Learning Algebra is easy with Slim Goodbody s X-Team! For Middle & High School Students Ages 12+ Meet the X-team and join them as they use their logic and problem solving strategies to tackle tough academic challen... more »ges. Together with history's great mathematical minds ... you ll help solve the mystery of ALGEBRA with this fun and innovative path to learning math. 10 Programs in all! Intent and Mathematical Overview of Program: Factors (A Doorway Through) focuses on decomposing a number by its factors or on building a product given the factors. Algebra Tiles TM are used to demonstrate how products can be represented by an area model. The program 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 TilesTM, 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. Principles and Standards for School Mathematics The Principles and Standards for School Mathematics (National Council of Teachers of Mathematics, 2000) includes standards and benchmarks that are related and aligned with the mathematical presentation in this program. These principles and standards have been followed in this program for Grades 6-8 and 9-12.« less
