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
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