Matchstick Brain Teasers

Browsing through a bookshelf of long-untouched childhood and school-era books, I found a couple that, upon leafing through them, made me wonder whether my mind was starting to slowly rust. I opened a few puzzles made from matchsticks.

I was reminded of primary school classrooms where, during maths lessons, we had to work with coloured sticks to perform addition and subtraction, as well as to arrange various geometric shapes. Hmm, interesting - do schools today still practise that?

First Puzzle

You will need to remember Roman numerals. Here are six equations. Move one matchstick in each to make a correct equation!

Second Puzzle

Using only six identical matchsticks 5 cm long, make one metre!

Third Puzzle

From 12 matchsticks, arrange the shape shown (see image)!

Then perform the following operations:
a) remove two matchsticks so that only two squares remain;
b) move three matchsticks so that all 12 matchsticks form three squares;
c) remove four matchsticks so that two squares remain.

So, how did it go? Did you manage?
I should note that all these puzzles are from a book intended for children under 12 - J. Mencis, P. Būmeistere, "A Little Box of Hard Nuts" (Rīga: Zvaigzne, 1986).