Three Act Lesson
Act 1
After being shared by one of our colleges, I couldn’t resist discussing
this photo and its mathematical relationships. You could pose questions like,
“What does the equation of the parabola have to be so that the walkway has symmetry?”
“What is the equation of the parabola’s seen in this photo?”
You could ask similar questions for the half pipe photo below.
I started thinking of all the different day to day things that would
really excite students without them even considering math. They would be so
excited to discuss the walkway that the last thing they would think about is
its relation to math. As soon as you mention that you’re incorporating it into
math, they’d be hooked.
Just as the water walkway, this half pipe from the X Games could really
grab the students’ attention. I thought that watching a portion of the X Games
would give the students opportunities to see different portions of parabolic
curves.
Act 2
Students could then take time to research necessary measurements to
determine the appropriate quadratics for these photos. This could be done in a
variety of different ways depending on the amount of time the educator wants to
spend on this specific topic. The following are a number of expectations you
could cover after introducing these ideas.

Collect data that can be represented as a
quadratic relation, from experiments using appropriate equipment and
technology, or from secondary sources

Identify the key features of a graph of a
parabola, and use the appropriate terminology to describe them

Explain the roles of a, h, and k in y = a(xh)^{2}
+ k, using the appropriate terminology
to describe the transformations, and identify the vertex and the equation of
the axis of symmetry

Solve problems arising from a realistic
situation represented by a graph or an equation of a quadratic relation, with
and without the use of technology
You could ask questions like, “How fast does the water have to flow in
order to clear the walkway?”
“How fast does a skateboarder have to move in order to make it up the
other side of the pipe?”
Act 3
In the end, students will determine the answers to questions like the
ones posed above. They can apply their knowledge to reallife situations, like
skateboarding, playing catch, kicking a soccer ball, or creating a neat
fountain that brings tourists from miles and miles just so they can experience
it.
Andrew  are you submitting these via the Dropbox as well? You are not supposed to submit these assignments here  this is an assignment in itself, posting about mathematics in the world, in teaching, etc. Just want to make sure you're handing them in properly so you can get your credit!
ReplyDeleteHe was unable to send me his assignment to edit because it was too big, so he uploaded it here for me to edit.
ReplyDelete