Reflection: Connection to Prior Knowledge Tech Time - Section 1: Set the Stage


As students posted their equations on the board it became clear that they had different ideas about what would work.  Before the class tried any equations in their calculators I asked the students who had posted them to explain how they got their answers. 

The student who created the quadratic equation told the class that he knew the quadratic could be made to fit almost any curve.  A classmate challenged him, saying his equation wouldn't work in the second and third quadrants and he replied that those usually weren't important because they were negative values and didn't work in the real world.  This discussion gave me important insight into this student's thinking, about both the quadratic and about functions with negative values.  I knew this student tended to be very strong at application, but I didn't realize how narrowly he viewed mathematics. 

The student who created the correct equation, 2^x - 3, explained that she expected the graph to be like the example because "Mrs. Rampy wouldn't try to fool us with hard stuff at the start of class".  She said she couldn't remember the exact rules for transformations, so she just plugged in options using the number 3 because that's how far down the graph moved until she got the right one. 

The student who created the cubic equation said that he anticipated  a change from the example, but not too big a change, so he just tried a different exponent and it worked pretty well.  The class pointed out that his equation did not fit the quadrant 3 values at all and he agreed that his equation didn't work.

After these explanations and additional discussion among the students, they graphed each equation and determined that the exponential was the best fit, although the student with the quadratic still argued that his equation fit fine in quadrant one.  At that point another student pointed out that his equation only fit well for f(x) between 0 and 10.  The first student finally conceded that his equation had limited application for the given graph and we moved on.

  Connection to Prior Knowledge: Misconceptions
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Tech Time

Unit 7: Building Functions
Lesson 5 of 12

Objective: SWBAT evaluate the effect on a graph of replacing f(x), by f(x)+k, k f(x), f(kx), and f(x+k) for specific values of k using technology. SWBAT explain the effects described above using technology.

Big Idea: Use graphing calculators as tools to evaluate and explain, yes, explain!, changes to a graph.

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Math, Function Operations and Inverses, Algebra II, function, master teacher project, 11th Grade, graphing calculators
  50 minutes
tech time
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