Sound (acoustics) moves through space in 3 modes: reflect, absorb, diffuse.
- Reflection - This happens on SMOOTH hard surfaces when sound waves are "reflected back" in the opposite direction they hit the surface/object. Examples of these surfaces/materials in a home are: glass windows, wood, floors, wood ceilings, metal objects, mirrors, glass objects, etc. This form is the has the LEASE amount of sound reduction.
- Absorption - This happens on ALL soft surfaces when sound waves are "absorbed into" the object/material in the same direction they hit the object/material. Examples of these surfaces/materials in a home are: fabric furniture (couch, bed, etc), clothing hanging/folded in closet, carpet, rugs, hanging textiles, curtains, leafy plants, etc. This form has the MOST amount of sound reduction.
- Diffusion - This happens on semi-hard/semi-soft IRREGULAR surfaces when sound waves are "scattered" in multiple directions away from and into the object/material. Examples of these surfaces/materials in a home are: a shelf full of books or magazines, vinyl records on a shelf, plants, furniture (hard/soft material combo), collectables, etc.
In the specific case you mentioned it would depend on factors like: are the kids allowed to wear shoes in the house, are they playing upstairs or downstairs, etc. Some architectural elements to assist with sound absorption could be additional padding under wood floor and under carpeting since sound travels THROUGH objects (much like temperature)...so the more you can slow it down, the less distance it travels.
Hope this helps!