Basic Mathematical Operations Using Mathtiles

Jones, Claudia R.             Farragut Career Academy
                              (312) 762-2421
                           

Objectives:

Using a concrete model, MATHTILES--
    1.  The students will be able to do addition-
    2.  The students will be able to do subtraction-
    3.  The students will be able to do division-
    4.  The students will be able to do multiplication-
of whole numbers, which will enable them to develop better math 
skills with the use of these manipulative materials.

Apparatus Needed:

Six (6) sizes of MATHTILES, which includes the following sizes -- Unit 
tiles or 1-tile (1x1); 5-tile (1x5); 10-tile (1x10); 25-tile (5x5); 
50-tile (5x10); 100-tile (10x10).  One display board, MATHTILES 
Manual, Overhead projector, magnetic tape, posterboard, transparency 
sheets, pen to use with the overhead projector, and Labsheets for 
addition, subtraction, multiplication and division. 
     The six sizes of Arithmetic Tiles used as visual aids in my Mini-
Teach were cut out of plexiglass in the lab.  The posterboard was 
laminated at 1819 W. Pershing and then I used a scale of 1/2 inch to 
an inch to cut out the manipulatives that were used by the class to do 
the mathematical operations on the labsheets.
   
Recommended Strategy:

     The class will begin with an explanation by the teacher of the
kinds, values and uses for the MATHTILES in the classroom.  Students 
will learn that MATHTILES are manipulative learning materials designed 
to be used in Arithmetic and Algebra and that they can be used at many 
levels, second grade through high school. 
     There are two kinds of tiles:  the Arithmetic Tiles which consist
of all the rectangles which can be built with sides measuring either
1, 5, or 10; and the Algebra Tiles which includes all the rectangles
whose sides are either 1 or X, where X is not a whole multiple of 1.
The Algebra Tiles will not be used in this lesson since we are doing
the basic mathematical operations of addition, subtraction, multipli-
cation and division.
     The six sizes of Arithmetic Tiles in the set are used to 
represent whole numbers.  The value of an Arithmetic Tile is the 
number of unit tiles needed to cover it.  For example:  The 1-tile or 
unit is (1x1); 5-tile is (1x5); 10-tile is (1x10); 25-tile is (5x5); 
50-tile is (5x10); 100-tile is (10x10).  At this point, the teacher 
will display the different sizes of tiles on the blackboard and also 
pass out a sheet showing the tiles and the value of each. 
     Discussion will continue and the teacher will describe the 
different things that you can do with MATHTILES, such as:  Finding the 
value of groups of Arithmetic Tiles; Predetermining values; Trading 
groups of tiles to solve problems; Computing addition, subtraction, 
division, and multiplication. 
     The teacher, with students helping, will do samples of each of
MATHTILES basic operations on the overhead projector; also an 
explanation will be given at each stage of the operations on the
procedure to follow while working with the MATHTILES.  For example:  
when trading tiles, students will be made aware of the restrictions 
that permit trading only between groups of tiles that have the same 
value.  You can trade a 5-unit tile with a 5-tile when needed, just as 
you exchange 5 pennies for a nickel. 
  
Procedures:

     ADDITION--when adding, represent each number to be added by a 
group of tiles.  Then combine these groups into one group.  The 
combined groups of tiles then represents the sum. 
     SUBTRACTION--when subtracting, only set out tiles to represent 
the first number in the problem.  Then take away tiles representing 
the second number.  The group of tiles remaining is the answer. 
     DIVISION--when dividing, display the product on the surface of 
the display board and the known factor along the vertical edge of the 
board.  Then use the tiles on the board's surface to build a rectangle 
having one dimension as indicated by the tiles along the edge.  Then 
we place additional tiles along the horizontal edge of the board to 
measure the rectangle's second dimension.  This length is our missing 
factor.  Division problems are computed using the MATHTILES Board. 
     MULTIPLICATION--multiplication problems are done on the MATHTILES 
Display Board.  The two numbers to be multiplied are shown by placing 
tiles in the grooves along the left and bottom sides of the board. 
Then a rectangle with these dimensions is built on the flat surface of 
the board using additional tiles.  The area of this rectangle is the 
product of the two numbers to be multiplied. 
     Throughout the lesson and at each step, students will be given
Labsheets to do the computations for practice.  Students will work
at their own pace since it is not necessary that every problem on
the Labsheets be done.
     Complete Classroom Sets with 180 reproducible labsheets is
available from--Key Curriculum Press
                1150 65th Street
                Emeryville CA 24702
                (888) 877-7240