Algebraic fractions, rational expressions and equations, are studied in the later part of every algebra I course. They are not enjoyed unless students are good at factoring. They are long, messy, problems (half a page or more in length vs a quarter or eighth per page for easier problems). They are useful for studying rational function in precalc, limits in calc I, and the mostly ignored partial fraction of calc II. Some algebra I students never "get it." They don't have the writing skills and factoring skills and perseverance for the completion of the problem. For these Term Tiles & Token introduce and reinforce the algorithm, make factoring easier, and facilitate the recording of work. For these, manipulatives are most important. Other students have already "outgrown" their use. Term Tiles, Multiple Strips & Fraction Bars are suited for manipulative rational computation. Fraction Bars, FB, are for arithmetic computation and Term Tiles, TT, are for both arithmetic and algebraic rational computation. Below the manipulative and topics are matched with their best use.
Info on Multiple Strips and Fraction Bars is found at www.mathnstuff.com/math/spoken/here/2class/60/mult.htm. Below is a sample. A three strip (showing the three times table results in order) is paired with a 4strip (showing the 4 times table results in order) to form a 3/4 strip. In the same way a 2/5 strip is created. The strips are aligned at the least common denominator to permit addition. Term Tiles do not permit the variety and complexity required of in depth use of algebraic fractions. The basic tiles include only the x³ tiles and x² tiles and x tiles and 1 tiles. Expressions like 4x²yz are not possible. The algorithms, and therefore Term Tile method, for multiplication and division are very different from those of addition and subtraction. Each method is consistent with algebraic computation.
