River of Time: Polynomials focuses on different types of polynomial equations that are represented by symbols, graphs, tables, and geometric shapes. The concept of using a quadratic equation written in standard form and factoring it is introduced. The program ends with the introduction of the Quadratic Formula.

The program begins with the X-team asking Holon to explain how he is able to send them back in time. Holon explains the phenomena through quadratic equations
that are similar to the formulas used when an object is thrown into the air. The equations are shown along with the associated tables and graphs. Students can
quickly see many relationships or patterns in the graph, such as the symmetry of parabolas.

In the second segment of River of Time, students have the opportunity to solve a geometric problem involving area. The problem is presented before students see
the symbolic representation that the X-team uses and thus they can be encouraged to use multiple ways to solve the problem.

When students view the segment illustrating how the X-team solved the problem using algebra, they have the opportunity to think about the relationships between
factors when the product is 0. While the process is not given step-by-step, students are exposed to the conceptual idea that if the product is 0, one or both of the
factors must be 0.

The final segment of River of Time ends with the X-team being given access to the Quadratic Formula. No formal discussion or use of the formula is done in the
program but it allows you as the classroom teacher to make the link between the ideas about polynomials to the Quadratic Formula itself. If students have used
Completing the Square as a method for solving quadratic equations, you can show how the Quadratic Formula was developed.

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