usually give them the task of having their turtle "draw" a square. Sometimes I
have them imagine the trail the turtle leaves; other times I have them leave a
trail made of string or ribbon (or toilet paper! Eighth graders love that!) Either
way a set of commands might be:

Go forward 20 steps.
Turn 90 degrees to the right.
Go forward 20 steps.
Turn 90 degrees to the right.
Go forward 20 steps.
Turn 90 degrees to the right.
Go forward 20 steps.
Turn 90 degrees to the right.
With younger kids I leave out the 90 degrees at first and just say "turn right."
But I begin using degrees as soon as possible no matter how young the kids are.

Somewhere along the line, I tell them that we can do all of this on the computer
screen with an animated turtle. I then show them how to type commands that
control the turtle on screen.

When they start up LOGO, the kids are presented with a small turtle in the
center of the screen and a blinking cursor at the bottom of the screen. If they
type "forward 40" the turtle jumps forward 40 turtle steps (maybe a couple of
centimeters) on the screen leaving a line behind. Typing "right 90" or "left 90"
causes the turtle to spin on its axis a quarter turn in the desired direction. Of
course they can turn the turtle any number of degrees; that's up to them.

It is amazing what interesting designs kids can draw just with forward, back,
right, and left. I usually give them plenty of time to experiment. Whenever I
think they are getting bored or a little frustrated, I give them some sort of hint
or question to provide them with more information. In this way, I try to lead
them to draw some mathematically interesting shapes. Pretty soon they always
discover squares and rectangles, either on their own or through my hints. Of
course, if they have played turtle on the floor, this goes along much faster. Here
are a couple of examples.