Order of Operations/Distributive Property Reflection.

This term has been crazy busy. I have neglected to follow up on my Explore-Flip-Apply journey this term in an Elementary Algebra-type class. I will attempt to summarize the activities we did during the first half of the term I will start with the first activities we did: order of operations and the distributive property

  1. The Explore part of the order of operations activity took longer than expected. Many of them struggled with the 2nd part of the first 6 problems where they are asked to insert parentheses to make it true. They handled #9 better than I thought. They seem to do better when there is more than one path to the answer.  The Explore part of the distributive property lesson was not concrete enough for them. The first problem was good.  However, I did not make a strong enough connection between the two methods of arriving at an answer and the property later on.  The geometric interpretation seemed completely irrelevant to them.  Again, in the past, I would normally eschew these constructions.  I attribute much of this to my own inexperience of conducting such activities. (I did not get to the input/output table and never revisited it.)
  2. The Apply part for order of operations was not as successful as I had hoped. Not all of them had watched the video lecture that I posted (for the flipped part).  I will redo this video to make it considerably shorter as it is the longest video so far (~20 mins). The students seemed a bit off with problems 5-10. And no one even tried the extensions. I should build those up more in class (praise for those who get it…or even get close.)  The Apply part for the distributive property was much quicker and went well, with the exception of problems where they had to distribute the “understood” -1.  Again, no one tried the extension.  I may have said do them for homework. I neglected to check up on it.

I always feel that I do a lousy job of teaching “Chapter 1” in any course I have taught (e.g. algebra, trig, Applied Calc, Applied Stat, Math for “Liberal Arts,” Finite math).  It seems as though all of the “exciting” material starts with chapter 2 FOR EVERY ONE OF THESE COURSES. I will consider skipping chapter 1 in the future and build those learning outcomes into other lessons.

Next week I will begin to post on other lessons we have done: Solving 1-step linear equations, Solving multi-step linear equations, Formulas and problem solving (3-Act tasks / 101qs), solving linear inequalities, and loads of good stuff on graphing with Mathalicious tasks galore.