Synthesis of 3-Methylenecyclopentene from 1-methylCyclobutene
Here is my try.


Ozonolysis
Aldol condensation using a hindered base (like LDA)
Wittig reagent to convert $\ce{C=O}$ to $\ce{C=C}$


Step 1:



Step 2:

I used $\ce{LDA}$ which abstracts a proton from the least hindered carbon near to a carbonyl group. (So that the resulting carbanion is stable).
I am not drawing the enolate ion formation etc. You can find the reaction mechanism for aldol condensation here and the reaction using $\ce{LDA}$ here.




After protonation, you can heat the compound to remove $\ce{OH-}$ which is a simple dehydation. There are two possible alkenes. One of them (the one given below) is more stable because of conjugation.



Step 3:

We are almost done. To replace $\ce{C=O}$ with $\ce{C=C}$, use wittig reagent.