In terms of relating the activity to Ancient Rome, I suggest starting with a great book such as "Roman City" by David Macauly or a movie like the one about Rome from "Engineering an Empire" by the History Channel. However, you'll need to pick out what is right for your child at his/her age. ALWAYS preview such material before using with your child.
You might take a look at the images and information below and look at how many of the featured structures use arches. Make sure to explain what an arch is and introduce the vocabulary "keystone" as well. If you have particularly young children introduce them to the Keystone first with THIS ACTIVITY to help make the building of your arch more successful. See if you can point to the keystone (top stone that was the final stone placed and was the "key" in keeping it all up) in any of the images.
Images of Roman Arches
Amazing Roman Structures
Stress to your child how important the use of the arch was in the success of Ancient Roman builders.
To really help kids understand why incorporating the arch into their structures was so important in attaining their building achievements check out Engineering the Impossible: Arches vs. Beams. If they find this interesting, you might also check out other videos from the science channel about Roman Building Achievements later. You might also want to try the breaking bridges activity.
Gather some pebbles. Oblong and fairly flat stones work best. You'll need an assortment so you have a few left over and can make decisions according to what fits best while you work.
If you are using a mortar that will need baking, line a cookie sheet with foil first and preheat your oven. Set a soda can on the foil. Start the arch by placing your largest pebbles on either side of the soda can on foil on a flat surface. Plop a bit of mortar on each pebble. Build your arch up and around the soda can finishing by placing the keystone at the top with mortar on each side.
After the mortar has dried, slide the soda can out and place your arch in a special location to remind your kids of the feats the Roman's achieved because of the discovery of cement and the use of arches in their structures. Then follow this lesson with "breaking bridges" as a great way to really drive their learning home. For more Lesson Ideas and Resources about Ancient Rome