5        C                  D

                                                                                                Assimilation       Adaptation
                                                                                            2        A                  B
                                                                                                Acquisition        Application
Gold Seal Lesson   Mrs. Farner—Tavares High School                                               1       2     3    4       5

Subject               MATHEMATICS/
                      SCIENCE                        Grades              9-12

                      Science as Inquiry: Students demonstrate knowledge and skills necessary to perform scientific
Instructional         inquiry.
                      Math: Students use a variety of tools and techniques of measurement in a problem-solving situation.
                      Students communicate the reasoning used in solving these problems.

                      Algebraic Concepts and Relationships: Students use algebraic methods to investigate, model, and
                      interpret patterns and functions involving numbers, shapes, data, and graphs in a problem-solving
                      situation. Students evaluate and communicate the reasoning used in solving these problems.
              1. Students will approximate initial velocity of a golf ball by calculating the velocity when someone
Performance   swings in only one direction. Since measuring the velocity of an object going straight up could be
Task          difficult, students are to measure in the horizontal direction.
                               a. Start from your initial position (you can assume it to be the origin).
                               b. You will make the “hole” at a set distance of 100 cm. Hit the ball with no vertical
                                    change (θ=0). Calculate your velocity 5 times; the average will be your initial
                                    velocity (V). You are going to swing your club at a (hopefully) constant rate.
                         (See graph #1)

                                   Initial Velocity V = _________
                   2.   Measure out approximately 100 paces away from the “hole”. This will be your tee off point or
                        your new origin. Measure exactly the distance from your origin to the hole using your
                        measuring tape. This value will be your x value (horizontal distance). What would the y value
                        be at this point?
                   3.   We are now going to hit the golf ball in parabolic trajectories. Would the center of the
                        parabola act as a maximum or a minimum?

                        Using your initial velocity calculated in Part 1 and the point of the hole in Part 2, you can
                        calculate how long it should take the ball to reach the hole using the given parametric
                        equations and the constant g     9.81       .
                        How long would it take to make a hole in one if you putted the ball from your origin?
                                     x  vx t
                                              1 2
                                     y  vyt    gt
                                     vx  V cos 
                                     v y  V sin 
                   4.   We are now going to try to make the hole with different angles on our shots. You will use the
                        protractor and a piece of string to make the angle as close to exact as possible. You need to
                        hit the ball with as close to the same velocity as possible.

                        Calculate the time it should take to make it to the hole for each of the following angles. After
                        you calculate the times, perform the experiment and record your observed times.
                                          x  vx t
                                                   1 2
                                           y  vyt   gt
                                          vx  V cos 
                                          v y  V sin 
                        (See graph #2)

                        Are the calculated times the same as the observed times? Why do you think so?
                        Would the time to the hole be the same (theoretically) if we hit the ball at 45° and 135°?

                   5.   We are going to locate the vertex of parabolic trajectory with an initial angle measure of 45
                        degrees. We can easily solve for the x coordinate given the initial point (origin) and point of
                        the “hole”. Where would the vertex of the parabola be located? In the center or could it be off
                        to one side? How do you know? What does gravity have to do with location of the vertex?

                   6.   Now that you have two points and the vertex (h,k) of your parabolic trajectory, you can solve
                        for the equation.
                         y  a ( x  h) 2  k

              7. We have measured the physical parameters of projectile motion and then using that data analyzed
              them using various mathematical tools. Since the data was collected within the earth’s
                       7. We have measured the physical parameters of projectile motion and then using that data
Performance    analyzed them using various mathematical tools. Since the data was collected within the earth’s
Task (cont.)   gravitation g  9.81 m . How far would the golf ball travel if we did the experiment on other
               planets? How high? How long would it be in flight? The data in table #3 can be used to calculate
               the answer to these questions:
Scoring Guide                                                        Below   Meets   Exceeds
                Outcomes with Criteria                               St'ds   St'ds   St'ds

                   1. Understanding of Physical Concepts
                     Motion accurately represented in multiple
                      formats (graphs, words, data, equations)       0-2     3-4      5-6
                     showed accurate and complete                   0-1       2        3      (out of
                      calculations with units                                                    12)
                                                                     0-1       2        3
                     accurately described the motion of the
                      golf ball using the language of physics

