If $M$ is finitely generated left module over a left noetherian ring $R$, then $M$ is a noetherian module.

I need to show that an arbitrary ascending chain of submodules of $M$ must satisfy *ACC*, or equivalently, every submodule of $M$ is finitely generated. 

Since $R$ is a left noetherian ring, every left ideal in $R$ is finitely generated. I am trying to find a 1-1 correspondence between left ideals of $R$ and submodules of $M$. 
Is it a correct way, or how can I show the assertion by a different way? Thanks.