In this paper, we design sub-linear space streaming algorithms for estimating three fundamental parameters -- maximum independent set, minimum dominating set and maximum matching -- on sparse graph classes, i.e., graphs which satisfy $m=O(n)$ where $m,n$ is the number of edges, vertices respectively. Each of the three graph parameters we consider can have size $Ω(n)$ even on sparse graph classes, and hence for sublinear-space algorithms we are restricted to parameter estimation instead of attempting to find a solution.