- the height of the person throwing the ball
- the height of the person catching the ball (these students were the windows)
- the time it took for the ball to reach the person
Using this information, the students plugged in their data into the vertical motion model y=-16t^2+vt+h to solve for their initial velocity. Once the students found their initial velocity, the students used their information to create the function for the path of the ball. The students graphed their function into Desmos and graphed the path of their ball. This gave the students the ability to apply what they did in real life and see it as a mathematical model. Let's just say, it blew their minds. The students were able to see that the x axis represented their time, and that the time it took for the ball to reach the person was the same as on their graph. The students then wrote a letter to their grandma apologizing for breaking her window, explaining what happened, and the math behind it. This incorporated English into the project. The students became very creative with the explanation to how they broke the window. It was a lot of fun listening to the students read their letter because they all wanted to make theirs the funniest. The last component of the project was each group was to find two examples of quadratics in real life. They had to explain what the object or example was and how it represented a quadratic. I did learn that you could not take the videos in slow motion, but their time would be off and give the students a huge initial velocity. They thought they were the hulk. I will definitely do this project again. I feel that the students saw the connections between the real world and quadratics, and that was a hope.
I really like this PBL. It seems so hard to do real world math with students. I can remember thinking especially in math class, "How will we ever use this, what do people really do with math in a job?" My son has a masters in Mathematics and he was sp good at explaining to me how all of his equations had real world applications. I think PBl is really a great tool to use to demonstrate to students in Math class that what you are doing is applicable to real life applications.
ReplyDeleteThis sounds fun! I love how math was included in this project. I may have to try this one next year!
ReplyDeleteHi Sarah,
ReplyDeleteI know that you worked hard to create a pbl unit of study for your students that would align with standards and your scope and sequence while also providing students with opportunities for real life problem solving and relevant math application within a pbl structure. No easy feat but you accomplished it with this one. I also really like how you included creative writing in this unit with the apology letter that also had to include a rationale for how the window was broken. I can't wait to see what you do next.
Sincerely,
Dawn