## 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!

# What Goes Up, Day 1 of 3

Unit 1: Modeling with Algebra
Lesson 7 of 15

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

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

### Jacob Nazeck

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