Published in American Journal of Physics, Volume 80, Issue 5, May 1, 2012, pages 367-375.
The definitive version is available at https://doi.org/10.1119/1.3698352.
As the universe expands astronomical observables such as brightness and angular size on the sky change in ways that differ from our simple Cartesian expectation. We show how observed quantities depend on the expansion of space and demonstrate how to calculate such quantities using the Friedmann equations. The general solution to the Friedmann equations requires a numerical solution which is easily coded in any computing language (including EXCEL). We use these numerical calculations in four student projects that help to build their understanding of high-redshift phenomena and cosmology. Instructions for these projects are available as supplementary materials.