For my geometry class for middle school teachers, I gave the students the Cartesian coordinates of the vertices of a quadrilateral and asked them to compute the area 3 ways: (1) Let Sketchpad do it. (2) Use the "Surveyor's Formula". (3) Use Pick's Theorem. I told them to observe that they got the same result each way. Unfortunately, this does not always happen! The problem is that Sketchpad computes the area in square cm, while the other methods compute the area in square units. It appears that the default is 1 cm = 1 unit, so the answers should be numerically the same. Two of my students returned files in which the unit had been changed to 0.8 cm, so the numerical value of the answers were different.
Here's where things get interesting. I explained to the students what had happened and asked them to start over and make sure that the distance between (0, 0) and (1, 0) was 1 cm. On student said she had done that but GSP changed the distance back to 0.8 cm as she worked! I am attaching her file.
I further suggested that as a work-around they could move the unit point to the right until the unit distance was 1 cm, and that they should use the arrow key on the keyboard for fine control of the point location. However, it seems impossible to get a unit distance of exactly 1 cm this way. One press of the arrow key moves the unit distance from approximately 0.99 cm to approximately 1.01 cm.
We are using Sketchpad 5. I don't know the point release they used.
Does anyone have any idea why this is happening or how the problem can be avoided? It is extremely frustrating to them and now to me.