Reflection: What Goes Up, Day 1 of 3 - Section 2: Individual Time


Many students assumed that the highest data point actually represented the maximum height of the stone.  When two students pointed out that they had tested some other t-values and found greater heights, I asked the class to calculate the exact maximum.  No one knew what to do.  After a bit of discussion, it was decided that we could find the other time at which h = 5, then “go to the middle” and that would be the time of maximum height.

Interestingly, one student pointed out that this question was a lot like the ones we’ve recently been answering since it was about finding a maximum or minimum of some sort.  I thought this was a keen insight, but it sent one other student on a wild goose chase to somehow use a system of inequalities to locate the vertex.  Oh, brother!

One student used an interesting method.  He reduced the equation to 16x^2 = 50x and then divided by x to obtain 16x = 50, or x = 25/8.  I applauded him for this solution (since no else had one at all) but then pointed out that we had only found one solution.  We already knew there was a second solution (x =0), but for some reason it didn’t show up.  Why?  No one could say.

After pointing out that we had eliminated the second solution when we divided by x (we'll return to this concept in great depth later), I reminded the class of the Quadratic Formula, and they were all able to use it to solve the equation - thank goodness!

  Working with Quadratic Equations
  Working with Quadratic Equations
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What Goes Up, Day 1 of 3

Unit 1: Modeling with Algebra
Lesson 7 of 15

Objective: SWBAT model projectile motion using polynomial functions. SWBAT answer questions about velocity and acceleration using quadratic function models.

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

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