There is a meme alive in the science education system and it must go. The meme is that rocket motion is best explained using Newton’s 3rd law.
Quite frankly the fact that an intelligent student who has worked this out herself and can be marked in an exam as if she is wrong is all the justification I need to support the homeschooling movement. Our teachers’ inability to wield 350-year-old logic tools is simply frightening.
If you would like a simplified “rockets motion in space” version here is one which excludes Newton’s 1st law: