TitleIII Learning Experience

Learning Context | Procedure | Instructional/Environmental Modifications | Time Required | Resources | Assessment Plan | Student Work | Reflection

LEARNING CONTEXT

Purpose or Focus of Experience

 Students have a difficulty with the concepts of frame of reference, speed and velocity as they relate to acceleration. Thorough understanding of these concepts is necessary before students can use concepts such as momentum and circular motion effectively. This experience helps to define those concepts.

Connection to Standards

MST#1-"Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions".

-Students will "organize observations and measurements of objects and events through classification and the preparation of simple charts and tables" when they enter their data in tables.

- Students will "interpret organized observations and measurements, recognizing simple patterns, sequences, and relationships when they prepare graphs from the data tables to represent the concepts under investigation.

-Students will use "abstraction and symbolic representation … to communicate mathematically" when they calculate speed using accepted algebraic relationships between measured variables.

-Students will "share their findings with others and actively seek their interpretations and ideas" when they assess agreement between original hypothesis and results and reconcile differences using team discussion.

-Students will "adjust their explanations and understandings of objects and events based on their findings and new ideas" when they compare results with colleagues in full class discussion.

MST#2-Students will use "information technology to retrieve, process and communicate information and as a tool to enhance learning" when they use photogate timers to acquire more accurate results of time changes than are possible using hand-operated stopwatches.

-Students will "use a range of equipment and software to integrate several forms of information in order to ... create good graphic and text-based presentations"when they prepare lab reports using spreadsheets and computer-based graphing programs based upon a class/teacher format of the results of the team exercises.

MST#6-Students will "use different types of models, such as graphs, sketches, diagrams, and maps, to represent various aspects of the real life" when they provide and or discuss models of frames of reference from their experiences outside of the classroom and construct graphs of position, speed, velocity and acceleration 

Essential Question

 How can motion be described?

Content Knowledge: Declarative, Procedural

 Declarative

-A frame of reference is a background or set of points against which measurements are made.

-A frame of reference is considered to be stationary.

-No frame of reference is truly stationary.

-Motion is a change in position.

-Speed is the time rate of change in position.

-Speed may be calculated by dividing total distance traveled by the time required to travel that distance.

-The formula is: Speed = Distance / Time

-Distance may be measured in metric units (e.g. mm., cm., m.,

km., etc.) or in English units (e.g. in., ft., yd., mi., etc.)

-Time is expressed in seconds, minutes and hours; seconds is the unit used most often in science.

-Speed may be expressed in metric units (e.g. cm/s, m/s, km/hr) or English units (ft/s, mi/hr).

-The scientific community prefers metric units of measurement.

-All speed calculated algebraically is average speed.

-Uniform/constant speed does not change over time.

-Instantaneous speed is the speed an object has at a point in time.

-No matter how precisely the measurements of distance & time are made, algebraically calculated values of instantaneous speed are approximations which improve as the time interval over which the measurement is made decreases.

-Uniform and instantaneous speeds may be defined conceptually but cannot be measured directly.

-The graph of uniform velocity (distance as a function of time) is a sloping straight line.

-The graph of uniform acceleration (distance as a function of time) is a curving line.

-The graph of uniform velocity (speed as function of time) is a horizontal straight line.

-The graph of uniform acceleration (speed as a function of time) is a sloping straight line.

,Procedural

-To be able to construct, demonstrate or describe a non-earth

frame of reference

-All speed calculated algebraically is average speed.

-Uniform/constant speed does not change over time.

-Instantaneous speed is the speed an object has at a point in time.

-No matter how precisely the measurements of distance & time are made, algebraically calculated values of instantaneous speed are approximations which improve as the time interval over which the measurement is made decreases.

-Uniform and instantaneous speeds may be defined conceptually but cannot be measured directly.

-The graph of uniform velocity (distance as a function of time) is a sloping straight line.

-The graph of uniform acceleration (distance as a function of time) is a curving line.

-The graph of uniform velocity (speed as function of time) is a horizontal straight line.

-The graph of uniform acceleration (speed as a function of time) is a sloping straight line.

,Procedural

-To be able to construct, demonstrate or describe a non-earth

frame of reference

-To be able to measure the distance traveled by a body to the

nearest 1/10 of a centimeter.

-To be able to measure time using a hand-held stopwatch and a

photogate timer.

-To be able to calculate the average speed of a body using a

format developed by teacher/class discussion.

-To prepare a graph with a properly numbered and labeled axes,

correctly plotted data, correctly drawn slope-line and

appropriately entitled.

PROCEDURE
(Chronologically ordered description of all teacher & student activities and interactions.)

1.  Assign background reading from student text on frames of reference. Summary questions from the text or of teacher construction should be assigned to assess student understanding of the text. (Prentice Hall,

2. Exploring Physical Science, chap.12, sect. 12-1)

3. Demonstrations: A. A battery powered vehicle pulling a large piece of

cardboard upon which a second battery operated vehicle is resting or moving.( I use a Radio Shack tank and a "Stomper" vehicle.)

