Expressions
The same quantity can be written as 3(x + 4) or as 3x + 12. What are the rules for changing one form into another without changing its value?
Where you are 12 inside
What this area is about
An expression is a calculation with letters in it, such as 15(g - 3) + 30. It has no equals sign and claims nothing; it stands for a number once its letters do. This area is about reading expressions and rewriting them by the rules of arithmetic, so that the new form gives the same value for every number put in.
How these fit together
Reading. Variables says what a letter can stand for and names the parts of an expression. Evaluating expressions and formulas puts a number in and computes. Interpreting the parts of an expression reads terms and factors as quantities in a story.
Equivalence. Equivalent expressions defines when two forms agree for every value. Combining like terms, the distributive property and distributing, then combining are the moves that keep that agreement. Rewriting to show meaning chooses the form that answers a question, as 1.09p does for p + 0.09p.
Products. Monomials and the exponent rules and multiplying two binomials.
Factoring, the distributive property run backward: the greatest common factor, then grouping for four terms with no factor common to all.
A path through it
Variables first. Then evaluating, equivalent expressions and monomials; combining like terms; the distributive property, then interpreting parts. After the distributive property: distributing and combining, binomials, rewriting for meaning, and the greatest common factor, with grouping last.
After this: linear equations and polynomials.