternative to the old abacus.
Basic idea:
The Table to the left shows the basic layout of the counting tray.
notice the rows labeled 1, 4, 16, and 64. also note how the cells have a max of 4 marbles in each.
The filled column contains the value 340. But how?
The Trick is those numbers show how much a marble in that row is worth.
64*4=256
16*4=64
4*4=16
1*4=4
256+64+16+4=340
Carrying couldn't be simpler:
Notice the Table with the 4 marbles in the 1 row. say we are done adding and want to optimize our table.
What we can do is simply add a marble to the 4ths row since its available, and remove the 4 marbles from the 1nes row.
If you want to count by say 5s, you would add 1 marble to row "4" and 1 to row "1", repeat this in adjacent columns as needed.
you could even multiply by 4 by shifting each row up.
Don't have marbles or a tray handy? you can use a paper grid, and perhaps paper clips?
Or you could go all out and make a fancy counting tray out of wood with plenty of rows and columns.
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