I think of algebra as a meta-math skill since it allows you to manipulate, simplify, or otherwise make use of structure in mathematical expressions. The most

I think of algebra as a meta-math skill since it allows you to manipulate, simplify, or otherwise make use of structure in mathematical expressions. The most important rule is the "do the same operation on both sides of the equation"-rule, but there are plenty of other "math verbs" that are useful: expand, factor, simplify, collect, etc. Interestingly, any expression in the computer algebra system SymPy has these methods: http://live.sympy.org/?evaluate=(x%2By)**2%0A%23--%0A((x%2By)**2 http://live.sympy.org/?evaluate=(x%2By)**2%0A%23--%0A((x%2By...).expand()%0A%23--%0A