A Doorway Through: Factors focuses on decomposing a number by its factors or on building a product given the factors. Algebra Tiles ™ are used to
demonstrate how products can be represented by an area model.

The episode begins with the X-team encountering a situation in which they work with whole numbers. Rather than listing the numerical factors of the whole
numbers, the X-team is asked to find all rectangles that have a given area. As they compare the number of rectangles that can be made from the factors of a
given number, the team begins to consider the relationship between the magnitude of the number and the number of factors. They sometimes make over-generalizations,
assuming that as the magnitude of the number increases, the number of possible rectangles they can make also increases.

The number of rectangles is explicitly linked to the integral factors in the initial segments of A Doorway Through. This helps students who sometimes do not see
the relationships between the dimensions of the rectangle and its area with the factors in a numerical situation that they may be more comfortable with before moving
to a more symbolic context. The numerical situation provides a means for you to discuss composite and prime numbers as well as finding ways of determining all
integral factors by using prime factors. It is also an opportunity to consider the relationship between the number of factors and the type of number. For example,
square numbers have an odd number of factors because one factor is repeated.

From the numerical context, the X-team then moves to reversing the thinking used to decompose a number to composing an area given the dimensions but now in a
symbolic context. By using materials similar to Algebra Tiles™, the X-team creates a rectangular area, forcing students to think conceptually about the relationship
between the dimensions and area. Unusual symbols are used to represent the binomials that form the dimensions of the rectangular area. The solution process that the
X-team uses can be generalized to any binomial multiplication.

Rights granted with the purchase of DVD or VHS include: a) life of media audiovisual use, b) public performance, c) campus or building closed circuit and
digital/video-on-demand transmission.