Recap: Functions and Algebra, Day 1 (July 27, 2015)

Welcome back to week 2!

Today we…

…walked the graph.   Fran had us up and about trying to imitated a time-vs-distance graph by using her Ti-84 calculator and a motion detector.  We touched on a lot of ideas that will show again this week, although in less formality.  During discussion we saw how distance from the detector, speed of motion, and direction of motion could all be visible in the graph.

PMI Walk the Graph

…learned about processes in Unit FA-1.  We started with how a process can correspond to a step of a larger procedure.  We then transitioned into invertible processes (and processes that could not be inverted), multistep processes, and then viewing algebraic expressions as the results of performing processes.

…talked math and talked about talking math.

…reasoned about proportions via examples in Unit FA-2.  We worked through the feet-inches conversion, and then started on the rice and water problem.   Completing the second half (on the inverse) is homework.

Math Homework

“Problems on Processes and Inverse Processes” (FA1.10), problems 1ade, 2(all), and 3(all).

Complete the Rice and Water: The Inverse Relation problems on FA2.11-12.  Challenge yourself to draw connections to the feet-and-inches conversion problem.

Pedagogy Homework

Read Principles to Action: “Pose Purposeful Questions” (p. 35-41) and “Elicit and Use Evidence of Student Thinking” (p. 53-57)

In your notebook, write a response to these two prompts:

  1. In questioning small groups of students working on a problem, a teacher noticed that when she asked a “focusing” question, the students continued to look at their work and continued to engage in their own dialogue. When she asked a “funneling” question, the students looked up at the teacher. Comment on these observations.
  2. Look at Maddie’s work and Gabe’s work, shown in figure 22 on page 55. How could Ms. Lewis leverage the students’ representations to develop Maddie’s understanding of the problem?

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