Matilda (film)/WMG

Matilda is a witch.
When witches and wizards are young, they often cause magical things to happen when under stress or pressure. Matilda's telekinetic powers were a result of this.

Matilda is a Muggle-born witch.
Doubt me? Re-watch the movie with this in mind.

In the movie, her powers can easily be seen as underage magic and look quite similar to it. They are activated and amplified with emotion and require practice to learn and control. Matilda would be a very powerful witch to have such control at such a young age, which is shown to be very possible from Tom Riddle and Lily Evans-Potter. Tom also shows us that wandless magic is the most common, if not the only option, for children who haven’t purchased their own wands yet.

It is logical that Matilda, being six or seven, is still attending a Muggle school because she's simply to young to attend her country's Wizarding School, and as Severus Snape once said, the law doesn’t count magic done by little kids who aren’t even in school as illegal magic.

Let the fanfiction and parallels begin.