                            2. Experimentation
                     used a trial and error method to
                      effectively manipulate materials to            0-2     3-4      5-6
                      accomplish the proposed purpose

                     data collection and reporting was accurate                               _____
                      and complete                                   0-1     2-3        4      (out of
                     interpretation and analysis of data was
                      accurately and explicitly shown
                                                                     0-1     2-3      4-5

                     proposed an appropriate and succinct             0       1        2

                            3. Technology Usage
                     submitted an attractively formatted,
                      completely word-processed lab report           0-2     3-4      5-6
                      (including a data table organized in a
                      row/column format)
                     successfully used Graphical Analysis to        0-1     2-3        4        __
                      plot and display data in report
                                                                                               (out of
                     generated a Sound 3.01 chart and included
                                                                       0       2        4        16)
                      it in report
                                                                     0-1     2-3        2
                     electronically sized, copied, and pasted all
                      graphs, charts, and diagrams into the word
                      processed document.

                             4. Communication
                     submitted a formal lab report containing
                      all the customary sections, including data     1-2     3-4      5-6
                      in table form
                                                                     1-2     3-4      5-6
                     presentation of data was organized and                                   _____
                      easy to follow submitted a lab report                                       _
                      which captures the essence of the
                      experiment in an organized and                                           (out of
                                                                       1       2        3        15)
                      informative manner; has style and is

                     followed rules of grammar, sentence
                      construction, and punctuation; spelling
                      errors were minimized
Essential   Science Sunshine State Standards
            Force and Motion
Skills      Standard 1: The student understands that types of motion may be
            described, measured, and predicted. (SC.C.1.4)
            1. knows that all motion is relative to whatever frame of reference is chosen and that
            there is no absolute frame of reference from which to observe all motion.
            2. knows that any change in velocity is an acceleration.
            Standard 2: The student understands that the types of force that act on
            an object and the effect of that force can be described, measured, and
            predicted. (SC.C.2.4)
            1. knows that acceleration due to gravitational force is proportional to mass and
            inversely proportional to the square of the distance between the objects.
            6. explains that all forces come in pairs commonly called action and reaction.
            The Nature of Science
            Standard 1: The student uses the scientific processes and habits of
            mind to solve problems. (SC.H.1.4)
            1. knows that investigations are conducted to explore new phenomena, to check on
            previous results, to test how well a theory predicts, and to compare different
            7. understands the importance of a sense of responsibility, a commitment to peer
            review, truthful reporting of the methods and outcomes of investigations, and
            making the public aware of the findings.
            Standard 3: The student understands that science, technology, and
            society are interwoven and interdependent. (SC.H.3.4)
            1.knows that performance testing is often conducted using small-scale models,
            computer simulations, or analogous systems to reduce the chance of system failure.
            6. knows that scientific knowledge is used by those who engage in design and
            technology to solve
            practical problems, taking human values and limitations into account

            Mathematics Sunshine State Standards
            MA.A. 3.4.1
            Understands and explains the affect of addition, subtraction, multiplication, and
            division on real numbers.

            MA.B. 1.4.2
            Uses concrete and graphic models to derive formulas for finding rate, distance, time,
            angle measure, and arc lengths.

            Solves real world problems involving rated measure (miles per hour, feet per

            Using a rectangular coordinate system, applies and algebraically verifies properties
            of two- and three-dimensional figures

            MA.E. 1.4.1
            Interprets data that has been collected, organized, and displayed in charts, tables, and
Pictures,      Graph #1

Tables,        d  rt
Graphs, Etc.                      Putt 1             Putt 2           Putt 3            Putt 4                Putt 5
                Distance (cm)
                Time (s)
                Velocity (cm/s)

               Graph #2
                Angle                 Time Calculated            Time Observed

               Graph #3

                Planet                     Relative Surface Gravity       Absolute Surface Gravity (m/sec2)
                Mercury                    0.38                           3.73
                Venus                      0.91                           8.93
                Earth                      1.00                           9.81 (sea level)
                Mars                       0.38                           3.73
                Jupiter                    2.34                           22.96
                Saturn                     1.06                           10.40
                Uranus                     0.92                           9.03
                Neptune                    1.19                           11.67
                Pluto                      0.06                           0.59

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