Recap: Functions and Algebra, Day 1 (July 18, 2016)

We began today talking about norms for our time together.  We came us with:

  • Don’t be afraid to try a problem even if you think it is too hard
  • Be respectful of the speaker
  • Give space for trying problems on one’s own
  • Enjoy the productive struggle
  • Be patient with yourself

We then watched a video of a first grade class and watched the class explain the thinking of the presenter and talked about the importance of listening to other ways of solving problems and being able to understand them.  It is important that we pay attention to the speaker and be able to rephrase it.

Charles began the discussion of our materials with everyday examples of inverse processes.  There was a good discussion about why squaring is not an invertible process.  The idea of writing the composition processes was a new idea to some but we discussed using boxes for the operations and thinking of them as verbs and the input and outputs were nouns and not boxed.

After a break Marina talked about the idea of equivalent expressions.

After lunch we began the next unit and introduced graphing of ordered pairs.  We discussed the idea of inverse functions as well.  We liked the video representation of the chocolate milk with the extra scoop of chocolate and how can we fix it.  Charles wrapped up the graphical representation of the proportionality and approximation.

At the end of the session we discussed some of the standards from CCSSM and then worked on a problem of graphing distance versus time.  We will pick up with those graphs tomorrow.

Homework:

Math:  Finish FA1.10 and challenge FA1.12 – pick one

Pedagogy:  Read P to A pages 35-41, 53-57  and the article Questioning our Patterns of Questioning.  In your journal respond to the following prompts:

In your notebook write a response to these 2 prompts:
1. in questioning small groups of students working on a problem, a teacher noticed that when she
asked “focusing” questions , the students continued to look at their own work and continued to
engage in gtheir own dialogue.  When she asked “funneling” questions, the students looked up at the
teacher.  Comment on these observations.
2.  Look at Maddie’s work and Gabe’s work shown in fig. 22 on pg. 55 of P to A.  How could Ms. Lewis
leverage the student’s representation to develop Maddie’s understanding of the problem?

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