The mass of a piece of metal that is originally copper will increase.
This is because an oxide layer forms on its surface:
The total mass of copper is unchanged.
Video of this reaction begins at 6:10 - observe the color of the copper before and after heating. The change in color is caused by the formation of the oxide layer.
video from: Noel Pauller
Depending on the type of copper used, it can be possible for students to observe a decrease in mass if the sample is heated so vigorously that some of the copper oxide formed actually flies into the air and causes the mass of the remaining solid to be lower than the starting mass (but actually the mass goes up as discussed above, it's just that some mass might leave the copper sample which is being heated. The more common result is for students to observe an increase in mass.