FOR MULTIPLICATION

1
LATTICE ALGORITHM
FOR MULTIPLICATION
Created by Paula Cantera Elk Neck
Elementary
2
The lattice algorithm for multiplication has
been traced to India, where it was in use before
A.D. 1100.
Many students find that this is one of their
favorites. It helps them keep track of all the
partial products without having to write extra
zeros - and it helps them practice their
multiplication facts!
3
With this algorithm, numbers are placed around
and within a lattice - a special kind of grid in
which the dotted-line rails within the cells
help form diagonals.
4
Write one factor along the top outside of the
grid, one digit per cell.
35
X 26
3
5
5
Write the other factor along the outer right side
of the grid, one digit per cell.
35
X 26
3
5
2
6
6
Begin with the first digit from the side factor,
and multiply it by each digit in the
top factor.
35
X 26
3
5
2
6
7
Record the product in the
upper right-hand cell.
Multiply 2 x 5.
3
5
1
2
0
6
8
Multiply 2 x 3.
Record the product in the
upper left-hand cell.
3
5
0
1
2
0
6
6
Since 6 is a product less than 10 you must
enter a zero in the top half of the cell!
9
Record the product in the
lower right-hand cell.
Multiply 6 x 5.
3
5
0
1
2
0
6
3
6
0
10
Multiply 6 x 3.
Record the product in the
lower left-hand cell.
3
5
0
1
2
0
6
3
1
6
8
0
11
Now, add along the diagonal. Begin with the
bottom right diagonal and work toward the upper
left diagonal.
3
5
0
1
2
0
6
3
1
6
8
0
Regroup each tens digit to the top of the next
diagonal as needed.
12
3
5
0
1
2
0
6
3
1
6
8
0
0
13
Notice we needed to regroup this time!
3
5
1
0
1
2
0
6
3
1
8 3 0 11
6
8
0
1
0
14
3
5
1
0
1
2
0
6
1 6 1 1 9
3
1
8 3 0 11
6
8
0
9
1
0
15
3
5
1
0
1
2
0
6
1 6 1 1 9
0
3
1
8 3 0 11
6
8
0
9
1
0
16
The product of 35 x 26 is 910 !
3
5
1
0
1
2
0
6
1 6 1 1 9
0
3
1
8 3 0 11
6
8
0
9
1
0
17
Of course you can use the Lattice Algorithm for
any number of digits.
Simply adjust your lattice grid to fit the
factors that you are multiplying!
18
Three digit by a two-digit 251 x 36
2
5
1
3
6
19
Shall we try to solve this one?
2
5
1
0
3
3
6
20
2
5
1
1
0
3
3
5
6
So far so good! Keep going!
21
2
5
1
0
1
0
3
3
5
6
6
Excellent work so far! You have the hang of it!
22
2
5
1
0
1
0
3
3
5
6
0
6
6
23
2
5
1
0
1
0
3
3
5
6
0
3
6
6
0
Youre almost there! Keep going!
24
2
5
1
0
1
0
3
3
5
6
1
0
3
6
6
0
2
Wasnt that easy? Do you remember what to do
next?
25
Of course! You add the diagonals!
2
5
1
1
0
0
1
3
3
5
6
0
3
1
0
6
6
0
2
9
6
0
3
26
The product of 251 x 36 is 9,036 !
2
5
1
1
0
0
1
3
3
5
6
0
3
1
0
6
9
6
0
2
6
0
3
27
Lattice Multiplication is lots of fun! Give it a
try!