Make Math Moments Academy › Forums › Full Workshop Reflections › Module 5: Planning Your Problem Based Lessons › Lesson 56: Proceed or Pivot › Lesson 56: Question › Reply To: Lesson 56: Question

This whole idea reminds me of 3 years ago where my administrator thought it would be a good idea to turn all learning goals into SMART goals. Which made a learning goal (which we had to post every day) into long phrases that students didn’t care about or understand. But the idea was if we did not achieve the measurable goal, we had to reteach. So really, it is an excellent practice, but I think putting the practice of pivoting into the learning goal went a little far. Also, the teacher complained about how this practice expected them to add to a timeframe that was already short. As you stated in the presentation, when pivoting to ensure student abilities to create concrete/visual representation will save time because it will allow students to understand that will fit into future learning goals. But I feel the fear is that every lesson will need to pivot, but that fear I think is never justified. But I digress and will go into the task at hand.
With my early experience with CPM, I felt I proceeded a lot when I should have pivoted because CPM trainers told me that the textbook would spiral back to concepts that students do not master. (I do think CPM is a great textbook, but that does put a lot of trust in a book that has no clue who my students are) I love the problem because it always gives me apparent struggles with the students when solving the Linear System of equations. The problem states,
“The Alpine Music Club is going on its annual music trip. The members of the club are yodelers, and they like to play the xylophone. This year they are taking their xylophones on a gondola to give a performance at the top of Mount Monch. The gondola conductor charges $2 for each yodeler and $1 for each xylophone. It costs $40 for the entire club, including the xylophones, to ride the gondola. We know two yodelers can share a xylophone, so the number of yodelers on the gondola is twice the number of xylophones. How many yodelers and how many xylophones are on the gondola?”
Great problem to break apart and slowly release information to the students (Especially since it is wordy, like my response). But the issue becomes that the following lesson has students solve the system using the equal values method. This is an excellent progression, but students often struggle writing the linear equations from situations like the yodelers and xylophone players.
So I feel a great pivot lesson would be a simple lesson where you are given starting values and rates of change to write two variable equations in slopeintercept form and then go back to uncovering different methods for solving linear systems. Sorry for the lengthy response.