What relationship do you see between a planet's speed of rotation and its length of day? was a question in my 3rd grade test and my answer was
"The speed of rotation and the diameter of the planet effects how many hours are in a day in a planet."
My teacher said I was wrong she said "The faster a planet spins and orbits the sun, the shorter the length of its day."
How does the orbit around the sun have any effect on the amount of hours in a planets day?
Your answer was more nearly correct. The teacher's answer was almost completely wrong. The correct answer would be that the rotation rate depends on the speed of rotation and the size of the planet, but the length of the day can be changed by the motion of the planet around the Sun. So your answer was partially correct. But your teacher's answer was backwards, as faster orbital motion usually makes the day LONGER.
The planet's rotation rate (turning once around on its axis) depends only on the rate at which the planet rotates (in miles per hour) and how big it is, and has nothing to do with the planet's motion around the Sun. So your answer was perfectly correct, if what you wanted was the rotation rate. However, the motion around the Sun causes a difference between the length of the rotation and the length of the day. For instance, Mercury rotates in only 56 Earth days, but its day is 176 Earth days long; while Venus rotates in only 117 Earth days, but its day is about 225 Earth days long. What is happening is that the motion of those planets around the Sun makes their days much longer than the rotation periods. This is only true for the two inner planets. For all the others, the difference between the rotation period and the day is at most a few minutes; but the statement "the faster a planet spins and orbits the Sun, the shorter the length of its day" is completely wrong, as you can see from the fact that the two planets with the fastest orbits have the longest days.
For a detailed discussion of the relationship between the length of the rotation period (which is what your answer would have given) and the length of the day, see http://cseligman.com/text/sky/rotationvsday.htm