Lesson Plan: Area Representation of the Distributive Property

In this lesson plan, students use area models to deepen understanding of the distributive property.  Using this visual representation bridges the gap between the concrete and abstract.  Many students struggle with the concept of distributive property when they are first introduced to it.  Simply writing the property, a(b + c) = ab +ac, and showing students some problems, is not an effective way to teach this important property. 

To introduce this lesson, give each student a copy of a rectangle with a base of 6 inches and a height of 3 inches.  Have students use a ruler to determine the base and height.  Then, have them find the area of the rectangle (18in²).  To find the area of a rectangle, multiply the base times height.   Next, have them find the area of a rectangle formed by two smaller rectangles.  Have the students show two ways for finding the area of the rectangle formed by two smaller rectangles.  Here are two methods:

It’s important to let the students discover this relationship without offering too much guidance.  Give them time and have them work through it.  After they figure both methods for finding the area, have them compare and contrast the methods. Some may find the first method to be easier and vice versa but what is important is their understanding that these two expressions are equivalent.  Students can create their own rectangles with dimensions and have their peers solve them using both methods.  Reinforce their knowledge by presenting the property a(b + c) = ab + ac. 

Move onto adding a variable into the rectangles and evaluating both methods.  Continue with reinforcing their knowledge by creating their own problems and sharing them with their peers.  An activity sheet should be distributed in order to practice this concept and work with variations of these types of problems.  This activity uses many instructional strategies that were mentioned like visual representations, creating own problems, working with peers, and comparing and contrasting.  The teacher can use additional methods depending on the needs and culture of the class.