This is the lesson that many teachers skip or fly through because they "assume" (in huge air quotes) that the students know what these things are before they get to high school geometry.
Unfortunately without a great understanding of points lines and planes it's almost impossible for them to grasp the tougher stuff.
Most students think that a point is something they can actually draw. They think you should be able to see it. They don't understand that it is a location and not a dot on the paper with your pencil.
One great way to start this lesson is to tell them to actually draw a point either on their paper or have one student draw it on the board. Them ask a different student to measure the length and with of the point with a ruler. They will do it or try to do it and give actual numbers.
Then you question them. If a point has no dimensions then how did you just give me measurements? This is where you explain that a point in geometry is a location. You can't actually draw it because the second you put your pencil on paper you can measure it.
Points have no dimensions!
A line has one dimension. So again you can't really draw one because when you put your pencil on the paper it has a length and a width you can measure both. The lines you actually draw in geometry class are representations of lines. We can't actually see them. Lines are used to measure distance. A great way to show this to them is have a really thin pencil and a really thick marker and tell two students to draw lines. They will visibly be able to see the thickness of the marker.
Lines are one dimensional!
Planes are where things get fun. Now you are talking about space. Planes have a length and a width and are made up of infinitely many lines which are made of infinitely many points! What?
A Plane is a flat surface that has no start and no end in two of the dimensions. So can you actually draw one? Nope!
Planes are two dimensional!
Here is a video to help out! Don't make it more confusing that it already is. Your lesson on [Dimensions
] will greatly reduce the confusion with these three things. The better they understand dimensions the better they will understand Points, Lines and Planes.