Macy’s Star Rewards Points

Wow! Check out this deal at Macy's.  For $25 I can join Macy's Star Rewards program. I get 10% back in rewards for every dollar I spend.  Its pretty cool that Macy's gives part of that $25 to charity.  Should you do it?  It seems like free money (or clothes) just for shopping at Macy's.  Factoring in the $25 enrollment fee, how much do you need to spend at Macy's to come out ahead? For what total shopping dollar amounts is this a bad deal for the consumer?  What dollar amount must you spend to at least break even?  Can you write a rule that gives the dollars earned at Macy's after the $25 registration fee for any dollar amount of purchases?

This task could be used to address many different Common Core Standards in various grade levels.  7th graders can create and solve equations in the form of y = 0.1x - 25, where y is the dollars earned and x is total dollars spent.  For example, after working through several examples, they might notice and create the equation y = 0.1(x) - 25.  From there they might consider equations like 100 = 0.1x - 25 in order to find the amount necessary to spend to come out $100 ahead.  8th graders and high school students can go through a similar process and focus more on thinking about inputs and outputs as well as the functional relationship between the variables.  The activity can easily be extended to consider slope and y-intercept while studying linear relationships.