Everyday Math Algorithm Guide
Today we began exploring multiplication using algorithms that the students may be
new to. As parents, we did not learn multiplication this way and it might be a little
confusing to help our children with their work. I have put together a packet of
resources to help you with the following algorithms:
*partial products
*lattice method
Multiplication Algorithms
In Third Grade Everyday Mathematics, a “partial-products” algorithm is the initial
approach to solving multiplication problems with formal paper-and-pencil procedures. This algorithm is done from left to right, so that the largest partial product
is calculated first. As with left-to-right algorithms for addition, this encourages
quick estimates of the magnitude of products without neces-sarily finishing the
procedure to find exact answers. To use this algorithm efficiently, students need
to be very good at multiplying multiples of 10, 100, and 1000. The fourth-grade
program contains a good deal of practice and review of these skills, which also
serve very well in making ballpark estimates in problems that involve multiplication
or division, and introduces the * as a symbol of multiplication.
1. Partial-Product Algorithm
In the partial-product multiplication algorithm, each
67
factor is thought of as a sum of ones, tens, hundreds,
*53
and so on. For example, in 67 * 53, think of 67 as 60 +
50 x 60 3000
7, and 53 as 50 + 3. Then each part of one factor is
50 x 7
350
multiplied by each part of the other factor, and all of
3 x 60
180
the resulting partial products are added together.
3x7
+21
3551
This method reinforces the understanding of place value and emphasizes
the multiplication of the largest product first.
Lattice Method
The lattice method employs a grid of squares. One
factor is written along the top, left to right, and
the other factor is written along the right edge,
top to bottom. In the example at right the factors
are 83 and 27. Each square of the grid defined by
the two factors is divided by a diagonal. The digits
of the factors are multiplied pairwise and the twodigit result written down in the corresponding
square in the manner shown. The result of the
multiplication is then obtained by addition down the
diagonals. The reference book suggests to use here
the "fast method" for addition, working right to
left and writing the carries in an appropriate box.
In the example at right I used instead the column
addition method of Everyday Mathematics,
although I don't know if the Everyday Math
teachers' guide would approve of that. In any case,
the reader can as well visualize fast addition down
the diagonals after the products have been filled
in. I'm a bit puzzled by Everyday Math's
preference for the use of fast addition here, since
it is not the preferred method in Everyday
Mathematics in the cleaner context of adding up a
set of numbers written above one another.
8
3
+---+---+
|1 /|0 /|
| / | / | 2
1 |/ 6|/ 6|
+---+---+
|5 /|2 /|
| / | / | 7
11 |/ 6|/ 1|
+---+---+
14
1
1,11,14,1
-> 1,12,4,1
-> 2,2,4,1
= 2241