they all start with math because they are telling you that it is about math and its trying to atract people who are looking for mathe stuff
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There are many properties and it is impossible to name them all. The question needs to be more specific.
First start with m a t h. If you put it all together math.
There are plenty of websites but not all of them are children friendly or virus proof but the one that is fine is bitesize or revise wise and then you just add your keystage( ks1, ks2 or ks3)
Quadrilateral, Parralellogram, and Rectangle. These are all correct names for squares. And yes, rectangle is a correct name for a square, just ask any math teacher.
There are several websites which offer math learning games for children of all ages. Try Learning Games For Kids or Tine 4 Learning, both of which are free to use.