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Math for Kids23 chapters | 325 lessons

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Instructor:
*Joelle Mumley*

Long multiplication can be... long! The good news is that there are different ways you can multiply numbers with two or more digits without the long multiplication model. In this lesson, we will discuss the lattice method and how it can be useful when multiplying multi-digit numbers.

The **lattice method** is an alternative way to do multiplication. The lattice method got its name from using a type of grid with a diagonal criss-cross pattern called a **lattice**. Can you think of an example of a lattice in the real world? Maybe Grandma's yummy lattice apple pie?

You might have heard that the lattice method is a new way to multiply, but the truth is the lattice method has been around since the Middle Ages, or even before (and that's way before your parents were born!).

The lattice method helps organize the process of long multiplication into smaller steps. It can be complicated at first but with practice you might find that multiplying large numbers can be fun!

Let's explore the lattice method by first multiplying with a multiplication table. Start with the following problem: 35 x 12.

If you wrote 35 x 12 in expanded form, we would get (30 + 5) x (10 + 2). You can use a multiplication table to get your answer.

The multiplication table is useful when multiplying smaller numbers, but not with larger numbers. The lattice method can help with this by dropping extra zeroes and splitting each box into a tens and ones place.

Let's multiply 35 x 12 again using the lattice method. Now you will multiply each corresponding row with each column and write your answer in the boxes.

Draw rows and columns based on the number of digits in each factor. Draw diagonal lines through each of the boxes. Write the first factor along the top columns and the second factor down the side of the rows.

Begin by multiplying each row digit by each column digit. Start by multiplying 5 x 1. That equals 5, so put a 5 in the ones section and a 0 in the tens section, since there is no tens value.

Repeat the first step until you complete the lattice. Every row number across is multiplied by every column number down.

The last step is to add across the diagonal boxes. Always work from the box on the farthest right towards the boxes on the left. The 0 to the far right is by itself, so just bring that down. Next add 5, 1, and 6. Since 5 + 1 + 6 = 12, bring down the 2 and carry the 1 into the next diagonal box. Add 0 + 0 + 3 + 1 = 4 and bring down the 4. You don't place zeroes in front of numbers, so you can do away with the last zero in the lattice.

To get your answer, read it from left to right. So 35 x 12 = 420.

Let's try a problem with larger numbers. Solve 6321 x 579.

First, make sure you draw a lattice that is 4 columns by 3 rows.

Next, begin to multiply each column number by a row number and record your answer in the boxes.

Finally, add diagonally and don't forget to carry over. Get your answer by reading left to right.

6321 x 579 = 3,659,859.

Let's review. The **lattice method** is an alternative way to do multiplication that's been used since the Middle Ages. It's based on a type of grid with a diagonal criss-cross pattern called a **lattice**. The lattice method uses the same concepts as long multiplication but in smaller, more organized steps. To use it, follow these steps:

- Multiply each row digit by each column digit
- Repeat the first step until you complete the lattice
- Add across the diagonal boxes

Your answer can now be read from left to right!

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Math for Kids23 chapters | 325 lessons

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