Lesson Title : Parabolic Equation of a Catapult



Lesson Title : Parabolic Equation of a Catapult

Course Title : Algebra 2 / Precalculus

Instructor : Ellen Byron

Materials : Small Catapult with projectile object. Contact Sierra College STEM project for assembly of a catapult.

Resources : Algebra 2 textbook or Precaclulus textbook to assist student with exploration of parabolic equations.

Time for Lesson : One or Two class periods (one if on block schedule) plus homework time. An additional 3 hour time slot allocated to building the STEM catapult.

Objective : Linking the study of parabolic equations to real-life applications. Students will collect data and write a parabolic equation of a catapult (trajectory) using the quadratic equation.

Course Standards:

8.0 Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.

9.0 Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x-b) 2+ c.

10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function.

Anticipatory Set:

1. Students must have enough catapults to form groups of 4-5 each. You can purchase catapult kits or contact Sierra College STEM project to arrange a separate lesson to manufacture the catapults as a class.

2. Have each group open their textbooks and write the standard form of the parabola equation. Let the students have a discussion of the different elements of the standard equation and how the group could possibly collect data using the catapult to write an equation. Make sure they talk about the vertex and sign of a (must be negative as the parabola is facing down).

Lesson using y=a (x-h)2 +k .

Materials (need enough for each group in class):

1. Catapults with ball

2. Long tape measure

3. Yard stick

4. Data Collection Handout (enclosed)

5. Video camera (optional). Students could use their phones to video the trajectory if allowed.

Lesson

1. Students will need to determine the vertex of the parabola as well as an additional point on the parabola (the endpoint) to determine the equation of the trajectory.

2. Ask students how they could determine the exact point of the vertex? This point is located exactly halfway (half the range) between the starting point and ending point. Have students lie out the tape measure and one student shoots the ball a few times while another group member records the exact location of the ending point. Make sure students use the launching attachment on the catapult provided so that the launch angle is the exactly the same each time. That will ensure the same trajectory every time.

3. Close the classroom door to ensure the ball does not fly out the door.

4. Note: Depending on the catapult you use, you might be launching the ball above the ground level, which alters the range. Most catapults launch from close enough to the ground that students will create a mostly accurate equation. To get a more accurate equation, please look for the lesson plan for Precalculus that utilizes the height of the launch.

5. Log the ending points on the worksheet and take the average. You can now determine the x value of your vertex by dividing the ending point in half.

6. To determine your y value of the vertex, first find the location (x coordinate) of where you will measure the height of the trajectory. After they have located the place to record the measurement, have students shoot the ball once more as a trial run to get an idea of how high the yard stick must be attached to the wall (or be held by a student) to make a reading. Once set, have the group launch the trajectory and either record the launch on a video camera or have one student stand back and read the height on the yardstick. Make sure to make at least three readings for accuracy.

7. Now each group has the exact location of the vertex (both h and k values) and can place these values into their equation.

8. To determine the value of “a “(should the final value of a be negative or positive for this problem?), use two known points that lies on your trajectory ( both your starting and ending points) and determine the value of a for both. How do the values of a compare? Should they be exactly the same? Which value is more accurate? (the starting point is slightly above the ground so it’s x value is an estimate)

Supplemental Lesson for the Sierra College STEM catapults.

1. Once students calculate the equation of their catapult, set up a bucket either inside or outside your classroom.

2. Task: Each group will get 15 minutes to determine the placement of their catapult in the vicinity of the bucket. Encourage they use the information collected in the previous exercise to help them locate the placement.

3. Let each group mark their location with tape prior to beginning the contest(if one group hits the bucket, subsequent groups would just copy the place of the successful group). Allow them only one or two trial shots when placing their tape to make sure they THINK about the placement of the catapult.

4. Each group gets 4 shots. Record the number of times each group hits the bucket.

5. As the teacher, you can decide the reward for the winning team.

Date: _______________

Group Names: ___________________

___________________

___________________

Data Collection for Parabola Standard Equation y=a (x-h)2 +k

Range

|Reading 1 |Reading 2 |Reading 3 |Reading 4 |h value average |

| | | | | |

Height

|Reading 1 |Reading 2 |Reading 3 |Reading 4 |k value average |

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Record Vertex ( , )

Equation Calculation

| |x Coordinate |y Coordinate |Equation Substitution |Solve for a |

| | | |y=a (x-h)2 +k | |

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|Origin | | | | |

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|Ending Point | | | | |

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Final Equation for Catapult Trajectory: _________________________

Catapult Target Competition

|Group Name |Successful Target Shots |

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