Multiplication Algorithm
There are many “ways” to solve multiplication problems, each of these defined “ways” is an algorithm. An algorithm is the process used to solve an addition, subtraction, multiplication, or division problem. There are three multiplication algorithms taught in the Everyday Math program: Partial Product, Modified Repeated Addition and Lattice. Just like with the addition and subtraction algorithms, some algorithms are better suited to a particular problem. If children have mastery of each algorithm then they could choose which one is best suited for a particular problem. What matters is that a student has at least one algorithm that they are successful, accurate and efficient with. The use of an algorithm to solve a multiplication problem begins in 3rd
grade. Students’ experience with addition and subtraction problems helps build the concept of multiplication and is the basis for Partial Products algorithm.
Partial Products This algorithm looks at each number as a factor. Each factor is multiplied by another factor in the problem and the partial products are listed separately. The sum of the partial products is the total product.
Example of Partial Products
To find the product of 46 x 25, think of 46 as 40 + 6 and 25 as 20 + 5. Multiple each part of one sum by each part of the other sum, and add the results.
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2 tens x 6 ones 20 x 6 = 120 |
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5 ones x 4 tens 5 x 40 = 200 |
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5 ones x 6 ones 5 x 6 = 30 |
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800 + 120 + 200 + 30 = 1,150 |
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Modified Repeated Addition
Multiplication is a quick way to do repeated addition. 8 X 6 is really 8 sets of 6 or 6+ 6+6+6+6+6+6+ This is great to think about conceptually but would be inefficient when multiplying large numbers.
55 x 23=
To solve this using Repeated Addition you would need to think about 55 sets of 23 or the reverse 23 sets of 55. Both problems are too large to use repeated addition. Using a modified repeated algorithm would make it easier and more efficient. Use multiples of 10, 100 and so on to simplify the process.
Example Repeated Addition
Think of 23 x 55 as twenty 55s (10 55's - 550 plus 10 55's - 550) plus three 55s. Since ten 55s is 550, twenty 55s is two 550s.
Now think about three 55s. Add all the groups of 55. So 55 x 23 = 1,265 |
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Lattice Multiplication
Lattice Multiplication is another algorithm used to solve multiplication problems. This algorithm doesn’t make sense conceptually, it just a series of steps that will lead to the correct answer. While it doesn’t build on or use number sense to solve, it is, for many students, one algorithm that works. They are efficient and successful with it. It has been around since 1100 A.D. and appeared in the first printed Arithmetic book, published in 1478.
Follow these steps to solve 55 x 23.  *Draw a 2 x 2 lattice grid. *Writhe grid and the other number along the right side of the grid. *Draw diagonals from the upper-corner of each box extending beyond each box. *Multiply each digit in one factor by each digit in the other factor. The ten digit of the product goes above the diagonal and the ones digit goes below the diagonal line.
*Finally, add the numbers in each diagonal. 5 is the only number in the right diagonal so there are 5 ones. The next diagonal has 5 and 1 so there are 6 tens. The next diagonal has a 1 and a 1 so there are 2 hundreds. The last diagonal on the left has only a 1 so there is 1 thousand. *Read the number from outside top left to bottom right. 1 2 6 5 is 1,265. 55 x 23 = 1, 265
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