Reflection: Discourse and Questioning Logs; but not for building - Section 1: Set the Stage


The hardest part about this activity for most of my students is figuring out how to see all the points.  Many just try a kind of guess and check, expanding the x-axis by random amounts in an attempt to encompass all ten required integers.  One student used an approach that was intriguing and showed good understanding of both his graphing calculator and the function.  When he explained what he done to whole the class he said he began with the standard 10x10 window but as soon as he graphed the function he looked at the table of x and y values.  When he realized that the first point with an positive integer value for y was (10,1) he said he quickly checked the y value at x = 20.  That sent him to check the value at x = 100, which gave him what he was looking for, an integer (100,2).  Another student interrupted to ask why he jumped from 20 to 100 and he said the value at 20 was still way too small, so he thought about how logs and exponents are inverses and that it might be going up by 10s.  He went on to explain that he checked the value for x=1000 to see if it was 3, which confirmed his idea that the first ten positive integer values for f(x) were going to be 1,2,3...9 and the corresponding f(x) values would be 10, 100, 1000...,1000,000,000.  His explanation was so clear and effective in explaining how logarithms work that I didn't need to add or edit it at all.

  getting graphing windows right
  Discourse and Questioning: getting graphing windows right
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Logs; but not for building

Unit 8: Interpreting Functions
Lesson 11 of 19

Objective: SWBAT graph logarithmic functions showing intercepts and end behavior.

Big Idea: So you think you know what a log is and how it works? Learn the secrets of logarithms in this lesson.

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Math, algebraic function, Algebra, Function Operations and Inverses, Algebra II, master teacher project, 11th Grade
  55 minutes
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