Category Archives: quadratics

Landmarks & Falling Objects #MTBoS30

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Algebra I Quadratic Equations

We have prom this weekend, FFA ( a lot of my students ) are gone to Mammoth Cave, so I thought this would be a valuable way to end the week with so many students out and distracted.

Dan Meyer’s 3 Act Falling Rocks

Dan Meyer’s 3-Act Dropping Glowsticks

So, our practice problems consisted of finding the heights of tall landmarks (student generated list) and solving to find the time it would take an object to hit the ground after being dropped from the top of that landmark.

tall landmarks


As we continue working with quadratic functions / equations next week, we’ll take a look at Coyote & Road Runner and the Catapult to introduce parts of a parabola. Post discussing these  files: Quadratic Files.

For more skills practice / workbook 356/357.

Just 1 Second / It Can Wait #MTBoS30

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As an introduction to Quadratics, we’ve been looking at speed and stopping distance in Algebra I.  The formula d = 0.045v^2 is a great way to start practicing solving quadratics by square roots.

We created a table of values for various speeds.  Asked the question, if you double your speed, will your stopping distance double?  If you triple your speed, will your stopping distance triple?  Hmmmm.  Good discussions.  Why/Why not?

For the speeds, 40, 50, 60 mph, which interval had the greatest rate of change?

Was Jake Speeding?


Jake had an accident.  The accident report states the skid was about 222 ft.  Was Jake speeding?  Provide evidence for your claim.  How fast was Jake driving?

Some compared the stopping distance to previously calculated for given speeds, then reasoned where to begin their own calculations.  Again, I am proud of their thinking – no trying to replicate something I had said or done.  I will take their reasoning any day over replicating my procedures and thinking.  There were students who solved the equation algebraically and some students picked up on their classmates procedure, once it was shared.  But it was their thinking, not mine.

Just 1 Second


If Jillian was driving at 58 mph.  How far would she travel in 1 second?  Hmmm.  One would think this was a simple conversion problem, but some students were stuck.  Okay, give me a value you believe is too low.  Too high. Pair share.  I wrote several values on the board and allowed students to confirm or dispute.  Finally, after some sharing, we agreed on 85ish feet.

We step out in the hall and student walks off 85 feet.  1 second.  That’s not much time.  That’s a pretty far distance.  When we return to the room, I play a PSA from ATT Close to Home, It Can Wait.

It Can Wait PSA

I’m using this as part of our Program Reviews (Integrating Arts/Humanities, Practical Living/Vocational Studies, Writing, Global Awareness). Students will include a math fact we’ve used this week in our intro to Quadratics to write a 20 second PSA or create a print ad for Distracted Driving… Just 1 Second.

 

 

Braking Distance and Speed #MTBoS30 Day 2

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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.