Reflection: What Goes Up, Day 2 of 3 - Section 1: Determining Average Velocity


Two students came to the board today.  The first explained – pretty clearly – how he was able to find the average velocity of the stone on a given interval, and why the calculations he was doing made sense. When he was through, it seemed that almost the entire class was on board; they saw both how 42 feet per second was calculated and why this number must be the average velocity on the first 1/2-second interval. 

Then a second student raised his hand.  This student claimed that “since the equation began with -16t^2, it made sense that the initial velocity would have to be 50.  Oh, also because the next term is 50t.”  Everyone understood what he was claiming, but I don’t think he won anyone over by his ‘argument’.  When I asked if he could clarify his thinking, he replied that he was basing his claims on outside information he had from physics.  It seems that no one else was privy to that information, and it was clear that he was unable to make it accessible by any further justification.  I thanked him and made a point of differentiating between his claim and the first student’s argument.  I also made sure to point out that these two students weren't disagreeing; the first number was an average velocity, while the second was an instantaneous one.  Everyone understood that the average velocity was an estimate, but at least they understood it!

This little episode illustrated for me once again that I have to be ready for anything, and that I should never be afraid of what a student may propose.  The important thing is that the classroom be an open environment for ideas, that all ideas be given the respect they deserve, but that in the end our discourse is about argument and arguments require evidence.

  Student Explanations
  Student Explanations
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What Goes Up, Day 2 of 3

Unit 1: Modeling with Algebra
Lesson 8 of 15

Objective: SWBAT interpret the average rate of change of a quadratic function in terms of the velocity and acceleration of a projectile. SWBAT make use of the structure of the quadratic equation to compare projectile motion under a variety of conditions.

Big Idea: Projectile motion provides context for average rates of change in the context of velocity and acceleration. What goes up, must come down!

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Math, modeling, Graphing (Algebra), Algebra, master teacher project, Quadratic Equations, rates of change, Projectile Motion
  45 minutes
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