When it comes to teaching multi-digit by multi-digit multiplication, I like to keep lots of strategies in my math toolbox. The lattice method is an essential long-multiplication strategy for every upper elementary classroom. If you have a student who is struggling to manage all the steps involved in multi-digit multiplication, or a student who needs something more visual, lattice multiplication just might be a strategy that works for them.
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Why Teach the Lattice Method?
Multi-digit by multi-digit multiplication (also known as long multiplication) is a challenging math skill for most upper elementary students. Even with lots of practice, some students struggle to remember all of the steps and basic facts required for long multiplication.
However, the days of teaching long multiplication with only the standard algorithm are gone! Teaching more than one strategy to multiply bigger numbers is a good idea because all students learn information differently. A student may not understand using standard algorithm to multiply. But show them a different strategy, and it can click quickly.
With lattice multiplication, students do not have to keep track of multiple steps in their heads. The lattice method provides a very visual way to multiply larger numbers in small pieces. Of all the multiplication strategies I have taught, the lattice method is one that consistently seems to click with my struggling students.
Using the Lattice Method to Multiply
The following step-by-step instructions show how to solve 68 x 34 using the lattice method.
Step 1: Create space to solve the problem. For 2-digit numbers, create two columns and two rows. Draw diagonal lines from the upper, right corners of the boxes and out through the bottom, left corners of the boxes. The lines should extend a little ways outside of the box.
Step 2: Represent one number horizontally by writing each digit above one of the boxes. Write the other number vertically to the right of the rows.
Step 3: Multiply the numbers on the right by each number above the boxes. Write the products in the boxes. When writing the product, the digit in the tens place should be written above the diagonal line, and the digit in the ones place should be written below the diagonal line. If there is not a digit in the tens place, write “0” as a placeholder.
Step 4: Add the numbers in each diagonal row, starting at the bottom right. Write the sums outside of the boxes. If a sum is greater than 9, write the ones-place digit outside the boxes. Carry the tens-place digit to the next diagonal row. The digit will be added to the row it is carried to.
Step 5: The final product is the numbers outside the boxes, from left to right. In this example: 2,312.
Help Tips When Using Lattice Multiplication
Here are a few helpful tips for multi-digit by multi-digit multiplication using the lattice method.
- Contrary to what some websites may tell you, you do not need to buy or make special worksheets with the lattice boxes already created. I like to use graph paper with large squares and have students create their own lattice boxes.
- Have students draw the diagonal line with a highlighter to make it easier to organize the information.
- If students are getting numbers confused, it can be helpful to have them color-coordinate the numbers. For example, color the products inside the boxes one color and the sums outside the boxes a different color.
More Strategies for Multi-Digit by Multi-Digit Multiplication
Using the lattice method is one of my favorite multiplication strategies that is not the standard algorithm.
But there are also many other long multiplication strategies you can use. My multiplication units teach students the following multi-digit multiplication methods in addition to the standard algorithm:
- the box method
- factor multiplication
- partial products
All of my no-prep multiplication units come with step-by-step instructions for teaching each strategy and lesson. They also come with worksheets, games and centers, digital activities, and assessments to use when teaching long multiplication.
Because each grade level is required to use different number ranges when multiplying, four versions of the unit plans are available—
- Multiply up to 2-digits by 1-digit
- Multiply up to Two 2-digit numbers
- Multiply up to 3-digits by 2-digits
- Multiply up to Two 3-digit numbers
