The goal is to map a magnetic field. The magnetic field is a vector quantity; it has a direction and a magnitude or strength. We can represent the direction of the field with arrows. Sometimes the vector length is altered to indicate the strength of the field. At other times the density of field lines indicates the strength (more lines indicating a stronger field.) There are two indications that tell us that the magnetic field is changing from one space point to another: the arrow changes direction and/or the density of field lines changes.
The map of arrows at grid points is a map of the direction of the magnetic field in the room the kids choose to work. When the grid points are connected, they should be connected in smooth curves (lines) and they should not cross other lines. That is, the field has a unique direction at each point in space, and in the absence of sources of magnetic field at the point of measurement, must show continuous changes from point to point. You might bring in a discussion of the topic of continuity at this juncture for the mathematically well prepared students.
The purpose of mapping the field due to a bar magnet is to give the kids a way of interpreting the curved patterns they (ought to) have found in their chosen map location.
The purpose of the predicting and checking of predictions is to apply the experimental process. Through discussion, draw out what the vectors represent, and what it means to connect each one. There is no "math" operation involved here (no sines and cosines, scalar or vector products.) The object is to establish that quantities for which our only measurement is "direction" are still valuable and contain information of interest and use.
Sample Map goes here