```Multiplying and Factoring Polynomials Using Algebra TilesMarshall, Regina                Curie Metro High School                                838-4050                           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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