Error Analysis: Finding Sides of Similar Triangles

I distribute a series of similar triangle problems (see Error Analysis handout) in which errors have been made in setting up the proportion.  I assign the students two tasks to work on in their groups:

1. Determine the logic that was used in setting up the proportion
2. Find and correct any errors by setting up a correct proportion (if necessary)

I am not asking my students to solve the proportions at this point. Tonight's homework will be to solve the proportions. As students work on the above tasks, I circulate throughout the room listening to the discussion and aiding with questions when a gentle nudge might be needed.

When the groups appear to have finished, I ask one group to send a member or two of their group to the board to explain their findings on the first problem and to take questions from the class.  I continue this process, calling on other groups to explain the remaining problems, until all of the Error Analysis handout has been completed.

I ask the students to work individually to solve the final proportion (Problem_6) contained in the Error Analysis handout.  When a majority of the students appear to be done, I ask for questions.  I am guessing that some students will have issues with multiplying two binomials and perhaps with the factoring step, and will use these final minutes to refresh their memories with regard to the algebra. 

For homework, I ask the student to solve the remaining proportions in the Error Analysis handout, with an eye to the question, “Does this answer make sense?” 

Problem #3 yields two positive solutions, but only one solution is actually correct in the problem as it is drawn, and I will begin the next day’s lesson by examining this problem.  I find that students, at least in my state, have been so drilled on “got to reject the negative solution” that I will use this problem as an opportunity to discuss making sense of all solutions, regardless of whether a number is positive or negative.