**MULTIPLICATION CHARTS AND COMBINATION CARDS
**

a.

__Passage from Chart I to Chart II__

The child copies Chart I. Later with the teacher or a group of children, they try to find those combinations which can be eliminated, that is, those which have like factors and equal products. Look at the first column 1 x 1 = 1 must remain. 1 x 2 = 2 and 2 x 1 = 2 are the same. 2 x 1 = 2 is crossed out. ( Or the combinations to be eliminated may be covered with green strips of the appropriate size) As in addition we can change the order of the multiplier and multiplicand, eliminating many combinations. At the end we find that half of the chart is eliminated giving us Chart II. The combinations of two equal factors were not eliminated1 x 1 = 2, 2 x 2 = 4, 3 x 3 = 9This was the same case in addition. Chart II has only 55 combinations to be memorized. (We can make the child see that only 45 of these must be memorized, as the table of ten is simply a repetition of 1)

b. __Passage from Chart II to Chart III (the Whole Chart)__

**Materials**:

…Chart III (products only- the numbers in pink serve as the multiplicand, blue as the multiplier; the one should be colored violet. -xAlong the diagonal are found the squares of the numbers)

…box of combination cards

…Chart I or II

**Control of Error**: Chart I or II

**Exercise**:

The child fishes for a combination, writes it down on a piece of paper 5 x 7 =. A finger of the left hand is placed on the 5 (pink) while a finger of the right hand is placed on the 7 (blue). Where the fingers meet, the product is found. This is written on the paper to complete the equation. The child fishes for another combination, and so on.

c. __Passage from Chart III to Chart IV (the Half Chart)__

**Materials**:

…Chart IV (half of Chart III)

…box of combination cards

…Chart I or II

**Exercise**:

The child fishes for a combination and writes it down 8 x 3 =. I know that 8 x 3 gives me the same result as 3 x 8. One finger is placed on 3, another on 8 (both on the pink column) The top finger goes to the end of the row, then the two fingers come together. Where they meet, we find the product. This is written down. The child fishes for another combination, and so on.

**Control of Error**: Chart I or II

Note: At his point, to verify memorization, the child may be given command cards.

Example:

Find these products:
2×3= etc. and their inverses |

d. __The Bingo Game of Multiplication (using Chart V)__

**Materials**:

…Chart V

…box of tiles with products

…(a) box of combination cards

…Chart I and III

**A. Exercise**

All of the tiles are lain out on the table face up. The child fishes for a combination and writes it down 8 x 4 =. He thinks of the answer and writes it down. The tile with the product is found and placed on the board. The child fishes for another combination.

Control: Chart I for combinations, Chart II for placement.

**B. Exercise**

With all of the tiles in the box, the child fishes for a tile. On the paper he writes down a combination that will yield that product, 18 = 3 x 6. The tile is placed on the chart appropriately.

Control: Charts I and III.

**C. Exercise**

All of the tiles are placed in stacks of common products. The child chooses one stack, i.e. 12’s. On the paper he writes down a combination that will yield 12, 12 = 2 x 6. One of the ’12’ tiles is placed on the chart where 2 and 6 meet. The child thinks of another, and continues until all of the tiles in the stack are used. Control: With Chart 1, we can check to see that all possible combinations have been considered.

Chart III controls placement.

Note: What shape is made when the stacks of tiles are lined up in order? No special figure is made this time.

**Group Games:**

As before the teacher may read a combination, the child responds with the correct product; or the teacher picks a tile. The children give all of the possible combinations. These games should be done frequently, as they encourage the child to go back to these exercise if he needs more practice.

Age: from 6-7 (this work lasts for one year)

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