I have given a talk to slightly older students, but the subject might be appropriate also to 9 year old students.

The talk was about bodies of constant width. Obviously circles have the properties that they are bodies of constant width (useful if you want to place stuff on a bunch of circles aka. "wheels"). This can be demonstrated by placing a board or similar on balls and move it around. The kicker is of course that (2D) circles (or 3d balls) are not the only bodies with this property (nowadays you can find 3D models printable by a 3D printer on the internet, I think the keyword here is Meissner body). There is a lot of applications one can talk about:

• Franz Reuleaux is said to have studied them to make buttons for his wife (I know different times) which do not roll away
• Canadian money is not round but made of shapes of constant width (some vending machines need this property to ascertain that they are handed in fact money)
• On a darker note, the challenger spaceshuttle catastrophe was at least partially caused by a "lack of roundness" (according to Feynmans memoirs) of the reusable parts which made the insulation fail. In said memoirs you find a beautiful little picture of a shape which is obviously not round but would have passed NASAs roundness test at that time (they checked roundness by measuring the width several times in certain fixed angles from each other, obviously such a test can never prove that we have constant width)

Finally, after all the hands on stuff, there are some nice mathematical theorems attached to it (e.g. Barbier's theorem 1) and even a lot of open questions when leaving 2D.

For inspiration one can look at the great book by Sagwin: How round is your circle? They made some promotional videos 2 and have great math and engineering examples collected. This might not be exactly what you had in mind, but I had great fun showing this to the students (especially since the 3D printer people at TU Berlin made a lot of great models for my talk)