What You Did
You discovered an easy way to make ice that’s as clear as glass.
Your boiled water, when frozen, should look very foggy.Your shaken water, when frozen, should be clear or nearly so.
If you jostled the boiled water too much, you may have shaken the air bubbles out, and didn’t see the ice as very foggy
Try observing the bubbles in the boiled-water ice with your microscope
states of matter, freezing point, water impurities