I like this strategy as a follow up to the area model (or box/window method), which you can read more about HERE.

When we use partial products to solve a multiplication equation, we can set it up like a traditional long multiplication equation, as shown below.

Just like traditional long multiplication, we multiply the ones digit of the second factor first. In this case there is only one digit in the second factor. So first we multiply 4×5 to make 20.

Here’s where this strategy differs from traditional long multiplication. We write the entire 20 rather than using carrying as in traditional long multiplication.

Next, we multiply the 4 by the tens digit of the first factor. However in partial products we use the value of this digit. In this example, the value of the 4 in 45 is 40. So we multiply 4×40 to make 160.

We write the entire 160 beneath the 20.

Now that we’ve taken care of the multiplication, we just need to add our products up, in order to make the final product. In this example, 20+160=180, so we know that 180 is the product of 45 and 4.

When we work with more digits, we just multiply the ones first, and then the tens. The example below shows how we would solve a 2-digit by 2-digit equation. Remember that we always use the VALUE of the digits, not just the digits themselves.

NEXT STEPS

• Learn about other multi-digit multiplication strategies with these blog posts on the box window method, and lattice multiplication.
• Looking for more support with multi-digit multiplication in your classroom? Check out my self-paced, student-centered Multi-Digit Multiplication Math Station HERE. It includes many different strategies for multi-digit multiplication so that all of your students can experience success in their own way.

The post Using the Partial Products Method for Multi-Digit Multiplication appeared first on Shelley Gray.

The area model is a useful strategy for multi-digit multiplication. This strategy places an emphasis on number sense understanding, as students use the expanded form of each factor. This helps students to understand what the digits in each factor REALLY mean.

This approach is sometimes also referred to as the “box” or “window” method by some teachers.

I’ve included detailed, step-by-step instructions for this method down below. However, if you would like to watch the steps in video format instead, simply press play on the video below. Otherwise, keep scrolling down to the step-by-step instructions!

I like the area model as an introduction to the partial products strategy. Although this basically is partial products, it is a more visual way to do the multiplication. Place value is emphasized because each factor is broken up into its expanded form, as shown below.

How to Multiply Using the Area Model (also known as Box/Window Method)

When we use the area model, we first draw a grid! The number of rows and columns will depend on the number of digits in the factor. The one below is drawn for a 2-digit by 2-digit equation; therefore there are two rows and two columns.

Next, we arrange the expanded form of our factors along the top and one side of the box. For example, the box shown below is for the equation 57×25.

Now it’s time to multiply! We multiply the numbers that meet in each space on the grid. The picture below shows the numbers that are being multiplied in each box. Once your students are used to using this strategy, they will not need to write the entire equation in each box anymore, but can just write the products instead.

Lastly we add all of the smaller products, to make our final product. In this example, the smaller products are added up to make 1425. This means that the product of 57 and 25 is 1425.

When you use this strategy with larger numbers, you simply increase the size of the grid to make room for more rows and columns. This is also an effective strategy for 2-digit by 1-digit multiplication, simply by making a rectangle divided into two separate sections, and finding the area of each section.

BUT WAIT!

This method is still too abstract for some students. We need to back up and get even more conceptual. Base ten blocks can help us teach the area model in a concrete way that will help build students’ understanding. To do this, we use the factors to set up the length and width of the rectangle. We then fill the area with base ten blocks by multiplying the smaller parts. The area becomes our product! Here’s an example of how we can use base ten blocks to solve 13×14.

Want to learn more about how base ten blocks can revolutionize the way you teach the area model? Check out this post!

Looking for more help with multi-digit multiplication in your classroom? Check out my self-paced, student-centered Multi-Digit Multiplication Station HERE. It includes many different strategies for multi-digit multiplication so that each of your students can experience success in his own way.

The post Using the Area Model for Multi-Digit Multiplication appeared first on Shelley Gray.

Lattice multiplication is an alternative to traditional long multiplication. Before I begin explaining this strategy, I do want to take a second to talk about multi-digit multiplication strategies in general.

We know that number sense is an essential component of today’s classrooms. We teach math in a way that enhances number sense understanding, so that students really understand what they are doing, rather than just memorizing a series of steps.

Now let me begin this post on lattice multiplication by saying that this is not necessarily one of those strategies that enhances number sense understanding.

So why would you want to teach this strategy?

Once students have a solid understanding of the place value concepts behind multiplication, some can thrive with traditional methods such as long multiplication, or this alternative – lattice multiplication. I do believe that before you teach this method, you should focus on mental math strategies that DO encourage number sense understanding, such as the partial products strategy, or box/window method (area model). If your students have mastered those mental math based strategies, and are ready for more, this is a fun one to teach!

Looking for support with teaching this strategy and many others for multi-digit multiplication? See The Multi-Digit Multiplication Station (a self-paced, student-centered approach) HERE.

How do you perform lattice multiplication?

Lattice multiplication utilizes a grid to keep numbers organized. This is especially helpful when it comes to regrouping, as the numbers that are carried are also written within the grid to make the adding easier.

I’m going to explain this strategy step-by-step, with lots of pictures, but if you’d rather watch my Lattice Multiplication video, simply press “play” below! Otherwise keep scrolling for the step-by-step instructions.

Let’s begin with an equation that does not require regrouping: 18 x 31. To solve this equation, we follow the steps below:

Step 1: Draw a grid. The number of rows and columns will depend on the number of digits in the factors. For example, if you are multiplying a 2-digit by 2-digit equation, your grid will have two rows and two columns.

Step 2: Next, we arrange the factors along the top and right side of the grid, as shown below.

Step 3: Now it’s time to multiply. We multiply the numbers that meet in each space on the grid. For example, in the top right corner, we are multiplying 8×3 to make 24. The tens and ones are split on either side of the diagonal line.

Step 4: We continue multiplying for each space on the grid.

Step 5: Lastly, we add! We add using diagonal rows, and write the sum of each diagonal row along the left side and bottom of the grid. So in this example, the final product is 558.

Now what happens if we need to regroup? Let’s take a look below.

When we regroup, we simply carry the tens digit to the next diagonal row. In the example below, we have done all of our multiplying on the grid. Now when we add, let’s see what happens.

First we add the diagonal row in the bottom right, to make 0. (see example above)

Now we add the next diagonal row. The sum is 15, so here we write the ones digit (5), and carry the tens (1) to the next diagonal row (I’ve circled that carried digit in this example so that it stands out). Now, when we add that diagonal row, we simply add that carried digit in there as well.

This is often helpful for students because the carried digits stay in the row that they need to be added in, eliminating the confusion that carrying can often bring in traditional long multiplication.

What if we have more digits in the factors?

Easy!

We simply increase the numbers of rows or columns based on the number of digits in the factors. The example below shows a 2-digit by 3-digit equation, so there are 2 rows and 3 columns.

I do want to reinforce one more time that this is not a strategy that you would teach students who are just learning multi-digit multiplication. Please make sure you are focusing on mental math strategies that reinforce number sense first. THEN strategies like this one can be a fun addition to your multi-digit multiplication, and can really be helpful for some of your students.

NEXT STEPS:

Looking for more help with multi-digit multiplication in your classroom? Check out the self-paced, student-centered Multi-Digit Multiplication Station HERE.

The post Lattice Multiplication: A Method for Multi-Digit Multiplication appeared first on Shelley Gray.