Multiplying and Factoring Polynomials Using Algebra Tiles

Marshall, Regina Curie Metro High School

Objectives: To eliminate the frustration and anxiety involved with Multiplying and Factoring polynomials through the usage of Algebra Tiles. Upon achieving this, accuracy in the operations will be reach. Apparatus needed: 1) Algebra Tiles 2) Math-Tiles display board 3) A collection of students labsheets Recommended strategy: Math is a frightening subject to most people. I feel that it can be due to an infinite amount of reasons, but the one reason cited most is the fact that it is a precise science. Either you have the right answer or the wrong answer. Thus most individuals tend to steer clear as much as possible away from it. Having knowledge of the above mentioned fact I would start out by playing a game called "The Rectangle game." In brief, you give the students a random number of blue, red, and yellow tiles. Then give the following instructions "make the largest rectangle you can using only these tiles." In some instances you may need to add these clarifications to the directions: (1) All tiles must lie flat on the board; (2) Only one layer of tiles is allowed; and (3) the rectangle must be entirely filled in. Once they have experimented and experienced this game they are expected to develop a strategy for rapidly arranging the tiles to create the largest possible rectangle. (For us, "the largest" means largest in area.) Using this meaning, the largest rectangle will always be the one that leaves the least amount of "left-over tiles." After the students have been stimulated by playing "The Rectangle game," I would then proceed to give the tiles names that are associated with their area. The correlation will be geometrically displayed on a poster board. Once the students have received the naming of the tiles, I would then proceed with my introduction to the multiplication of polynomials. It is extremely important that they can visually see the process of putting the factors to be multiplied on the outer vertical and horizontal space provided with the simulated Mathtiles display board given to them, and how to create the rectangle in the innermost space. It must be emphasized that the length and width are determined by the factors on the outer horizontal and vertical spaces. Also, when creating the rectangle in the innermost space, use the strategy develop with "The Rectangle game." Once you have given the students a sufficient amount of time to make the innermost rectangle, list what particular tiles were used. Show the actual problem that they did on the board making sure they understand the procedure for doing this. I would then make sure that I do a wide variety of problems to make the students analyze their results. A labsheet parallel with the topic of multiplying polynomials will then be pass out. Having sufficiently motivated the students to get involve, I would then proceed to show the students how to factor polynomials using this truly wonderful manipulative. It's in factoring polynomials that the mathtiles will perhaps provide you with the greatest rewards. The tiles make factoring so easy that difficult problems turn into simple puzzle-type exercises. In fact, the students will see that "The Rectangle game" was actually an exercise in factoring second-degree polynomials. Hopefully, with the usage of manipulative students will in time began to understand and accept math without all of the fear that has been associated with it throughout the years. References Material: Mathtiles Manual Book by Peter Rasmussen
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