What could you put in the middle of a lunch table to make the room quieter?

Putting something on the table isn't going to solve this.

Wall length curtains will kill the echo...as it makes the walls softer and it absorbs sound. Would be cheaper than the cardboard box. Or even quilts nailed onto the walls stretched out is a buffer.

Until you can get some acoustic treatment on the walls, try different management techniques entirely (with permission from your supervisor):

Play chill (moderate) music at an acceptable level in the room. This tends to quiet people down. Then tell the children that if you can't hear the music, the talking has to stop until you can hear the music again.

Or, use an automated traffic stoplight: green means the noise is at an acceptable level, yellow means it's starting to get too loud, red means it's too loud and everybody has to stop and quiet down.

No I don't think that would work at all. Try ear plugs.

The problem you face is in the room itself, not the tables or students. I'm pretty sure this is a cement block room, with a high ceiling. Add to that linoleum floors and you have a very "live" room. Something in the middle of the table would have a lot of wear, not to mentions spills so you would do better with a larger wall project. Include the students.

Start with as many cardboard egg crates as they can bring in. Make it a contest for the room who brings in the most. The egg portions are cut off the tops and the students can then paint the raised outsides. Having the students bring them in makes this project cheap cheap cheap. Just make sure they are clean. :)

Once dry, each egg crate can be then glued to a large piece of cardboard. (Just like those boards students use for science projects. You could even use cheap flat cardboard boxes like those found at Walmart or U-Haul) As I say, it will take a lot of egg boxes.

Place these (as many as you can make) spaced evenly apart on the walls. This will cut down on a lot of the echo effects and will be easier to handle than something which is placed on the table every day.

(Edit to add: I'd love to see photos of the finished room, too! )

Anything that absorbs sound will help, but acoustic foam in the center of each table would make it hard for the people at the table to interact. Aren't interpersonal skills something that we want to encourage? It could go one of two ways....either the kids will only speak to those seated next to them, or they will have to yell around the foam to the kids across the table.

I have to wonder if there aren't better solutions. How about banners to hang on the walls and from the ceiling? They aren't as effective as acoustic tile, but everything helps, especially if the wall banners are mounted with an airspace behind them...maybe an inch or two. You could make banners as part of the art curriculum. Cork bulletin boards also absorb sound. So do folding dividers (like used in dressing rooms) which could be moved around and folded when not in use.

Take the cardboard and make a bunch of dividers out of it and set it on the table. Like a pie that has been sliced. Then tell the kids that the divider is part of teaching them table manners, and they need to learn them without looking at the other kids so that they know these things themselves. Then, teach each kid good table etiquette and he will remember you forever. Which includes being quieter at the table. Just be sure you know it yourself.

imagine that....... someone working in an education position, yet doesn't know how simple physics work.