Students learn different algorithms and strategies for multiplying multi-digit factors. Some are familiar to parents, others look quite different. Many students benefit from learning different strategies to solve multiplication problems because it strengthens their computation skills and provides them with different strategies for working with numbers.

Ms. Gale's class explores several algorithms, relating the different algorithms, and then choosing one that makes the most sense to them. When students can successfully use and relate different algorithms for multiplication, they increase their repertoire of strategies and strengthen their understanding.

	This strategy is called Partial Products because students complete each part of the multiplication algorithm as a separate muliplication problem. The student first multiplies 7 ones x 5 ones. Then, 9 tens x 5 ones, or 90 x 5 ones. At each step, students are thinking about the place value of the digits. Finally, the student adds together the four partial products.
This strategy is called the lattice method. The student has written one factor, 97, at the top, and the other factor, 25, on the right.	Students then write the answer to each multiplication fact in the corresponding cell of the grid. For example, 5 x 7 = 35, so the student has written the digits 3 and 5 in the lower right hand cell. 9 x 2 = 18, so the 1 and the 8 are written in the upper left hand cell. Students continue writing the facts in until every cell is filled.
	Students then add the columns diagonally to find the final product. It is important for students to understand why this algorithm works. Looking at the bottom right hand cell, 7 ones x 5 ones= 35. Therefore, the 5 is in the ones place, and the 3 is in the tens place. Looking at the upper right hand cell, it is important for students to realize that the 2 in the original factor 25 is worth 2 tens. Therefore, 7 ones x 2 tens = 14 tens (or 140). The 1 falls in the hundreds column, and the 4 falls in the tens column. In this example, the student adds up the diagonal columns (regrouping when necessary) to come up with the answer: 97 x 25 = 2,425 .
	This is an algorithm that has been adapted from one shared with the Oakland Terrace staff by head teachers visiting from the UK. In this method, students write the two factors above and to the left of the grid. As with the lattice method, students fill in each cell with the multiplication fact. And like the partial product method, the problem is broken down into each of its component parts. To focus students on the place value of each digit, Ms. Gale's students have written a small zero next to the 9 and the 2 in the factors to remind them that those digits actually represent 90 and 20. As the students fill in each cell of the grid, they are aware that 2 x 9 in the upper left hand grid is actually 20 x 90, or 1800. Students then add up the four partial products to find the final product.
The lattice method used to solve 912 x 68	The traditional algorithm for solving 912 x 68.

Why so many algorithms?

An algorithm is simply an efficient way of performing mathematical computation. There is no right method or wrong method, as long as the student arrives at the correct answer. The non-traditional algorithms place an importance on the place value of each digit in the factors as the students perform the computation. Students tend to understand the procedures of these algorithms because they are tied to their understanding of place value. For many students, the non-traditional algorithms are also more efficient than the traditional algorithm.

For many adults, the traditional algorithm for multiplication is the most efficient because it is familiar. The traditional algorithm is more procedural, with little emphasis on place value. For many students, the traditional algorithm is confusing and leads to many errors. For other students, the traditional algorithm makes sense and is the most efficient.

Regardless of the algorithm a student uses, parents and teachers should question students' understanding of each and every step in the procedure to encourage student understanding. And no matter what algorithm a student uses, students' knowledge of the basic facts is imperative.