Jordan canonical form (JCF) is one of the most important, and useful, concepts in linear algebra. Mathematics, physics, biology, science and engineering undergraduates often find the first application of real JCF in the discipline of differential equations (continuous models) to solving systems of differential equations. In this work, we apply real JCF to understand, through analytical and numerical methods, the two-dimensional linear discrete dynamical systems. After that, we present a schematic model of red blood cell production. An advantage of discrete models over continuous models is that they readily yield numerical exploration, whether by calculator or computer (in our case we will use "Mathematica" software). This fact provides us with a valuable pedagogical resource because we can find a simple model to show the links between mathematics and other areas of knowledge without the need for sophisticated mathematical concepts beyond linear algebra. Following Paul Halmos's suggestion, 'The only way to learn mathematics is to do mathematics', some classroom exercises are given to better understand the subject, and a project for further student investigations is suggested.