Questions: Are you moving? Is the tank moving? Is the stomper moving?

(The answer to each depends upon the perceived frame of reference.)

B. Place two students on a "rotatable" platform of a 4x8 sheet of plywood and direct them to roll a small ball back and forth. The platform should be stationary relative to the floor as they roll the ball. Then, begin rotating the platform slowly and ask the students to again roll the ball back and forth. This time the ball will appear to curve. Point out to the students that if a point in the room is used as a frame of reference the ball will appear to roll straight at that point.The students who are on the platform are in a different frame of reference, a non-inertial frame of reference. Questions: What other non-inertial frames of reference can you name? (e.g. The rotating Earth which causes Earth-bound creatures to experience the Coriolis Effect or a vehicle moving around a curve causing occupants to experience centrifugal force)

• After a review of their assignment, students are asked to formulate and write-out a description or demonstrate the effects or construct a demonstration of a non-Earth frame of reference for the next class.
• Assign background reading and summary questions (as in #1) on measuring motion (Prentice Hall, Exploring Physical Science, chap. 12, sect. 12-2.)
• Students complete a measurement of the speed of a small cart that rolls down a ramp. They first use a stopwatch and then photogate timers to find the speed over diminishing distances. A lesson of the proper format for calculations is entered into at this time. (I use the Cambridge Physics Outlet (CPO) materials but have modified them to suit my needs. I have added questions concerning the type of velocity being measured (average, constant, and instantaneous). The teacher discussion of the topics included is very good for teachers with a limited physics background. The exercises are developed so that they may be used at three different levels of understanding.) Students work in groups to complete the data taking process but prepare their own report for the next class.
• After a review of the reports, a second data taking session follows. In part A, time of travel is recorded using a horizontal "ramp" arranged so the cart travels with approximately constant speed. Values are taken at intervals of 10 cm. In part B, the data is recorded in the same manner but the ramp is inclined to cause uniform acceleration. Students record the data in a table based upon teacher/class model that follows a discussion of necessary data. A lesson in graph preparation follows. Students follow the 8 step model outlined by the instructor for preparing a proper graph. The model includes the following steps:

1. Draw the axes on the graph paper.
2. Determine which variable is independent, which is dependent.
3. Label the y-axis with the dependent variable, x with the independent being sure to include proper units in parenthesis.
4. Determine the proper scale to use on each axis
5. Number the axes
6. Plot the data
7. Draw a best-fit line through the data points
8. Label the graph with a descriptive title

1. The assignment is to prepare a total of four graphs using this model: Distance vs. Time and Speed vs. Time for each "ramp" arrangement.

INSTRUCTIONAL/ENVIRONMENTAL MODIFICATIONS

1.  For all exercises optional questions/ inquiries are added for those students who wish to achieve at the highest level (95%).
2. Special needs students are provided with an in-class aid where deemed appropriate by the CSE.
3. Special needs students are given appropriate modifications by resource teachers for all exercises and assessments. (e.g. More help in the actual preparation of a graph but held accountable for interpretation of graphs they have prepared.)

4. Since aides who "push-in" to help special needs students may not have a strong background in math/science, more time must be spent with these students. The instructor must circulate throughout the classroom to reinforce the graphing lesson.

TIME REQUIRED

 About 8 to 10 class periods are required but well-worth the time spent. With some prompting, even the integrated special needs students are able to formulate a model for the concepts of frame of reference, speed, velocity and acceleration. These are the essential building blocks of kinematics.

RESOURCES

 The rotating platform was built using the base from a rotating sign from a service station. This makes the platform heavy-duty enough to stand up to the weights of even the heaviest of students and the weight of plywood platform and 2x10’s I place under the platform to offer more strength and rigidity.

Photogate timers may be acquired from a variety of sources including Pasco Scientific and Cambridge Physics Outlet or they may be built using parts purchased at Radio Shack. The reliability and repetition of results that they afford is worth the expense. A few times of recognizing the "Human Error" in timing results is enough!

Ramps may be made from plywood or purchased through CPO or Pasco. Vehicles to roll down the ramps are readily available from Toys R Us or from CPO and Pasco* (expensive but excellent quality)

ASSESSMENT PLAN
(Include samples of rubrics, checklists, etc.)

 Quizzes: (5 to 10 minutes)

#1 Frames of Reference

1. Define the term frame of reference.
2. Identify the frame of reference most commonly used.
3. Name two other frames of reference different from the answer to question #2.
4. Evaluate this statement: "All frames of reference are considered to

be stationary but no frame of reference is truly stationary"

#2 Motion and Speed

1. Define the term motion.
2. Define the term speed.
3. State the formula for calculating the speed of an object.
4. What units do most scientists use to measure distance?
5. What units do most scientists to measure time?

