the 'low-cost' part of your query
Most of popular HW for Arduino - is low-cost. So, why to want costlier.
But strange that no "easy googling" popular solution for 10-15m.
Ultrasonic meters always depend on the sensor itself, working as US loudspeaker and receiver. Industrial sensor-components, say Murata, are all 10...16 mm, for 3...6 meters.
I've seen some reference device were some custom ultrasonic meter is built-in, and there is some unique 30 mm sensor. And this one allows to declare 10m.
But the circuit is also custom, with opamps, variable resistor to setup.... not a ready-to-use module.
Laser ones, i think, are not for school, even if low power, better not to touch, IMHO...