When students first begin to understand two-digit multiplication, we often jump to using the algorithm too quickly. Students need time to develop multi-digit computation skills. This will help them build a solid foundation for the algorithms later. Today’s post is the second in my multiplication series and offers ways that a Base 10 model can help students connect to the algorithm. (Missed the first post? Read it here!)
One of the most daunting tasks in grades four and five is teaching two-digit multiplication. As a former fourth grade teacher, I can remember the challenge of this process during my first year in the classroom. Is was easy for me, so why couldn’t I teach my students?
This challenge brought many restless nights and even a little desperation. Some years ago, I started using Base 10 blocks to introduce multiplication with larger numbers. My students found a great deal of success with this tool, so I’m sharing the strategy with you today.
Why Not the Standard Algorithm?
We’ve all been there. Your two-digit multiplication unit rolls around and you feel pressured, either by your colleagues or well-intentioned homework-helping parents, to just teach the standard algorithm. After all, why does it matter?
The National Council of Teachers of Mathematics state the “effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems” (Principles to Actions: Ensuring Mathematical Success for All, p. 42).
What is Fluency?
Fluency is a student’s ability to “choose flexibly among methods and strategies to solve contextual and mathematical problems” (p. 42). Selecting strategies that are “strongly related to number sense” force students to go beyond memorizing basic facts or a series of steps that are not connected to meaning (p. 42). Trying to rush students to develop fluency before they are ready can even cause some of our students to develop math anxiety. (Read Jo Boaler’s Fluency Without Fear article here!)
How to Build Procedural Fluency of Two-Digit Multiplication from Conceptual Understanding
Using Base 10 blocks to model multiplication is a great way to use a model and connect to the algorithm at the same time. In the picture below, I model how Base 10 blocks can be used side-by-side with a multiplication area model to illustrate the connection between an area model for multiplication and its often confusing and hard-to-understand algorithm.
Specifically, the model shows how using Base 10 blocks to model two-digit by two-digit multiplication relates to the area model and the traditional algorithm. Here’s how it works:
- First, students break down two-digit numbers into tens and ones and create a rectangle using the two factors as the side lengths. This provides students with a visual of the product.
- Second, students begin drawing a model of the Base 10 blocks and label the side lengths and inside areas. Then, they add all four areas to find the total.
- Third, students connect the area model to the partial products strategy using a familiar format.
- Finally, students use the traditional algorithm with a correct understanding of place value.
Getting ready to teach two-digit multiplication? Consider how using the strategies above may help your students develop computational fluency. In fact, both the Texas standards and the Common Core standards emphasize the use of strategies to develop multiplication skills.
Reference: National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all, p. 42-48.