Lattice Multiplication, What is it & How do I Multiply the Lattice Way

When I was student teaching (way too many years ago) I had a transfer student in my math class. We were working on multiplication and I called him to the board to show his work. He politely refused stating that I wouldn't like his method because it wasn't the "correct" way.

Now being a curious and very accepting teacher I asked him to show me anyway. Thus began my lesson into lattice multiplication. I don't think my cooperating teacher approved, but this boy could multiply just not the traditional way that the rest of us had learned it. So I did my research and found it really was a method that was taught in various curriculum.

I have found over the years when i have student that really struggles with the traditional methods of multiplication (but know their math facts) that the lattice method can helps them.

I think it is important as a teacher to accept students for what they know not just the way we expect them to do something. Creative thinking and different methods are always welcome in my classroom as long as they can explain it to me.

Let's start with a simple two digit by two digit multiplication problem.

This requires a four by four grid. Each square is divided diagonally from the upper right hand corner to the lower left hand corner. See picture #1.

I am going to do the problem 81 times 23. I set the numbers on the top and right side of the box, each number in a separate box area. ( see picture #2).

Now what I am looking at is a series of multiplication problems. Going across the top row I have 8 x 2 & 1x2. 8 times 2 is 16. I write the 1 in the upper part of the diagonal and the 6 in the lower part.

1x2 is 2. There is only one digit in this problem so I put a zero in the upper part and the 2 in the lower part. The zero is similar to a place holder and simply shows that we understand that 02 is the same as 2 so that we don't put 2 in the upper diagonal which would mean 20.

Now it is time to multiply the second row.

I have two problems in this row 8x 3 & 1x 3.

I fill in the row similar to the top row.

I multiply the basic problems. 8x3 = 24 & 1x3 = 3. I fill in the diagonals with the appropriate numbers as seen int he pictures.

I have finished all the multiplication part of lattice multiplication

Now I am ready to add. This is where we start to use the the diagonals and why they are so important.

I start with the diagonal furthest to the right. Since there is only a 3 in this diagonal that is what I write below it.

The next diagonal had 4 + 0 + 2 = 6. I write 6 below the diagonal

The next diagonal is 2+6+0 = 8.

The final diagonal is 1.

The answer to the problem is 1, 863

So here it is both types of multiplication. Notice how when you get to the addition part you are adding the exact same numbers.

Lattice is perfect for those kids who need a better visual line up or less abstract thinking. Some people claim that it takes additional time to complete but I have seen students do either type of problem in a remarkable fast period of time. The real issue with time is kids that don't know their basic math facts.