# Unpacking Algebra I, Module 4

The Algebra I session was focused on presenting the rationale behind the lessons of Module 4, “Polynomial and Quadratic Expressions, Equations and Functions.” Participants discussed many scaffolding ideas, which reconfirmed the power of the Algebra I standards and how they lay the foundational pieces for the mathematics studied in Algebra II and Calculus (exploratory exercise 2 from lesson 8).

The first hour of the session was dedicated to the mathematician in us all, as it provided an adult experience/perspective that dealt with the foundation of quadratics. This foundation was explored in three pieces:

1. How do sequences and their leading diagonals coupled with basic polynomial building blocks help generate quadratic equations?
2. Gravity is why we study quadratics. If acceleration is a constant, the formula for defining height is a quadratic.
3. Can any U-shaped graph be represented by a quadratic? Answer: No.

Participants engaged in an excellent activity that is not in the modules, but should be part of every mathematics classroom. Educators taped the ends of a chain together so that the lowest part of the chain was at the origin. They then identified points that the chain went through. The task was to create a quadratic equation to fit the curve. Looks can be deceiving, and not all of the chain curves ended up being quadratic. This was a challenging, thought-provoking activity for all, and a question not usually tackled until Algebra II.

For most of the morning and part of the afternoon, participants focused on Topic A, which covers the following:

• Reverse multiplication (factoring) and the connection to the geometric models (rectangles);
• The zero product property;