Please make sure you are focusing on mental math strategies that reinforce number sense first. 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. The example below shows a 2-digit by 3-digit equation, so there are 2 rows and 3 columns. We simply increase the numbers of rows or columns based on the number of digits in the factors. What if we have more digits in the factors? 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. Now, when we add that diagonal row, we simply add that carried digit in there as well. 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, let’s see what happens.įirst we add the diagonal row in the bottom right, to make 0. In the example below, we have done all of our multiplying on the grid. When we regroup, we simply carry the tens digit to the next diagonal row. Now what happens if we need to regroup? Let’s take a look below. So in this example, the final product is 558. 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. Step 4: We continue multiplying for each space on the grid. The tens and ones are split on either side of the diagonal line. For example, in the top right corner, we are multiplying 8×3 to make 24. We multiply the numbers that meet in each space on the grid. Step 2: Next, we arrange the factors along the top and right side of the grid, as shown below. For example, if you are multiplying a 2-digit by 2-digit equation, your grid will have two rows and two columns. The number of rows and columns will depend on the number of digits in the factors. To solve this equation, we follow the steps below: Let’s begin with an equation that does not require regrouping: 18 x 31. 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. 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. Lattice multiplication utilizes a grid to keep numbers organized. How do you perform lattice multiplication? 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. If your students have mastered those mental math based strategies, and are ready for more, this is a fun one to teach! 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). 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. So why would you want to teach this strategy? 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. 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. We know that number sense is an essential component of today’s classrooms. Before I begin explaining this strategy, I do want to take a second to talk about multi-digit multiplication strategies in general. Lattice multiplication is an alternative to traditional long multiplication.
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