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Created by Paula Cantera
Elk Neck Elementary
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 oftheir favorites. It helps them keep trackof all the partial products without havingto write extra zeros - and it helps thempractice their multiplication facts!
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.
Write one factor along the topoutside of the grid, one digit per cell.
35 X 263 5
Write the other factor along the outerright side of the grid, one digit percell.35 X 26 3 5
2
6
Begin with the first digit from the sidefactor,
35 X 26 3 5
2
6
and multiply it by each digitin the top factor.
3 5
2
6
Multiply 2 x 5.
10
Record the product in the upper right-hand cell.
3 5
2
6
Multiply 2 x 3.
10
Record the product in the upper left-hand cell.
06
**Since 6 is a product less than 10 you must enter a zero in the top half of the cell!
3 5
2
6
Multiply 6 x 5.
10
Record the product in the lower right-hand cell.
06
30
3 5
2
6
Multiply 6 x 3.
10
Record the product in the lower left-hand cell.
06
30
18
3 5
2
6
10
06
30
18
Now, add along the diagonal. Beginwith the bottom right diagonal and work toward the upper left diagonal.
Regroup each tens digit to the topof the next diagonal as needed.
3 5
2
6
10
06
30
18
0
3 5
2
6
10
06
30
18
0
8 + 3 +
0 = 11
1
1
Notice we needed to regroup this time!
3 5
2
6
10
06
30
18
0
8 + 3 +
0 = 11
1
1
1 + 6 + 1 + 1 = 9
9
3 5
2
6
10
06
30
18
0
8 + 3 +
0 = 11
1
1
1 + 6 + 1 + 1 = 9
9
0
3 5
2
6
10
06
30
18
0
8 + 3 +
0 = 11
1
1
1 + 6 + 1 + 1 = 9
9
0
The product of 35 x 26 is 910 !
Of course you can use the Lattice Algorithm for any numberof digits.
Simply adjust your lattice gridto fit the factors that you aremultiplying!
Three digit by a two-digit: 251 x 36
2
6
3
5 1
Shall we try to solve this one?
2
6
3
5 1
03
2
6
3
5 1
03
15
So far so good! Keep going!
2
6
3
5 1
03
15
06
Excellent work so far! You havethe hang of it!
2
6
3
5 1
03
15
06
06
2
6
3
5 1
03
15
06
06
30
You’re almost there! Keep going!
2
6
3
5 1
03
15
06
06
30
12
Wasn’t that easy? Do you remember what to do next?
2
6
3
5 1
03
15
06
06
30
12
Of course! You add the diagonals!
630
1
9
0
2
6
3
5 1
03
15
06
06
30
12
The product of 251 x 36 is 9,036 !
630
1
9
0
Lattice Multiplication is lotsof fun! Give it a try!
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