Multiplying and Factoring Polynomials Using Algebra Tiles

Marshall, Regina                Curie Metro High School
4219 W. 21st                    838-4050
Chicago, IL 60623 
762-4450

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