How does balancing on a board relate to mathematics?

Answer 1

This depends on how you meant the question -- "How does mathematics help me balance something on a board" versus "why is mathematics like balancing on a board"

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"How does mathematics help me balance something on a board?"

Balancing on a board is a study in Physics, and mathematics is the language of Physics (and essentially all of the other sciences as well).

Mathematics is how scientists and engineers MODEL and DESCRIBE what is happening in the world.

By calculating the different weight and the different distances from the balance point to the place on the board where the weights are attached, you can figure out whether or not they will balance -- like this:
http://library.thinkquest.org/27948/lever.html

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"Why is mathematics like balancing on a board?"

If your teacher was just explaining that a mathematical equation is like balancing on a board and you were wondering what the connection is, the answer from the first person is correct -- let me explain a bit further:

Imagine a board, balanced on a point. That point is the equals sign, and there are expressions to either side of it just like there is a length of board to either side of the balance point. There is some weight (one expression) on one side, and some weight (the other expression) on the other side.

It doesn't matter how you express the weight on each side, it is the same thing:
16 ounces = 1 pound

If you have 16 ounces on one side of the board and 1 pound on the other, it still balances. They are different ways of saying the same thing.

If you add the same weight to each side (assuming the original sides and weights are the same as each other), the board remains balanced. In the same way, you can add the same number to both sides of the equation and it will remain balanced:

16 ounces + 1/2 pound = 1 pound + 1/2 pound

You have added the same amount to both sides, so it stays balanced. By the same token you can do this:
3*x - 5 = 40
3*x - 5 + 5 = 40 + 5
That allows you to simplify things by adding the bits together on each side to come up with:
3*x = 45

If you multiply or divide the weight on each side by the same amount, the board stays balanced.
Divide the 16 ounces + half a pound on one side by 3, and the 1 pound + half a pound on the other side by three. You end up with half a pound (8 ounces) on each side:
16 ounces + 1/2 pound = 1 pound + 1/2 pound
(16 ounces + 1/2 pound) / 3 = (1 pound + 1/2 pound) / 3
(16 ounces + 8 ounces) / 3 = (two half-pounds + 1/2 pound) / 3
24 ounces / 3 = three half-pounds / 3
8 ounces = one half-pound

Similarly you can do the same with variables:
3*x = 45
(3*x) / 3 = 45 / 3
1*x = 15

That is explained a bit more here:
http://www.syvum.com/cgi/online/serve.cgi/squizzes/algebra/equations.html?0

Answer 2

I would think it is like an equation in Algebra that has to be balanced.

Answer 3

it relates to math because you have to calculate gravity and weight and force.