Properties of Lines & points can be studied even through paper folding activities. Some are given here.
Fold a simple paper plane. Throw it in the air and see if it glides smoothly.
Fold a line.
Fold a line which intersects with the first line
Fold a line which intersects with the first line but with a larger angle of intersection.
Fold a line which is parallel to the first line
Fold a line perpendicular to the first line
Mark 2 points on the paper. Fold a line which passes through both the points.
Find the point on the line folded in (6) which is equidistance from both the points.
Mark 3 points on the paper. Fold a line which passes through the 3 points.
Fold a cone
Fold a cone with a bigger base than that in (10)
Cut out a shape which can fold into a cone which can rest stably on a table surface
Fold a cylinder
Cut a shape which can fold into a square or rectangular box with one side open.
Fold a paper, without cutting, into a flat triangle
Fold a paper, without cutting, into a triangle with 2 sides which are equal.
Fold a paper, without cutting, into a rectangle
Take a paper strip, shaped like a ribbon, and fold into a 5 sided figure
Make a Mobius Strip. Find out how many faces, edges and corners it has.