Our oldest students (those who will begin grade one in September) have been doing a lot of work with the Mathematics exercises which focus on the memorization of the four operations - Addition, Subtraction, Multiplication and Division. They have a firm grasp of their addition and subtraction facts and are now focussing on the memorization of their multiplication and division facts. One of the materials used for the introduction and eventual memorization of division facts is The Unit Division Board.
This is a picture of the Unit Division Board material. It consists of a board with eighty-one little indentations, eighty-one green unit beads, nine green skittles and a green cup.
As with all Montessori lessons, the language used is very specific. In the simpliest terms, division is sharing a quantity evenly. Keeping this in mind, the green unit beads seen in the above photograph represent the dividend, the quantity we will attempt to share evenly. The green skittles seen in the above photograph represent the divisor, the number of people we will share our dividend with. Our answer is the quotient. The quotient is what one person gets. The remainder is any amount that cannot be shared equally. Note that the remainder cannot be larger than the divisor.
To illustrate how the board is used, we have opened our Division booklet to a dividend of 49.
With a dividend of 49, the child would place 49 green unit beads into the green cup. The child would begin with a divisor of 9. The child would place 9 green skittles across the top of the board.
After the child has shared the beads 5 times, s/he realizes that there are only 4 remaning in the green cup. This is not enough to share evenly with 9 skittles. In his/her Division booklet the child writes a quotient of 5 with a remainder of 4.
The next question in the Division booklet is 49 divided by 8. The child would remove one of the green skittles and share the 49 unit beads.
When the child has shared the beads 6 times, s/he is unable to continue as only 1 bead remains in the green cup. In his/her Division booklet, the child writes a quotient of 6 with a remainder of 1.
When the child shares 49 beads with 7 skittles, the beads are shared evenly with no remainder.
In his/her Division booklet the child writes a quotient of 7 with a remainder of 0.
The Division booklet enables the child to explore dividends from 1 to 81 and is done over a period of time.
Here are some photographs of a child working with this material. He is working with a dividend of 4.