Storing tiles in sorted piles is suggested for the following reasons.
 In algebra, answers are usually written in descending order. Sorting tiles in descending order
parallels this practice if tiles are ordered from left to right.
 Grouping tiles of the same type emphasizes that they represent different kinds of terms. Constants are
not linear or quadratic or cubic terms. This means the constants, the x terms, the x² terms, and the x³
terms are different even though one might have the same number of each.
 Creating piles of many tiles visually differentiates them from the displayed tiles of a phrase, equation,
or answer which requires individual tiles of pairs of zeros.
For addition and subtraction, a display area created by an additional sheet of
paper is suggested. For multiplication, division, and factoring it is even more important. For solving
equations and inequalities and addition or subtraction of fractions, two display areas are required.
There are a variety of ways to manipulate the tiles and a variety of situations in
which movement is required.
Writing expressions or equations is the most mentally taxing operation. Simplifying
expressions and solving equations or inequalities are not nearly as difficult. WHEN WRITING OR
REPRESENTING EXPRESSIONS OR EQUATIONS PERMIT THE MOST FLEXIBILITY.
Once the expressions is represented, SIMPLIFY THE EXPRESSION FROM
LEFT TO RIGHT to foreshadow the way in which written expressions are simplified.
This lefttoright manipulation might be discussed with a class or simply
modeled by the teacher as the teacher discusses the math that is being performed on the tiles.
SOLVE AN EQUATION WITH TWO HANDS OR FROM LEFTTORIGHT WITH ONE HAND. This will
be discussed in greater detail when solving equations is discussed.
