Why does the resistance of a brushed Dc motor from an experiment kit vary?
A motor isn't just a resistor. It's not just a resistor and BEMF source either. You cannot use V=IR to try and calculate a motor winding resistance while it is spinning because a bunch of other variables are also present.
At the absolute minimum, your model should also include an inductance:



simulate this circuit &ndash; Schematic created using CircuitLab



simulate this circuit
You can then measure the current and voltage at the motor terminals at various supply voltages and RPM/loads to figure out what the kV (BEMF voltage per RPM), inductance, and winding resistance are.
But you will need to be able to measure the RPM for this since the impedance drop presented by the inductance varies with frequency which varies with RPM (and so too does the BEMF voltage).
But if you have a smart meter to measure things that is able to separate out the reactive voltage drop due to the inductance from the resistive voltage drop, it will still measure a higher resistance while running, and the faster it runs the higher this resistance will measure.
The rotating magnetic field induces eddy currents to circulate with the iron core itself. These only appear while the motor is running and increase with frequency (RPM). They manifest as a voltage drop and with all the characteristics I listed, at first glance you would think they appear to be just like the voltage drop due to the inductance. But they are not. They have one critical difference: They are still resistive losses that permanently remove energy from the system unlike the inductance which absorbs energy only to release it later in the future. So there is actually a fixed resistor in the motor due to winding resistance but eddy currents in the core also produces the equivalent of a second resistor which is frequency dependent.
If this is for a science fair you can try to weed out those parameters and if you do it well, you should be able roughly predict things how it will behave.