This lesson plan explores a concrete way for students to conceptualize multiplication that ultimately leads to a deeper understanding of abstract algebraic topics, including multiplication and factorization of polynomials. We hope that this approach will allow both teachers and students to come away with a better sense of how multiplication of polynomials is connected to multiplication of integers.
In this lesson, we start with intuitive images of arrays, move to concrete representations of area with manipulatives and graph paper, and continue in scaffolded steps towards an abstraction of the area model of multiplication, which we will use to multiply polynomials.
This lesson is made up of the following sections, which should be
followed in order:
- Using Arrays to Explore Multiplication
- A Measured Area Model
- The Distributive Property
- An Abstract Area Model
- Applying an Area Model to the Multiplication of Polynomials
We recommend using these activities over a series of classes. In addition
to developing fluency with multiplication of integers, fractions, percents,
monomials, and binomials, the area model has the added usefulness of
helping students understand area and perimeter. This model can create
a shared visual language to refer back to when students struggle with
multiplication in different contexts.
