Compute $\operatorname{Tor}_n^R(I,R/I)$

Compute $\operatorname{Tor}_n^R(I,R/I)$

The problem is as follows:
Let $I=\langle x^2,y\rangle\subset R=\mathbb{Q}[x,y]$. Compute
$\operatorname{Tor}_n^R(I,R/I)$ for all $n\geq 0$.
Thoughts:
Usually when I see these types of problems, I consider a SES of the form(s):
$0\rightarrow I\rightarrow R\rightarrow R/I\rightarrow 0$ or
$0\rightarrow R\rightarrow R\rightarrow R/I\rightarrow 0$ where the first
map in the last SES would be multiplication by an appropriate factor.
The first SES does not seem promising in our case, since it boils down to
computing $\operatorname{Tor}_n^R(I,I)$, which I don't see any immediate
ways of doing.
To use the second SES I was thinking of letting $f:R\rightarrow R$ be such
that $x\rightarrow x^2$ and $y\rightarrow y$.
I'm not sure if this would work?