Ah! Indeed, the original disk image transferred to a larger micro SD ignores the added space until you supply two essential Terminal commands to re-size the file system in order for the Pi system to recognize the increased storage available on the 16GB micro SD card.
fruitoftheloom has wisely referred you to the developer site of Ubuntu Mate for Raspberry Pi. Scroll down the page,
http://ubuntu-mate.org/raspberry-pi/ until you see the large-font topic: "
Re-size file system".
[
Now follows my rehashing of this peculiar concept of "Re-size":]
The solution provided there on the developers page is awe-inspiring because of the way it accomplishes this task. Since I had not previously encountered this method (due to my noobness), it was an exciting revelation to me.
The first command uses the "
fdisk" Terminal command to delete the partition. At first, I recoiled at this recommendation to delete the partition I had just written to a new larger card, but then I realized fdisk does not delete the data, it deletes the table of information
about the partition -- and then recreates the information to include the additional space on the card. Wow, I really appreciate the awesome power of fdisk.
However, read the Ubuntu Mate developer page instruction
carefully. Fdisk is a command which is interactive and accepts specific and sequential single-character sub-commands: (d, 2), then (n, p, 2, enter, enter), then (w).
After the partition's info reconfiguration and a reboot, the second Terminal command, "
resize2fs"(also specified on the Ubuntu Mate developers page), is used to apply the newly-created partition information to the /dev/mmcblk0p2 partition.
Viola! like magic, the additional space becomes available. I very much hope you will find this to be the case. I hope it works as well for you as it does for me.