Water is one of the few substances with a solid form that is less dense than its liquid form.
Descride what would happen to a small lake if ice were more dense than water and the lake started to freeze
Remembering that less dense materials float on top of more dense materials, we would expect as the water began to freeze, its density would increase and it would sink to the bottom where it would eventually form a solid. The sinking water/ice would create convection currents which could alter the chemistry of the water. The ice settling to the bottom would also eliminate the insulating property of the ice layer on top thus causing the mud at the bottom to freeze over time. This would probably kill aquatic life that uses the warmer bottom of the lake to survive the winter. In fact, a pretty good argument could be made for the extinction (or lack of evolution) of many forms of life if water ice were more dense than liquid water.
Let's start by defining "dense" in scientific terminology. "Density" means "the mass of a unit volume of some material." In the case of your problem, the unit volume we're discussing is the amount of H2O contained in the small lake. In a liquid form, H2O is called water. In a solid form, H2O is called ice.
In your problem, you are imagining that ice (the solid form) is more dense than water (the liquid form). As the more dense substance, the ice would have a higher specific gravity. If the top one inch of water in the lake froze and became ice, that top one inch of ice would become more dense than the water below it. Because of that greater density, the ice would sink down into the less dense, still liquid water below it.
In reality, the solid form of H2O is less dense than the liquid form. That's why ice floats on top of the lake as lake water freezes.