The purpose of this course is for the students to discover the principles of Mathematics through exploration, and then to solidify this knowledge through practice. The reading of Discovering Algebra: An Investigative Approach leads the students to their own discovery of the mathematics. This will be complemented with problem sets that will allow the students to solidfy their skills. This course examines 1) the acquisition, analysis, and display of data (graphs and charts), 2) multiple representations of linear and quadratic relations, equations, inequalities, and functions, and 3) factoring and multiplying expressions. As time permits, we may examine 1) experimental and theoretical probability and 2) simple trigonometry. Throughout, careful reasoning and real understanding are encouraged and prized.