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Changing Ramp Heights

Grades: 5-8
Author: Dr. Kathie Owens


Abstract

Module Description

Participants will discover the relationship between the height of a ramp and the energy of a ball rolling down the ramp. As they conduct the investigation, they will discuss the factors that cause variability in results and the need for multiple trials. Participants will experience the substantial connection of mathematics and science in this lesson. In addition, participants will evaluate the samples of students' work (already scored using a rubric) to learn about assessment of students' investigations.


Objectives

  • Participants will formulate a hypothesis, conduct an experiment, gather, process and analyze data, and report findings.
  • Participants will use mathematics in the analysis of their data.
  • Participants will define and describe the conversion of energy from kinetic to potential.
  • Participants will discuss assessment of students' investigations.
  • Participants will design and implement in their classrooms a lesson on using mathematics within a science investigation.
  • Participants will develop and use a rubric for assessment of their students' scientific investigations.

Materials

For each group: books of the same size; plastic cup or bowl; 30 cm ruler with groove; golf ball; metric measuring tape; masking tape; calculator

Substitutions: *Uniform wood blocks may be used in the place of the books for the ramp. *A rubber ball may be substituted for the golf ball. *A piece of wooden molding may be used in place of the ruler for the ramp.

For the presenter: scissors of craft knife; black or blue marker


Procedures

Engagement

Give each participant a rubber band and ask each participant to stretch it. When each rubber band is stretched to its maximum (without breaking), direct the participants to release their bands - caution should be exercised when choosing a direction to aim the rubber band as these will sail across the room and may injure those persons in the path. Ask the participants to describe the energy at each stage of this activity - the pre-stretch, the stretch, the release, and the drop to the floor. Tell the participants that in this lesson they will be investigating the type of energy experienced in this activity, and the transfer of such energy. After they have conducted an investigation and discussed their findings, they will look at the findings of students who conducted the same investigation and study the assessments of each of these students' work as scored by a rubric. Posed problem: measure the effect that the height of a ramp has on the distances a ball is able to move a stationary cup.

Assessment: Be sure that the participants understand the posed problem and the science (i.e. energy types) behind the activity before proceeding.

Exploration

Follow the procedures as outlined on the student task sheet.

Assessment: As the participants are working, monitor their use of procedures, ask questions to enable them to realize that more than one test of the effect of the ball on the movement of the cup at each height should be done, and assist them (as needed) with data recording and analysis.

Explanation

Participants report their findings and answer the posed problem. To assist in making comparisons you may wish to ask each group to post their data on a large poster, chalkboard, or display where all group's data can be seen at once. Enter into a brief discussion of the science content behind the experiment (see "Explanation of the Science"). Ask them to think of the movement of a playground swing, to make a simple drawing of it, and to label in their drawing situations where the swing could display potential energy and/or kinetic energy. Have a brief discussion of their drawings with labels.

Ask the participants where they used mathematics in this experiment. Expect participants to recognize the use of math in making measurements and displaying data using charts and/or graphs. Ask participants if looking at discrepancies in their data charts prompted them to retest - finding and analyzing patterns (and any deviation from the expected pattern) are math skills employed by scientists in their work and one of the reasons why scientists make re-tests.

Look at the examples of students' work provided on the website. Give participants time to study the rubric, the students' answers to the questions, and the scores they were given. Ask questions - for example: do you agree with the scores? Why or why not? If the student did not get the maximum score, how could his/her work be improved? How would you improve the questions asked of the students? What modifications would you make to the rubric? Do you think the students were given the rubric when they were answering the questions? What reasons can you suggest for giving students the rubric?

Assessment: Monitor participants' answers to questions. Ask the participants to share (orally or in writing) an example of a science experiment that their students conduct in their classrooms. Have them tell how they currently assess their students' learning in this investigation; ask how they might amend their current assessment procedures to include a rubric.

Elaboration

  1. Ask the participants to look at examples of science investigations that they teach in their classes to identify the use of mathematics in these investigations. Encourage the participants to link the math in these lessons to the state, local, or national standards (whichever drives their curriculum), so as to reinforce in science class the skills/concepts taught in the math class.
  2. Ask the participants to examine the examples of science investigations that they teach in their classes for evidence of assessments of students' learning. Give participants time and opportunity to amend existing questions or develop additional questions (as appropriate) and a scoring rubric to be used when this investigative lesson is implemented in the classroom. Remind participants that writing rubrics can be a time-consuming task, but can be made easier when remembering to begin with an "ideal" answer and a "totally unacceptable" answer. Then assigning points may be somewhat streamlined.
  3. Give each participant a copy of the lesson plan template on which to record an outline of the implementation lesson and assessment.

Assessment: Check the participants' implementation lessons for the presence of the features listed in the procedure part of the participants' lesson. If possible, visit the science classes when the participants are teaching the lessons and/or using the assessments developed at this professional development session.


Rationale

In this simple experiment participants will experience the use of mathematics in the analysis of the data collected. Experiencing the connection of mathematics and science in this lesson will help participants realize how mathematics is the language of science. Assessment of students' investigations can be difficult because there cannot be an "answer key" for the task. An opportunity to study, to discuss, and to reflect upon samples of students' write-ups of their investigations, which have been scored using a rubric, gives the participants insight into how to assess their own students in similar tasks.


