What’s the Multiplication Area Model and How Do You Teach it? Comprehensive Guide

The area model is a strategy for multi-digit multiplication, allowing students to build conceptual understanding before transitioning to the traditional algorithm. But there is more to teaching the area model than you might think.

Free Area Model Activities to Help You Get Started!

This is where we're headed. But it's not where we begin.

When we use the area model, we decompose the factors into tens and ones, use them to represent the side lengths of our rectangle, and then multiply the parts. The sum of the parts gives us the area, or the product of our equation.

In this example, we multiplied 10×10 to make 100, 10×3 to make 30, 2×10 to make 20, and 2×3 to make 6. Then we add up all four of these parts to find the total area of the rectangle, or the product.  100+30+20+6=156. 

But this is too abstract for students who are just learning.

The example above is where we are eventually headed, but it’s too abstract for some students during the learning phase.  We want our students to understand WHY we are putting the numbers where we are putting them. So we need to start in a more conceptual way.

As we know from the CRA model, ALL students will benefit from working with concepts concretely, and then connecting that understanding to more abstract representations.

So how can we make the area model more concrete? 

Using Base Ten Blocks To Teach The Area Model

With base ten blocks, students are able to touch, move, and manipulate concrete models to solve an equation. This is where the understanding is built. Not to mention, it’s fun! 

Step 1: Use the factors to represent the length and width of the rectangle.

For example, if we are solving 13×14, our side lengths become 13 and 14. We represent these with base ten blocks.

Step 2: Fill the rectangle.

Now it’s time to figure out the area of the rectangle, which will become our product. First, we see that 10×10 is 100, so we place a hundred block in the rectangle.

Next, we see that 10×4=40, so we add 4 tens.

Now let’s keep multiplying. 3×10=30, so we add 3 more tens.

Lastly, 3×4=12, so we add 12 ones.

Step 3: Add the parts.

Now we can see that the product of 13×14 is 182.

area model

Thinking Deeper About the Area Model

When we work with a strategy like the area model, it’s important to work with it in different ways so the focus isn’t always on finding the product. Some ideas are:

  • Create different equations that have the same product.
  • Given the product and one side length, find the missing side length (factor).
  • Given the product (area), find both factors.
  • Give students a variety of base ten blocks. Have them create different area models using the same number of blocks. How does the product change? Why is this?

Transitioning to Representational and Abstract

Once students have had adequate opportunity to build their understanding with base ten blocks, we can transition to pictorial and abstract representations. It’s important that students see the connections between what they were doing with the base ten blocks and this new learning.

But isn't this more work than long multiplication?

In some cases – yes! But we have to remember – our goal is not to create human calculators that simply find answers to problems. We have computers and calculators for that! Our goal is to help kids think in flexible ways, reason, and strategize. We need kids to be able to truly understand and to solve problems in different ways.

What Comes Next?

The area model transitions beautifully into another strategy called partial products. This is essentially the same strategy, but we record our thinking differently. Partial products is set up like the traditional algorithm, but as you can see we are multiplying by place value, exactly as we do in the area model.

If you plan to teach the traditional algorithm, it should come after students have used the area model and partial products extensively to build their overall understanding. Remember – math is not all about the answer. It is about the ability to think in flexible ways. Strategies like the area model allow our students flexibility in their thinking, and give students the opportunity to really SEE the math.

Don't miss these free area model activites!

Help your students use base ten blocks to work with the area model, and transition to more abstract representations with the free activity sheets!

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