Strategies for Gamma: Multi-Digit Multiplication with Manipulatives

Lesson 21 introduces one of the more challenging concepts in multiplication, especially for students who are just beginning to grasp multi-digit multiplication. Instructors often encounter difficulty when students reach this point, requiring a deeper understanding of multiplication concepts and fluency with basic facts. To effectively guide students through this lesson, instructors must approach it with patience, a solid understanding of the teaching tools, and a readiness to revisit fundamental skills if necessary.

Here are three essential strategies to keep in mind:

1. Leverage the Manipulatives

The manipulatives are central to the Math-U-See approach; this level is no exception. These physical tools help students visualize the process of multiplication in a way that abstract numbers alone cannot. Further, using manipulatives reinforces the understanding of place value in multi-digit multiplication, ensuring that students can accurately break down and organize the numbers. This hands-on approach helps them internalize the concept, making it easier to retrieve and apply when solving complex problems later on.

Using the Hundred Block

As you move into equations with factors larger than 10, it is important to know how to use the hundred block. For example, when we build 12 x 13, we know we have an over factor of 12 and an up factor of 13.  When you ask your student what they should start with, they may intuitively know to start with the hundred block, but don’t panic if you have to guide them through this scenario. 

You can say something like, “We know our 10 X 10 block, also known as our hundred block, is 10 over and 10 up” so your student understands that they need to use the 10 over and 10 up block to start our building process. Then, since that block is 10 over and 10 up and we need to get 12 over and 13 up, we can add 2 10’s vertically next to the hundred block, and we can place 3 10’s horizontally on top of the hundred block.  We will still see a gap in the upper right-hand corner, so we must fill that in for a complete rectangle. We can do this with two 3 blocks.”

Good news! These multiple-digit multiplication problems are simply bigger rectangles and involve multiple steps of solving smaller multiplication problems that should be familiar to the student once broken down step-by-step. These problems also become multi-step because they often include addition to solve and arrive at the complete solution. This is a familiar (but also new) skill set, so give your student plenty of modeling and practice to gain confidence.

Build, Write, Say

As an instructor, it’s vital to continue using the Build, Write, Say method, which reinforces concepts through multiple learning modes. Speaking the process out loud (the SAY of Build, Write, Say) allows the brain to properly catalog the information for later recall and helps expose errors in the multi-step process. Demonstrating multi-digit multiplication with the manipulative blocks helps students see how the numbers interact, making the process clearer and more intuitive. Skipping this step can lead to confusion, so it’s essential to integrate manipulatives into every part of the lesson.

2. Address Gaps in Multiplication Facts Mastery

If students haven’t fully mastered their basic multiplication facts and still rely on skip-counting, they will likely struggle with the multi-digit multiplication introduced in Lesson 23. This is a critical point where you may need to pause the progression and invest time in strengthening their multiplication fact fluency. You can use our practice sheet generator in the Digital Toolbox for a refresh. 

If your student needs to develop a more complete mastery of the facts, our Accelerated Individualized Mastery (AIM) for Multiplication program may be right for your student. It’s an excellent intervention tool to help students catch up and become more confident in their skills. Taking time to ensure students have this foundation will set them up for success in this lesson and in future ones.

3. Stick with the Math-U-See Methodology

It can be tempting to revert to the way you learned multiplication when your students begin to struggle. However, Math-U-See’s methodologies are designed with long-term understanding in mind, and stepping away from them can hinder progress. Take the time to revisit and understand the concepts yourself if needed, ensuring that you’re demonstrating and explaining the process in a way that aligns with Math-U-See’s structured approach. This helps students grasp the material and avoids confusion that can come from switching between teaching methods.

Prior to this lesson, our focus was on the basic multiplication facts using the method of “over factor times up factor equals area.” We do it this way because it is the perfect way to visualize this concept as we build our rectangles. If you haven’t modeled building the multiplication tables with your student, we highly recommend this be done before moving forward.  This process of Build, Write, Say takes them through the full process of connecting the abstract equation to concrete and tangible tools.  The more senses we can engage in this learning process, the more successful the outcome and retention.  Building is critical to their success.

By remembering these three strategies, instructors can more easily navigate the challenges of more difficult Gamma lessons, helping students build a solid foundation in multiplication and prepare for more advanced math concepts.

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