HSE Math: Unit 9

Many happy students working together in a group

Using Area Models to Understand Polynomials (lesson)

The lesson plan featured in this unit models a progression for using area models, starting with arrays and building all the way up to multiplying polynomials. It is intended to be taught over a series of classes. This lesson plan explores a concrete way for students to conceptualize multiplication that ultimately leads to a deeper understanding of what are typically taught as a purely abstract algebraic topics - multiplication and factorization of polynomials. It is a model of coherence in instruction, where students (and teachers) not only gain the ability to multiply polynomials, but also understand how it connects to the multiplication of integers they have been doing for years.

This lesson starts 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:

  1. Using Arrays to Explore Multiplication

  2. A Measured Area Model

  3. The Distributive Property

  4. An Abstract Area Model

  5. Applying an Area Model to the Multiplication of Polynomials

Read the full Unit 9 document.