Is It a Home Run?

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Objective

Students will be able to apply what they have learned about the graphical effects of the parameters in vertex form and their understanding of x-intercepts.

Big Idea

Students apply what they have been learning about vertex form and x-intercepts to solve a fun, real world problem.

Opening

10 minutes

Before you get ready for class, make sure you have graphing calculators out and accessible to students.

Begin class with a warm up problem for the whole class to work on individually that reviews what they have learned about the vertex form and x-intercepts.  A good sample problem would be something like, “Find an equation for a parabola that has its vertex at (20, 10) and has an x-intercept at (40, 0).”  Review with students what they already know about the vertex form and how to solve for a.

Tell students that today’s task will focus on applying these specific skills they have learned to a real-world problem.  

Investigation

40 minutes

Group students in homogenous groups of three to four students.  Hand out Is It a Homeroom? and read through the problem together.  Let them get started on the work.

Things to watch for while students work:

  • This problem has two different measures of distance on the x and y axis.  Be sure students are clear about the distance along the x-axis being the distance from home plate and the distance along the y-axis being the height of the ball.
  • You may need to emphasize the symmetry of the parabola to make sure students get the idea that the ball will also land 200 feet from its highest point.  You might ask students “What will be the height of the ball when it lands?” to help them clarify what one of the x-intercepts will be.
  • Some students may use (0, 0) as one of the x-intercepts. This will work for the problem but you may want to have a short discussion about in reality the ball would be leaving from the bat which would not be a height of zero.
  • Watch for students who confuse the x and y value of the x-intercept.  Make sure they understand that the x value is 200 because the ball would be 200 feet from home plate.
  • Students may struggle to use the information about the fence in the problem.  You can ask them, at what point on the x-axis would it be useful to know the height of the ball? This should help them see they need to plug in the x-value in order to figure out if the corresponding y-value (the height) will be high enough for the ball to clear the fence.

 

This is a great assignment to help students work on SMP1, Make Sense of Problems and Persevere in Solving Them. Push students to really think about what they have learned about the vertex form and x-intercepts and how they can combine and apply that knowledge to this context.  You can also say that this is a challenging problem, but you know they are up to the task.  You might cut up the problem solving guide and give out different pieces as hints if students need them to keep them moving forward and engaged in the problem.

Closing

10 minutes

If time permits, have groups that finish work put their work up on the board.  You can have students share out the steps they went through to the solve the problem.  Because the problem will have been challenging for most students, they will benefit from another look at how they went about solving it. You can ask them specific questions like, “how did you use the vertex to help you solve this problem?”  “How did the x-intercepts come into play?”

At the end of class, be sure to allot students time to reflect on their problem solving.  You can ask students a specific reflection question that references SMP1.  You could guide this reflection by asking students a questions like: 

  • What was your entry point into this problem?  How did you start the problem?
  • What were you thinking when you made decisions or selected strategies to solve the problem?
  • What changes did you have to make to solve the problem?
  • What was the most challenging part of the task? And why?

 

 

This material is adapted from the IMP Teacher’s Guide, © 2010 Interactive Mathematics Program. Some rights reserved.