# M8.4.12

**symbolic statements in mathematics can be manipulated**by rules of mathematical logic to produce other statements that preserve the basic relationships but are more easily interpreted.

### Proving the Pythagorean Theorem

A guided classroom exercise that contributes to the long-term development of creative thinking and analysis.

### Finding All Solutions to a Puzzle

The non-zero digits can be organized into a 3-by-3 array such that each row, rneach column, and each diagonal adds up to the same total. How many solutions rnare there? Find and describe them.

### Grandpa's Social Security

This simple example shows how algebra can be useful in the real world: Should Grandpa start receiving his Social Security Benefits at age 62 or should he wait until age 65?