The multiplication table consists of the 100 combinations of single digit multiplication problems. These are known as the primary multiplication facts, and many children have difficulty with them. However, they must be memorized if children are to be successful in mathematics beyond the third grade level. This importance is increased by the fact that we must to know how to add in order to be able to multiply, and how to multiply in order to be able to divide. Furthermore, we must know how to subtract in order to be able to divide. So, all these operations are very closely connected. This is sometimes fereffed to as a heiarchy of learning.
The multiplication facts are best learned by repeated use. Following are some suggestions for ways to provide repeated use.
1. Divide children into pairs.
2. Each pair of children should have two decks of cards with the digits 0 through 9 on each deck.
3. One child draws one card from the first deck and one card from the second deck, and shows them to the other child.
4. The other child multiplies the two numbers together and enters them into a multiplication table like the one below.
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X |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
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0 |
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1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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56 |
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8 |
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56 |
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9 |
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1. Be sure to note which card comes from which deck. If, for example, an 8 comes from the first deck and a 7 from the second deck, the product goes in the cell occupied be the red 56. On the other hand, if a 7 comes from the first deck and an 8 from the second deck, the product goes in the cell occupied by the green 56.
2, The distinction required by note 1 illustrates the commutative property of multiplication. That is, the order in which the factors appear is different, but the product is the same.
3. When all 100 cells are filled you have a multiplication table, which is sometimes called the 100 primary multiplication facts. However, do not attempt to fill in the entire table solely be drawing cards. The more entries you make in the table, the less likely you are to hit an empty cell on the next draw. At some point, the teacher needs to see that the remainder of the table is filled in so the children can use it.
4. The primary facts must be memorized if one is to be able to multiply together any two given numbers. However, using the table to multiply provides the needed repetitive drill needed to do the memorization. So, my advice is: Let children construct and use the multiplication table until the table is committed to memory.
5. The experiment can be conducted with number cubes instead of cards.
6. A similar experiment can be done at an earlier stage to construct an addition table.
7. A multiplication table is also used to divide, and an addition table is also used to subtract.
Obviously, some primary multiplication facts cause more trouble than others for young learners. No drill is needed for multiplying by 0 or 1, and very little is needed for 2. The most difficult, of course, are the products when 6 or higher is involved. Multiplication tables can be abreviated to meet the needs of particular children instead of requiring unnecessary drill on the smaller numbers. Thus, this technique can be used at many different grade levels to provide for individual differences.
The following table includes some practice with the more difficult parts of the multiplication table, and some practice with multiplication and division problems. The entire table can be completed from what is given. This type of sheet can be quickly constructed to fit the needs of individual students in grades three and higher.
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X |
6 |
8 |
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9 |
4 |
25 |
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37 |
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84 |
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5 |
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35 |
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6 |
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48 |
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12 |
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8 |
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444 |
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11 |
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625 |
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17 |
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108 |
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78 |
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3354 |
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