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.