# MathBait™ Multiplication

# The Lattice Method

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Ready to introduce multi-digit multiplication to your students? In this article we breakdown the Lattice Method providing key information on the mathematics behind the method, when and how to introduce the Lattice Method to students, and the pros and cons teachers and parents must consider.

## Details

Resource Type

Method

Primary Topic

Multiplication Methods

Unit

4

Activity

2

of

6

We are going to come right out and say it: this method is mind-boggling, complicated, and does not support student understanding. It is unfortunate as at its core, the Lattice Method relies on Napier's Bones, and we are a huge proponent of learning with Napier's Bones. (You are in luck! MathBait™ Multiplication Part 5 is all about *Dem Bones*. We will provide you with some amazing resources to amp up fluency, understanding, and give students a major confidence booster using Napier's Bones.) However, the Lattice Method strips away all discovery and exploration and distills multiplication down into a set of memorized steps, leaving students with a procedural view of mathematics and little understanding.

That being said, we know many teachers rely on the Lattice Method so let's take a look at this approach to multiplication to better understand its origins and process.

#### Step 1: Create a Lattice

Construct a lattice based on the values you are multiplying. For instance, if multiplying a 3-digit number by a 2-digit number, your lattice should have 3 columns and 2 rows. For our example, we will multiply 871×57.

#### Step 2: Calculate the Smaller Products

Next, calculate the product of the digits in each row and column. Place the tens value above the diagonal and the ones value below. For instance, since we are multiplying 871, we start with 8 and find the product of 8 and each digit in 57. As 8×5=40, our first entry will be a 4 above the diagonal and a 0 below. And as 8×7=56, our next entry will be a 5 above the diagonal and a 6 below. We continue for each column.

#### Step 3: Sum the Diagonals

Starting in the bottom right corner, sum the diagonals. In the case your sum is more than 9, we must carry the overage to the next diagonal.

#### Step 4: Transcribe your Solution

The bottom right corner represents the ones digit, as it is the product of the ones digit of 871 and the ones digit of 57. This means, to read this product you must start in the top left corner and move down, followed by moving along the bottom from left to right.

Thus, the product 871×57 is 49,647. If you are not familiar with the Lattice Method, this might look like magic. That feeling of awe is what makes the idea behind this method so outstanding and also why most students who learn the method have no understanding at all why it worked!

The Lattice Method is akin to using Napier's Bones, the first practical western calculator and an amazing tool for students. However, it is vital students develop an understanding of w*hy* this method works if introducing it. While we highly encourage playing with Napier's Bones and having seen wonderfully positive effects from rod multiplication, the Lattice Method falls flat.

#### Why it Works

This method is simply a different way of organizing the Standard Algorithm and implores the power of the Area Model.

We can consider 871×57 as (800+70+1)×(50+7). Distributing provides us with exactly the six intermediate products shown above.

871×57

=(800+70+1)×(50+7)

=(800×50)+(800×7)+(70×50)+(70×7)+(1×50)+(1×7)

Because of the lattice organization, students need not worry about place value. Thus, this product is calculated as,

(8×5), (8×7), (7×5), (7×7), (1×5), and (1×7).

Finally, students sum the amount in each place to reach the final computation.

#### Overall Assessment of the Lattice Method

##### PROS

Focuses on lower multiplies (1-digit products)

Excellent organization helping to avoid place value confusion

Based on a strong mathematical concept

##### CONS

Drawing out a lattice is tedious and time consuming

Too many steps and procedures to remember

It is so far removed from a mathematical principle, it is almost impossible to develop an understanding of the why behind the process

#### Our Rating:

This method stinks and it is not on our recommendation list. However, the Lattice Method stems from Napier's Bones which is a powerful tool and an excellent way for students to explore and build number sense.

#### Our Recommendation

Skip this method entirely. The cons far outweigh the possible benefits. That being said, the mathematics this method is based on is powerful. Explore MathBait™ Multiplication Part 5, where students will have the opportunity to play and explore Napier's Bones, developing a strong number sense and graduated levels of understanding.

If your district or curriculum insists on the Lattice Method (or you just love it), there is hope! While we maintain this method is not a viable long-term strategy as it is time consuming and easy to make an error, before introducing your students to the Lattice Method, take the time to explore Napier's Bones. This will help ensure students understand the method and why it works, helping them to make fewer errors and improve effectiveness.

Remember, in this century we aren't teaching multiplication for our students to do complex calculations, we have a tool for that! We are teaching them to recognize and understand patterns, to solve problems, and to build a foundation for higher-order thinking. This method alone doesn't do that.

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