Using an area model is a great way for students to gain a deeper understanding of multiplication. When using an area model, the two factors in the multiplication problem are the length and width of the rectangle and the area is the product. To provide students with a hands-on approach to this concept, we are going to explore teaching this with Base 10 blocks. We will be progressing through the 3 stages of learning: concrete, pictorial and abstract.

Concrete
Let’s take a look at the problem 23 x 5. Students will line up 23 Base 10 blocks as the length of the rectangle and 5 Base 10 blocks as the width.

Next, students will fill in the area, making a rectangle with a length of 23 and a width of 5.

Finally, students will find the area of the rectangle. We can see that we have 5 groups of 10, another 5 groups of 10 and 5 groups of 3. We can add that all up to get an answer of 115.

Representational 1

Once students are comfortable using the Base 10 blocks to solve multi-digit multiplication problems, they can begin drawing the area model on graph paper.  This is the representational stage.  For this topic I like to progress through the representational stage in two steps.  For the first representational stage, students will use graph paper and will count the boxes to find the length and width of the rectangle. 

Students will section off pieces of the area to find the total area as shown below.

Representational 2

Once students have mastered the idea of the area meaning the number of boxes inside a shape, they can begin drawing a rectangle without counting the specific number of boxes as shown below.

Abstract

In the abstract stage of multi-digit  multiplication, students will use the number only, without drawing a model.  Students can do this with partial products or with the standard algorithm.  It is important when teaching the abstract method to connect this stage to the concrete and representational stages.  Students should understand where their partial products are coming from.