Assessment Rubric

Standards #1, #2 and #6

Because I emphasize the proper preparation of a graph (the 8 step model), this is weighed more heavily in the preparation of the rubric. Use may chose to weight other areas more heavily simply by changing the number of evaluation categories in the rubric for that area. (Note that a student may therefore be awarded up to 5 points for a properly drawn graph but a maximum of 2 for following the general format of the experiment we have designed in class discussion.)

STUDENT WORK
(Include samples of student work showing different levels of performance.)

 Design, describe or demonstrate a frame of reference.

1. A student described a situation on a space station which was revolving around the Earth in free-fall so that everyone was in a "weightless" condition but further described adding a rotation to the space station that would create an artificial gravitational pull.
2. A student used a father’s hand-held drill to demonstrate the effect on paint added while a sanding disk is moving compared to stationary. He noted the difference in the effect of adding paint near the center and the edges of the disk in motion.
3. A student rolled a marble across and old record player turntable and noted the effect. The marble was also placed on the turntable before it was switched on. Observations were made as the turntable was started.
4. Most students chose simply to describe in written words a frame of reference they observed on Earth (escalators in stores) or those they imagined off the surface of the Earth (traveling in a space ship through the solar system). Some were in error (e.g. describing their motion in a jet plane as they jumped off the floor of the jet plane) but they were fuel for subsequent lessons in Newton’s Laws of Motion.

Measuring Speed

Problem: A. To measure data for calculating speed

B. To calculate speed

Procedure:

1. Set up the car and ramp as shown in the diagram on the

chalkboard.

• Use the 5^th or 6^th hole of the stand.
• Put clamp A near the top so that the car breaks the light beam about 1 centimeter after it starts moving down.You will record the time at A each time the car travels through the timer.
• Put clamp B at different places on the ramp.
• For each position of clamp B record the distance from clamp A to B, the time at B and the time from A to B. NOTE: The width of the wing on the cart should be measured to the best accuracy possible using the small plastic rulers being used.
• You should have at least 8 different sets of data at 8 different positions for clamp B.
• Calculate and record the speed at A and at B for each set of data as well as the speed between A and B.
• All data should be recorded in a data table using a format similar to the one we discussed in class.

Conclusion:

1. What pieces of data are needed to calculate the speed of the

cart on the ramp?

• Is there just one type of speed that can be calculated? Explain your answer to this question. Give examples.
• What units are used to record each piece?
• What is the formula you used to calculate speed? Show a sample calculation of the work you did.
• Compare the values for the speed at clamp A in each data set. Explain the results.
• Compare the values for the speed at clamp B in each data set. Explain the results.
• Compare the values for the speed between A and B. explain the results.

Extension:

You may have noticed that the values for speed change under

certain circumstances. Discuss the circumstances and introduce

into your discussion any new terms you may be able to apply.

Graphing Uniform Speed and Acceleration

Problem: A. To prepare graphs of uniform speed

1. To prepare graphs of acceleration

Part A: Procedure:

1. Set up the ramp so that it is horizontal: i.e. parallel to the

surface of the table . Connect a string to the ring in one end of the cart. Fasten enough washers on the string so that the cart just moves and continues to move the same speed on the ramp with a small push.

• Place the first photogate(a) 15cm. From the beginning of the ramp. Place the second photogate(b) 10cm. Down the ramp.
• Giving the car a small push, record the time at (a) and (b) and (a) to (b). Calculate the speed at (a) and at (b).
• Leaving photogate (a) in place, move photogate(b) 10cm. Farther down the ramp. Giving the car the same small push, record the time at (b) and (a) to (b). Calculate the speed at (b).
• Repeat step #4 until you have made 7 "runs".
• Organize your data neatly in a table to include times at (a) and (b), calculated speeds, distance traveled {from (a)}, and elapsed time {time (a) to (b).}
• Using the data prepare two graphs:

1. Distance vs. Elapsed Time
2. Speed vs. Elapsed Time

Part B: Procedure:

1. Set up the ramp so that it is at hole #6 of the stand.
2. Follow the same procedure as in Part A. {Note: the cart will accelerate this time when you apply the small push)
3. Prepare two graphs using the data you collect in Part B.

1. Distance vs. Elapsed Time
2. Speed vs. Elapsed Time

Conclusion:

1. Compare the speeds in Part A with the speeds in Part B.
2. Describe the graphs in Part A:

1. Distance vs. Elapsed Time
2. Speed vs. Elapsed Time

1. Describe the graphs in Part B:

1. Distance vs. Elapsed Time
2. Speed vs. Elapsed Time

Extension:

You have seen that graphs can express results of the same experiment in different ways. It is possible to prepare a graph of acceleration and time for each part of this experiment you did.

1. Discuss what acceleration is as you understand it.

Find an equation in the textbook for calculating acceleration. Try to calculate the acceleration for each set of data. What units are used for expressing acceleration?

REFLECTION

 The carts must move with little friction in order to get "expected results" from the constant motion graph. That this is so difficult to achieve in practice emphasizes the fact that uniform speed is only a concept, not a reality that can be achieved. Measurement is approximate.