For purposes of engineering education, computer experiments or simulations are powerful tools to demonstrate and emphasize physical concepts instead of relying on complex and ambiguous mathematics. The main advantage of MC methods in the discipline of neutron transport that facilitates teaching is the simplicity of the Random Walk concept; thus, allowing the use of trivial arguments and visualization of problems. Simple applications of MC methods for neutron slowing-down and diffusion through elastic scattering and absorption in a homogeneous media from a monochromatic beam were illustrated separately by Peralta (2002 Eur. J. Phys. 23 307) and Capizzo et al. (2005 Eur. J. Phys. 26 85). In this contribution, the two applications are merged to serve as a course project, a few corrections to the original manuscripts are provided and important theoretical aspects are highlighted. In essence, conservation equations of neutron-nucleus collisions are solved using frame-of-reference transformation and analytical formula independently to demonstrate the equivalency using the case of slowing-down in a mixture. 1-D/3-D transformation of coordinates are reviewed and deployed to eliminate any bias in the MC simulation.