Solutions of aqueous methylcellulose, a hydro-phobically modified polymer (molecular weight approximate to 270 kg/mol, methyl content,approximate to 130%), are mixed with either dilute coumarin fluorescent dye or carboxylated latex (20 nm diameter), and the tracer diffusion is contrasted as a function of temperature and polymer concentration (from dilute to 36 times the overlap concentration) in deionized water. From two-photon fluorescence correlation spectroscopy (FCS), mean-square displacement is inferred. At room temperature, which is the fluid state, we observe Fickian diffusion provided that the tracer particle size is less than the polymer mesh size, whereas tighter meshes produce subdiffusion followed by Fickian diffusion at long times. At elevated temperature, which is the gel state, subdiffusion is observed over the entire experimental time window. To quantify subdiffusion, the data are described equally well as two discrete relaxations or a stretched exponential, and the former is analyzed in detail as it is considered to be more meaningful physically. These measurements allow us to discuss the structure and degree of inhomogeneity of methylcellulose in the gel state. This industrially relevant polymer produces simple, physically meaningful diffusion patterns that we find to be repeatable, obeying systematic patterns described quantitatively in this paper.