How to Teach Multi Digit Multiplication so Your Students Actually Get It -

When I first started teaching, I thought that teaching multi digit multiplication would be super easy. All you have to do is follow a few steps in the multiplication standard algorithm, and you are done. Simple, right? While it is a pretty easy algorithm, jumping right into an algorithm will leave your students with no conceptual understanding.

Students who have a hard time understanding an algorithm, are usually relying on memory rather than understanding.

To build this conceptual understanding and get your 4th grade and 5th grade students to successfully multiply, I recommend using the CRA (Concrete-Representational-Abstract) approach. It will help your students have a deeper understanding of multiplication and will eventually lead them to understanding (therefore remembering) the algorithm.

What is the CRA Method?

CRA stands for Concrete-Representational-Abstract. This is the process students should move through in order to build conceptual knowledge, which can be applied across multiple mathematical concepts. Ultimately, this is what we want! We don’t want students who know an algorithm but can’t figure out how to use it. We want them to use it in real life across multiple situations and scenarios!

Here’s an overview of CRA:

Concrete – In this stage, students use objects to model problems. For example, using base ten blocks to build arrays to show the larger numbers they’re multiplying.
Representational – Students move from manipulatives to drawings in this stage. In multi digit multiplication, this is often in the form of an open area model.
Abstract – This is the stage people typically think of with math: algorithms and equations! Here the actual mathematical symbols, notation, and algorithm will be used.

Before Introducing Multi Digit Multiplication

Before you begin teaching your students how to multiply multi digit numbers, there are some prerequisite abilities that students must have: unitizing, skip counting, decomposing large numbers, using multiplication properties, and creating arrays and area models.

If students don’t already have these skills, they aren’t ready for multi digit multiplication. That can be tough to hear as a 4th or 5th grade teacher who has a lot of standards to cover this year. But if students don’t have foundational multiplication skills, they are going to struggle.

*Notice I didn’t say students had to have all of their multiplication facts memorized. It is SO much easier for students to multiply large numbers if they are fluent in their facts. But it is not a requirement in order for them to be introduced to multi digit multiplication.

Multiplying with Concrete Models

Even upper elementary students need access to manipulatives! Beginning multi digit multiplication with concrete models helps students to visualize what is happening to the numbers. It also will help them understand more abstract methods later.

The best way to model multiplication of large numbers is by creating an array with base 10 blocks. Here’s how to model the example 3 x 17:

When you’re creating an array, you’re using rows and columns to model multiplication. So you should think of 3 x 17 as “3 rows of 17.”
Decompose 17 into 10 and 7, then use base 10 blocks to build 3 rows of 17. I like to label the dimensions on each side–this will help students transition to the open area model later.
Just like with arrays for smaller numbers, the total number of blocks is the product.

If you are multiplying two 2 digit numbers, the process is the same, but both numbers will need to be decomposed. Make sure students are comfortable with creating arrays with one 1 digit factor before moving on.

Representing Multiplication

When students are ready, start modeling problems using representations. This is the “seeing” stage where students show what is happening with pictures or diagrams. These pictures and diagrams are often area models–first on grid paper, then drawn as an open area model.

The key is to make sure students understand the concrete model before you move to representation. You may even transition them by having them build with concrete models, then draw an area model to show what their model looks like. They cannot master multiplying multi digit numbers if they are moving on before they are ready!

Just like the concrete phase, students need to master multiplying a two, three, or four digit number by a one digit number before they can multiply two 2 digit numbers.

Using Abstract Algorithms for Multi Digit Multiplication

Now that students understand how to multiply multi digit numbers with concrete and representational models, you can move to the abstract – using an algorithm. I like to have students “discover” the algorithm using their understanding of their models.

When having students discover the algorithm, you should first expose them to using a partial products algorithm, where they are still able to see the same numbers as the area model.

Once students are able to use a partial products algorithm, they may move on to the traditional standard algorithm for multi digit multiplication. When I do this, it is important to make sure that students still understand where the numbers are coming from.

Now, I want to be honest. The standard algorithm doesn’t always need to be the goal. There are so many more efficient abstract strategies–ratio tables, the “over” strategy, doubling and halving, etc–that some students will never want to use the standard algorithm. And that is just fine!

You’ll also have some students who won’t be ready to multiply with any abstract method just yet. Some students will need to stick with the concrete or representational models – and that is okay. There will also be students who need to move back and forth between the different stages, depending on the problem!

Helpful Resources

If you’re feeling overwhelmed with teaching multi digit multiplication, try out some of these resources. They are filled with examples, guided practice, and more to help students master multiplying 2, 3, and 4 digit numbers.

#1 Guided Notes: These 5th Grade Multiplication Guided Notes will help you easily scaffold students’ learning. The notes go over multiplying 2 and 3 digit numbers using area models, partial products, and the standard algorithm. The notes really come in handy when reinforcing the representational and abstract portion of the CRA method, and you can use the problems in the notes to introduce the concrete stage.

If you love these guided notes, you can grab the entire 5th Grade Math Guided Notes Bundle.

Or if you’re teaching 4th grade multiplication (multiplying up to a 4 digit number by a 1 digit number), check out these guided notes! They scaffold students’ understanding of multiplication with multiple strategies.

If you love these guided notes, you can grab the entire 4th Grade Math Guided Notes Bundle.

#2 Interactive Worksheets: If you have students that are struggling with multiplying fractions or need extra help, interactive worksheets make it a breeze. Each worksheet includes a QR code that links to a mini-lesson video. Plus, you can choose between worksheets with a word problem, just the algorithm, or the algorithm and the model to fit the stage your students are at.

Find them here:

#3 Math Riddles: Add a bit of fun to multiplication with math riddles! These fun food-themed riddles will have students giggling as they practice multiplying multi digit numbers. As students solve the problems, they will fill in the blanks to answer the riddle. This makes for great morning work, early-finisher practice, and independent work.

Find them here: