# Applying Turing Tumble to Algebra 1 or Algebra 2

Our school hasn’t gotten our Turing Tumble yet (we’re still working on getting Upper Story to become an approved vendor). But, I wanted to see if anyone has thought about what I’d like to try with it.

Is it possible to act out Algebra 1 or Algebra 2 concepts with the Turing Tumble? Any concepts that I could tie to my state standards for Algebra 2 would be great. For example, maybe exponents or logs?

Thank you!
Kevin

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Algebra is a bit too complicated for TT, mainly because there is not enough space on the board to accommodate all the values and logic. Unfortunately, you can’t just buy more sets and get more space because you can’t link the boards together. However, you can easily fit simple math and logic like addition, subtraction, and lots of logic gates. You can even do multiplication as long as you use small numbers, and division with a hard-coded divisor.

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The functions log_2 and 2^x are clearly linked to TT. How many bits would you need to use to build a counter up to N? (log_2 N). How high can you count with these N bits? (2^N). So, asking what is the largest number that they can count up to and stop (if they have enough parts) could be a good exercise. Some kids might try to build it. Or, you could just reason it out based on the number of bits you have available, and the height of the board, whichever is smaller, and take into consideration the space needed for an interceptor.

Perhaps you could get them to solve some simple linear equations. Implement the function 4*n, where n is set in a column of bits. Cover up the counter to 4 (which is used to multiply) with a piece of paper taped over it loosely, then have them set the n bits to a value (say 7) and observe the output (28). From this, they need to write the equation 7x=28, where x is representing what is hidden. When they take off the cover, surprise… there are two bit pieces, so x is 4.

Here’s a question: using multiplication, what is the largest value they can multiply up to using a stack of x bits and a stack of y bits?

Another: if I give you n bit pieces, using multiplication of a stack of x bits and a stack of n-x bits, what is the largest value you can multiply up to? (2^x times 2^(n-x) will always be 2^n, so it shouldn’t matter - a nice surprise!) To discover this, give them, say, 8 bit pieces, and have different kids build an x times y counter, where x+y=8, for different values of x and y. Ask them to see how high it counts (multiplies). They should all get the same answer. Why? (Again, 2^x times 2^y = 2^8 in every case.

That’s all I got for now.

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This is great!

Thank you!