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The older child, police said, was recorded grabbing, pulling, dragging and swinging the smaller child.
As the younger student tried to get away, other students would stop her and hold her down, WBNS reported.
Police said Dietrich and Tennant watched it happen, but didn't do anything to stop it.
Eventually, police said Tennant picked the girl up, holding her upside down by the ankle and put her down on a rug, WCMH reported.
Police also released a still image from the video showing the girl hanging from her ankle.
They were both arrested this week and charged with endangering children in connection with the Aug. 13 incident.
Once the facility's owner saw the video, she fired Tennant and Dietrich, telling WBNS that she has "zero tolerance" for behavior like she saw on the recording and that all of her employees go through extensive training.
Police said Tennant and Dietrich said they allowed the bullying to happen as a form of discipline, WCMH reported.