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Yes, the reaction between sodium metal and water is a chemical change.
A chemical change is said to take place when two or more substances interact if this interaction results in the formation of one or more new substances.
SImply put, if you start with a substance and end up with another substance altogether, a chemical change took place.
In your case, the interaction between sodium metal and water will result in the formation of two new substances, sodium hydroxide and hydrogen gas.
The balanced chemical equation for this reaction looks like this
##2Na_((s)) + 2H_2O_((l)) -> 2NaOH_((aq)) + H_(2(g))##
Sodium hydroxide, ##NaOH##, is very soluble in aqueous solution, so it will exist as
##NaOH_((aq)) -> Na_((aq))^(+) + OH_((aq))^(-)##
The ionic equation will thus look like this
##2Na_((s)) + 2H_2O_((l)) -> 2Na_((aq))^(+) + 2OH_((aq))^(-) + H_(2(g))##
As you can see, sodium no longer exists as metal after the reaction, it exists as sodium cations, ##Na^(+)##. Moreover, hydrogen gas and hydroxide ions were produced as a result of this reaction.
So, you started with sodium metal and ended up with sodium cations, hydroxide ions, and hydrogen gas.
This means that your reaction was indeed a .
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