In this video, students learn how to determine if they have written an algebraic expression correctly by analyzing real-world scenarios. They are taught to define the variable, identify the unknown amount they are looking for, and consider the operations involved. The video also emphasizes the importance of not simply writing expressions word for word and provides examples to demonstrate the correct order of operations. By analyzing different expressions and using substitution, students gain a clear understanding of how to match algebraic expressions to real-world situations.