On Monday, Renata was out sick and I got to do math all by myself. First we worked in Singapore books, then we did modular origami. I taught those who hadn't learned yet how to make a Sonobe unit (less technically known as a "box side"). Six units can be assembled to make a cube. More units can be assembled to make other things.
We also made sure everyone was familiar with the Fibonacci sequence, which is the sequence of numbers
1,1,2,3,5,8,13,21,34,55,89,...
The first two numbers are predetermined. To get each number from the third number on, we add the previous two numbers. The next number if we continue the sequence above would be
55+89 = 144.
Today, Tuesday, we reviewed how to write numbers in base 3. It can be helpful to break the numbers up first - for example, to write 17 in base 3, first we notice that
17=9+6+2
and then we can write 17 in base 3 as
122.
We also broke numbers up into sums of Fibonacci numbers. The rules:
- Use the biggest Fibonacci numbers you can
- No Fibonacci number may be used more than once.
Some examples:
11=8+3
12=8+3+1
40=34+5+1
We wouldn't write 40=34+3+2+1, because we can write 5 instead of 3+2, and the first rule says we should use the biggest Fibonacci numbers we can. We also wouldn't write 12=8+2+2, because we're not allowed to use any Fibonacci number more than once.
The kids also came up with their own Fibonacci-type sequences, by deciding what they wanted the first two numbers to be, adding those to get the third number, and so on.
Here they are writing their sequences up on the board:
And here are the completed sequences:
Finally, here's Maria's origami "other thing," using 12 units:
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