How to do: Lattice Multiplication
What is lattice multiplication and when would we use it?  Lattice multiplication is a way to multiply larger numbers (bigger than a 1-digit number times another 1-digit number)  You can use lattice multiplication with any big multiplication problem as long as you can draw a big enough grid!
Sounds great! How do we get started?
Let us start with a 2-digit by 1-digit example‌ If you want to multiply: 42 x 9 First, you have to make a 2 by 1 grid (because it’s a 2-digit by 1-digit problem)
Next, in each box, you need to draw a diagonal line from the upper right hand corner through the lower left hand corner. The line should go past the lower left hand corner to the outside of your grid.
Put the 2-digit number across the top of your grid and the 1-digit number on the right side of your grid.
4
2 9
Then, multiply the number on the top of each column with the number to the right of that row. 4
2
4x9
2x9
9
The digit in the tens place of the product goes to the left of the diagonal. The digit in the ones place of the product goes to the right of the diagonal. *If there are no tens or no ones in the product, do not forget to put a 0!
4 3
2 6
1
8
9
Now, you are finished with the numbers 42 and 9. Be careful not to use these numbers in the next step! 4 3
2 6
1
8
9
Finally, you need to ADD the numbers inside the grid along the diagonals. Start with the diagonal on the right. Write the answer in the space outside the grid.
4 3 + nothing =
3
3
2 1
6
6+1=
7
8
8 + nothing =
8
9
Your answer is the number outside of the grid. 4 3 3
7
2 6
1
8
9
8
42 x 9 = 378
Now let us try a 2-digit by 2-digit multiplication problem‌ Let us multiply: 54 x 97 Start by making your grid (a 2 by 2 grid this time):
Add the diagonals:
5 And the numbers: Since they are both 2-digits, it does not matter which one goes on the top and which one goes to the right of the grid.
4 9 7
Multiply the number at the top of the column with the side of the row.
5 5x9 5x7
4 4x9
4x7
9 7
5 4
4 3 6 9 5 3 2 5 8 7
Finally, add the numbers along the diagonals. If the sum is greater than 10, carry the 1 into the next diagonal.
5 4 1 1 4 3 9 6 5 5 3 2 7 5 8 2 8 3
The 1 is carried from the previous diagonal: 5 + 2 + 6 = 13 The 3 goes at the bottom of that diagonal. The 1 gets added to the next diagonal.
54 x 97 = 5,238
Now, try these two examples on your own. The grids are drawn for you. Do not go on to the next slide until you have given these problems a try. Look back to previous slides if you need help.
1.) 26 x 4 =
2
2.) 31 x 62 =
6
3
4
1 6 2
See if you got the answers! 2.)
1.)
2 1
0 0
1
8
6 2
4 4
4
26 x 4 = 104
3 1
1 0
1
6 6 1 0 0 2 6 2 9 2 2 8
31 x 62 = 1,922
Now that you have learned lattice multiplication, you can practice with any numbers of your choice! Good luck!