Card Houses, Patterns, and Algebraic Expressions

 My pre-algebra and algebra classes are learning about algebraic expressions, also called variable expressions.  It is important for them to be able to observe patterns, to identify the constant and changing parts of those patterns and to write variable expressions that represent the patterns. Yesterday we built card houses with that intent.  I demonstrated and off they went.  With each layer, they had to measure how high the top was from the floor. They quickly found they didn't have to measure from the floor each time, because the height of the table didn't change. The house of cards were approximately 9cm tall per story, so each additional story added 9cm to the total.  We built a table of the data, and decided what would happen with a card house any number of stories high. We made the table below, then the students told me how far from the floor a card house of 10 stories would be, 15 stories would be.  They've got this... finding patterns, writing expressions, making predictions.  And, they had a blast.