Mathematical Operations

     A child in a Montessori class learns mathematical facts by actually performing the operations which concrete materials. When the child wants to do arithmetic, she is given a sheet of paper containing simple problems. She works these problems with appropriate materials and records her results. Similar operations can be performed with a variety of materials. This variety maintains can be performed with a variety of materials. This variety maintains the child's interest while giving her many opportunities for the necessary repetition. As she commits the addition facts and the multiplication tables to memory, she gains a real understanding of what each operation means. In a Montessori classroom there are many materials that can be used for adding, subtracting, multiplying and dividing.

THE SHORT BEAD STAIR

     The Short Bead Stair represents the quantities One through Ten in easily recognized colors. A single red bead represents 1. A bar of two green beads represents 2. A bar of three pink beads represents 3, and so forth, with the bar of ten golden beads representing 10. If a child wishes to do the sum 4+6, she places the of four yellow beads beside the bar of six purple beads, counts the total number of beads and records her results; 4 + 6 = 10.

THE SQUARING AND CUBING MATERIAL

     This same color scheme is used for the beads that make up the squares and the cubes of the number 1 through 10. For example, 5² is represented by 25 blue beads fastened together in a square. 5³ is made up of 125 blue beads fastened together as a cube. The square of 5 is also represented by a chain of five bars of 5 blue beads, the cube by a chain of twenty-five 5 bars. The chains are used for skip counting (in this case counting by fives) and for learning the squares and cubes of the numbers 1 through 10.

MULTIPLICATION

     The colored bead bars are also used for multiplication. If a child wants to multiply 3 x 5, he takes three of the blue bars with five beads on each and places them on a small mat. Then he counts the total number of beads and records his result: 3 x 5 = 15. Working with this equipment gives him a real understanding of what the term multiplication means; in this case the quantity of 5 is actually taken three times.

SUBTRACTION

     The child can use Unit beads for simple subtraction. To do the problem 9 - 3, she puts nine Units on a small felt mat, and then removes three of the Units. She counts the remaining Units and records her result: 9 - 3 = 6.

     Quite often a child will learn subtraction facts by simply reversing the addition combinations 4 + 4 = 8; therefore 8 - 4 = 4.

THE DIVISION BOARD

     A square board with green skittles and beads is used for simple division. The skittles represent the divisor or the number of people who are sharing the quantity. To do the example 12 divided by 3,  the child puts three skittles at the top of the board. Then she carefully takes twelve beads and shares them one by one. Each skittles gets four beads. She records: 12 divided by 3 = 4, because each skittle has four beads.