Eileen First of all I don't mean that life's experience will necessarily teach you to think algebraically. Life's experience gives you the background to formally learn to think algebraically.
As to what kind of experiences, It could be any thing one does that stimulates thinking and curiosity. Example: Kids playing cowboys and indians ( I know, politcaly incorrect but I'm thinking back to my younger days when I played cowboys and indians). One kid has made a make shift bow and arrow, when he shoots the arrow he notices that the arrow does not go far . He/She may question why. The child might also notice the "arc" of the arrow's flight. Extend this idea to playing baseball or softball.
How about Mom and Dad taking their children to museums? or to the zoo? or to a state park?