a. Introduction and List of Materials:
The child has encountered multiplication before. The first impression was given with the number rods, finding that the double of 5 is 10. Later with the decimal system material, the child learned that multiplication is a special type of addition. In the exercises that follow this concept will be reinforced and the child will be given the chance to memorize the necessary combinations.
…Bead Board, and corresponding wooden box which contains:
xx….100 red beads (the product), numeral cards of 1-10 (the multiplicand), and
xx.xone red counter (this, when placed by one of the xx…numerals 1-10 across the top, indicates the multiplier).
…Booklet of Combinations (10 pages of 10 combinations each)
…Box of Multiplication Combinations (same combinations as are found in the booklet)
…Box of green tiles for bingo game
…Multiplication Charts I-V (for control)
b. Initial Presentation:
To familiarize the child with the materials, the teacher suggests a problem and writes it down, i.e. 3 x 4 = (three taken 4 times). The 3 numeral card is placed in the slot. The counter is placed over 1 as 3 beads are placed in the first column…(Attempt to get children at this point to be counting by threes up to whatever level they are capable, in place of counting every bead.) …’three taken one time…’ As the three beads are placed in each column, the counter is moved along, until ‘…three taken four times…’ We’ve taken 3 four times, what is the product? The beads are counted and the result is recorded.
c. Multiplication Booklets
…Bead Board, and box with beads, cards, counter
…Chart I (for control; a summary of the combinations found in the booklet)
Control of error: Chart I
(Starting with 1 is a problem because it doesn’t give the concept of multiplication) Start with any other unit like the number 3. The numeral card is placed in the slot. The child reads first combination 3 x 1 Three beads are placed in the first column with the counter over the numeral 1. The child records the answer in the booklet. The next combination is read: 3 x 2 =. The counter is moved over and three more beads are added. The product is recorded in the booklet. At 3 x 3 = the child should notice the geometrical form created when the multiplier and multiplicand are equal. If he doesn’t, the teacher may set up a situation wherein he may easily make the discovery himself forming several doubles in a row.
Note: In the material the child ends his work with the table of 10, rather than 9 as was the case in addition and subtraction. This is to show the simplicity of our decimal system. The table of 1 is very similar to the table of 10. It differs only in the presence of zero.
d. Combination Cards
…Bead Board and box with beads, cards, counter
…box of loose combinations
…Chart I (for control)
Control of error: When the child has finished his work, he controls with Chart I. This control reinforces memorization of the combinations.
To facilitate the child’s work in this exercise, the number cards used to indicate the multiplicand are arranged in a row or column on the table. The child fishes for a combination, 3 x 9 =, reads it, and writes it on his paper. The number card 3 is placed in the slot, the counter is placed over column 1; 3 beads are placed in the first column. The counter is moved to column 2, as three more beads are placed in that column, making a subtotal of 6. This continues up to 9. The result of 3 taken 9 times is 27. This product is written on the paper.
NOTE: In the beginning the teacher should supervise the child’s work to see that he skip counts the beads as he goes along3, 6, 9, 12, 15, 18, 21, 24, 27. For if the child counts the beads one at a time when he is finished, he will never memorize the combinations.
The child removes the beads, number card and counter and fishes for another combination.