Three Act Lesson
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.
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(x-h)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?”
In the end, students will determine the answers to questions like the ones posed above. They can apply their knowledge to real-life 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.