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University of Nebraska–Lincoln

Mid-America Transportation Center

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Lesson Overview
Lesson Title:
Falling Marble

Teachers:
Mr. Kyle Schumann (Primary)
Mr. Philip Monroe

Brief Description:
Students will see a marble dropped through a PVC pipe at an incline, roll off the table, and hit the ground. The students will need to use their knowledge of the Falling Object model and the Distance Formula to predict where the marble will hit with a given speed. They will also be asked to find the equation of the parabola formed when the marble falls off the table.

Topics Introduced:
Quadratic Equation and Distance Formula

Transportation, Distribution, and Logistics Curriculum Framework Components Addressed:
Transportation Systems/ Infrastructure Planning, Management and Regulation
Suggested Grade Levels:
9th Grade
10th Grade
11th Grade
12th Grade

Subjects:
Mathematics
Science
Standards Taught:
12.2.1 Math 2006
12.5.3 Math 2006
12.6.1 Math 2006
12.6.2 Math 2006

Lesson Information
Learning Expectations:

-Students will be introduced to what a civil engineer does.
-Students will use the distance formula.
-Students will use their knowledge about parabolas to see the graph and determine the maximum and roots.

Plan Of Action:

Students will:
-Use what they know about quadratic equations and the distance formula to predict the landing point of a marble rolling down a PVC pipe.
-Students will see the scenario modeled by the teacher. Then, they will be given the speed of the marble.
-Students will be able to measure their own dimensions of the model.
-Students will collaborate as a team of 4 or 2.
-Students will sketch a diagram of the model on paper.
-Students will write an equation of the parabola formed by the marble falling off the table.
-Students will graph the parabola formed by the marble falling off the table.
-Students will use their gathered information and prediction to determine where a road will be constructed that is at a safe distance from the hill, where falling objects will not hit the road.

Data Set Used:

Because this is a prediction based on mathematical calculations and problem-solving, there will be no data given and no "trial runs". Students will only be given the speed of the marble and they may use their measuring devices to measure any distances necessary.

Materials Needed:

-Writing utensil
-Paper and Graph paper
-PVC pipe
-Books (or objects to stack the pipe on for elevation)
-Measuring device/meter stick per group
-1 steel marble (or normal marble)
-Duct tape
-Calculator (preferably graphing)
-Marking device (pennies)
-(Optional) Photogate - to measure speed
-(Optional) Logger Pro software

Preparation Period:

10-15 minutes to set up and conduct a trial run to determine the speed and the actual landing distance.

Note #1: The teacher must place a piece of duct tape at the end of the table for the marble to hit to reduce the bounce by adding some friction.

Note #2: The teacher must calculate the speed by using the equations d=1/2at^2 and d=rt.

d=1/2at^2 where d = the height of the table, a = 9.8m/s, and t = time. Another variation is h = -9.8t^2 + h(initial height).

d=rt, where d = the distance from the table the marble will land, r = speed of the marble, and t = time.

Implementation Period:

45-50 minutes, allowing time for discussion afterward.
1-2 days, depending on the level of extension with your class.

Science, Math, Engineering and / or Technology Implications:

Students will better understand the mathematics and physics behind road construction, taking into consideration environmental facotrs. Also, students will improve their problem-solving skills when presented a situation and data to help them arrive at a conclusion.

Unexpected Results:

-Students' predictions of the distance may be a little off. It is important that they use their knowledge and problem-solving skills to come up with an accurate prediction.
-The teacher must not change the PVC pipe once it is set up. If the slope of the pipe is changes, this will change the data.
-I have found that a pipe that has a smooth ridge works best so the steel ball doesn't bounce as high.

Considerations for Diversity in Education:

-This lesson works for people in all areas of the world. It is especially relevant for people who live in mountainous regions.
-This lesson is great for kinesthetic learners and students who like "hands-on" activities.


Lesson Files
Distance Formula Wksht
This is a review of some distance formula problems and story problems
[size: 35840] [date uploaded: Jul 06, 2010, 3:50 pm ]

Quadratics Worksheet
This is a review of graphing simple quadratics and solving story problems with the free-falling object formula.
[size: 58368] [date uploaded: Jul 06, 2010, 3:51 pm ]

Exit Visa
Closure question to gauge learning of the concept.
[size: 26112] [date uploaded: Jul 07, 2010, 12:36 pm ]

Lesson Plan Outline
Time requirements and materials
[size: 19968] [date uploaded: Jul 07, 2010, 12:36 pm ]

Investigation
Student worksheet for the investigation
[size: 31232] [date uploaded: Jul 07, 2010, 12:37 pm ]

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