How to muffle sound in noisy classroom?

I teach in a dance studio and it's loud as well. For an inexpensive way to reduce sound we got square egg cartons and pinned them to the ceiling and they work great!

go to yourlocal HI FI store...the foam packing used for electronics makes fabulous sound absorbing panels...glue to walls with contact cement...

it's what studios use too as well as Insulation batts held by chicken wire...

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If student chairs are the metal legged type, cut slits in old tennis balls and slip over each foot of the chairs. This will let chairs slide on floor without all the noise. Cork boards on the walls will help too with the added benefit of using for student work display.

Used tennis balls from the community tennis club work well on chair legs. Obtain foam alternatives for manipulative like dice, dominoes, & alphabet tiles. I don't allow those plastic snap pencil cases because they frequently drop and the contents scatter and sound like marbles. Instead, insist on zippered canvas pencil cases available in most dollar stores.

Teach students your management system for volume control for indoor activities with whole, small group, and partner work. Charts with finger signals for 1 to 5 with practice throughout the first weeks of school should help. Provide incentives initially for tables or individuals for compliance.

Use fabric and pillows where you can. Plastic is usually not as jarring as meta and stone furniture pieces when they drop.

I have a fetish for woven baskets. When they drop there's not as much noise because of their texture. They can be pricey. Wait for sales at your local craft shop but better still there's usually a dedicated section at the Goodwill store. Yard sales and flea markets are always options.

Soft background sounds can set the tone for a calming mood. Introduce your students to your quiet self and be consistent. Choose light classical jazz, Native-American, or sounds of nature tracks.

Remind them of how loudly they speak when they're loud unnecessarily. If others are not respectful, causing classmates to speak loudly, remind them it's not their turn to speak and listen to the speaker.

Hopefully, with your training your class will enjoy the fruits of your labor in an ideally active yet productive environment where the sounds of actual learning can be heard.

Best of Luck!

Some fabric on the walls may help. Hang some old curtains.