Is a piece of ice melts and reacts with sodium a physical change?

When a piece of ice melts, it undergoes a physical change as it transitions from solid to liquid without altering its chemical composition. However, if the melted ice (water) then reacts with sodium, that reaction involves a chemical change, as it produces new substances (sodium hydroxide and hydrogen gas). Therefore, the melting itself is a physical change, while the reaction with sodium is a chemical change.