beware, be aware

Beware or beware means be careful or cautious, most commonly used as a warning of potential danger--
The sign says "beware of dog".
"The night is like a lovely tune, beware my foolish heart..."

Be aware or be aware ( two words ) means be in a state of ( be ) consciousness or knowledge ( aware )--
Every student should be aware of the location of the emergency exits.
Please be aware that skateboards are not permitted in the park.

Now that you know that, you can say--
"We should teach the children to be aware of their surroundings, and to beware of strangers."

Note--"be wary" means be in a state of ( be ) watchful, on guard, or cautious ( wary )--
When the press is running, be wary; the moving parts can be dangerous.