I just learned that I may be teaching Algebra 2 instead of Algebra 1 next year. So I found an old Algebra 2 book on my shelf and thumbed through the first chapter. I know that our first unit will be "foundations of functions" reviewing linear functions.
The problem that caught my eye is this one from Holt Algebra 2, 2004:
I understand why the textbook provides the scaffolding in the first question (a) but I'd like to remove that. I would also reword the question to make it more personal. Mine might look like this:
Your English teacher knows you are taking Pre-AP Algebra 2 so she quietly asks you to help her with some math. She gave a test and the scores were lower than she expected; they ranged from 40 to 80. (In fact, YOU scored an 80!) She wants to adjust those grades and make them range from 60 to 90 but she isn't sure how to change the scores accurately. Explain to your teacher how to set up a function and create a table of adjusted scores.
I would expect an equation, a table of adjusted scores (in a spreadsheet, preferably), and a graph. In a written explanation, I would expect students to interpret the meaning of the intercepts and the slope.
In completing this problem students would explain the variables in the given context, identify the domain and range, and predict the value of the independent variable when given the dependent and the other way around.
Pre-AP students will be grateful that the 80 they scored on their English test is being scaled to a 90. They may also feel some pride in being chosen to help the teacher with her math!
Would you use the original problem? If you would revise it, what would you do?
PS ... I look forward to seeing what textbook revision is in Dan Meyer's tweet today! Are you participating in rewriting problems?