  Unstable modules over the Steenrod algebra with only the top $k$ operations
are introduced in the language of ringoids. We prove the category of such
modules has homological dimension at most $k$. A pratical method, which
generalizes the $\Lambda$ complex, to compute the $\mathrm{Ext}$ group from
such modules to spheres is proposed. We are also able to establish several
functors to relate such modules and unstable modules over the Steenrod algebra,
and to describe the connections between the $\mathrm{Ext}$ groups in them.
