Braking Distance and Speed #MTBoS30 Day 2

Standard

8 minutes…here goes…

A quick retrieval from last week’s exponential growth / decay to begin our day in Algebra I. Four functions:

  • y=1200(1.13)^x
  • y=1200(2)^x
  • y=1200(.91)^x
  • y = 1200(2)^-x
  1.  60 seconds:  Tell how they’re alike / different.
  2. State which ones are increasing and decreasing without “doing any math / graphs.”
  3. Graph each, sketch, noting the end behavior…does it support your description?
  4. Let x=3, find the function value for each.  Is it greater or less than the initial value?

Texting Olympics!

Whaaaat?

That’s right, thanks to Heather Khon, we did a little sprinting and hurdles in class today.  

Sprint:  staying for help in math pick me up at 4

Hurdles:  Laker baseball has a winning season!!! woooo!  #lakerproud

Recorded our times and will use them tomorrow as we look at breaking distances more…adding on to our distances how far we’ll travel in just 1 second at various speeds, then leading up to a written PSA, print PSA, recorded 30 second PSA to support ATT’s campaign, Its worth the Wait.

Here’s where we began our new content – a look at some quadratic data.

These lessons are taken from A Visual Approach to Functions, 2002, Key Curriculum.

brake

  1. Notice / Wonder about the speeds and braking distances.
  2. Create a scatterplot, then run a quad reg because we don’t see a constant rate of change for linear and no common rate of multiplication for exponential.
  3. Some are amused when they see this crazy function pop up and just how well it models their data when graphed.

f(x) = .0975x^2 – 2.5x + 65.25 (its pretty close to this, but I don’t have it written down with me.)   What’s that, you want to know how far you’ll travel at 90 mph, Brooke?  Let’s see.

The lessons go on with varied graphs asking students which models given sentences.  Three tables of values are shared, asking them which is likely the data for their chosen graphs.  And finally, equations – which one matches each data set.

Again, open questions because students were not limited to a single strategy.  Some students chose to use x-values as inputs into the equations and find the one that modeled.  Another group used their data to create a scatter plot and/or regression equations, and others found the rates of change within the tables and compared to determine if linear/quadratic.

All in all, I was please to see such varied approaches – and  correct in their reasoning.  Looking forward to continuing these conversations tomorrow as an intro to quadratic functions.  Maximizing Area will follow braking distances.

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