Science Standards

Content, Technology, and Professional Development:

NSES Content - Physical Science:

  • All students should develop an understanding of motion and forces.

NSES Content - Science as Inquiry:

  • All students should develop abilities to do scientific inquiry (Content 5-8)

NSES Professional Development:

  • Professional development for teachers of science requires learning essential science content through the perspectives and methods of inquiry. Science learning experiences for teachers must involve teachers in actively investigating phenomena that can be studied scientifically, interpreting results, and making sense of findings consistent with currently accepted scientific understanding.

NCTM Algebra:

  • Understand patterns and functions. Analyze change in various contexts.

NCTM Measurement:

  • Understand measurable attributes of objects and the units, systems, and processes of measurement.

NCTM Data Analysis and Probability:

  • Develop and evaluate inferences and predictions that are based on data.

NCTM Communication:

  • Use the language of mathematics to express mathematical ideas precisely.

NCTM Connections:

  • Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

Best Teaching Practices

  • Inquiry
  • Integration of mathematics and science
  • Ongoing and embedded assessment

Time Frame

Two hours; data collection and analysis may take 45 min. The remainder of the time should be devoted to discussion of assessment and to initiation of classroom implementation activities.


Preparation

At the website you will find several files whose contents give useful directions to teachers and students, connections to the standards, and a detailed rubric. Examples of students' work are available; these will be used as an integral part of the discussion. There is no "printer friendly" option for printing the files on the site. You can print each file, however, margins on the paper will not agree with what you see on the screen. We recommend that when using the contents of this site you should use a projection of the material rather than provide hard copies for each participant.

You will need a rubber band for each participant for the engagement part of the lesson. Prepare enough materials for each group of three participants (one serves as materials manager, one as recorder, and one as chief scientist) in the exploration part of the lesson. Since groups will be repeating their tests and comparing their findings with those of other groups, it is important that each variable (for example, book thickness) be kept uniform. We suggest using multiple copies of the same book - dictionaries would be a good choice. Rulers with a center groove must be sturdy and not buckle under the weight of the golf ball. Use wooden rulers, if these are available. To save time during the session, we recommend that the bowls be pre-cut ahead of time. While not entirely necessary, the calculator is useful for data processing.

Substitutions

  • * Uniform wood blocks may be used in the place of the books for the ramp.
  • * A rubber ball may be substituted for the golf ball.
  • * A piece of wooden molding may be used in place of the ruler for the ramp.

Suggestions from the web-lesson:

  • * Cut a hole in the side of the plastic cup or container large enough to allow the golf ball to roll through it freely.
  • * Designate the part of the cup that the students will be measuring from (back or front).
  • * Students must have a large flat surface to do this task; laboratory tables, cafeteria tables, or the floor work well. A single student desk is not large enough.
  • * A ball release point should be marked on the ramp or ruler with permanent marker.

The procedure of this lesson suggests adaptations to lessons currently used in the science classroom and future implementation of lessons using science investigations. To make completion of this part of the session appropriate to your local curriculum, ask the participants to bring copies of their textbooks, curriculum guides, or other science resources, from which they derive and use science lessons.


Safety

Except for using the craft knife there are no safety concerns with this lesson. When teaching this lesson to students, participants should make all the cuttings with the craft knife. We recommend that this preparation be done ahead of time.

Remind the participants to handle all materials carefully.


Assessment

  • Throughout the lesson, assess participants' learning using questions (informal). Assess their reports using rubrics/suggestions from the lesson for students. See http://pals.sri.com/tasks/5-8/changeramp/rubric.html
  • By your actions (asking questions, monitoring the participants' work, giving time for participant-talk) model for participants the assessment techniques they should use in their science classrooms. Ask the participants: In what ways was the PPD doing assessment during this lesson? How can science teachers use these ways of assessment in their classrooms?
  • Ask the participants to share (orally or in writing) an example of a science experiment that their students conduct in their classrooms. Have them tell how they currently assess their students' learning in this investigation; ask how they might amend their current assessment procedures to include a rubric.
  • Give the participants a few examples of potential and kinetic energy and to explain how energy is transferred between these two in everyday situations. Some examples include: the ball of a juggler, an automobile from idle to acceleration to steady speed to stopping for a red light; the water over Niagara Falls; an arrow shot from a bow & hitting the target.
  • Check the participants' implementation lessons for the presence of the features listed in the procedure part of the participants' lesson. If possible, visit the science classes when the participants are teaching the lessons and/or using the assessments developed at this professional development session.

Explanation of Science

The energy of motion is called kinetic. The kinetic energy of an object depends on its mass and its velocity - the faster it moves, the larger the kinetic energy. Changing the velocity of an object has more effect on the kinetic energy of the object than changing the object's mass. Energy that is stored in an object and gives it readiness to do work is called potential energy. The greater the weight of an object or the greater the height it is lifted results in greater potential energy.

A very common conversion of energy is that of potential to kinetic. The ball at the top of a ramp has potential energy by virtue of its position; when the ball rolls down the ramp it changes its potential energy to kinetic energy while it is moving.


Handouts

N/A


Extensions

The developers of the PALS activities welcome feedback from users of the site. There is a place on the website where comments may be posted and where the user can read the comments of other users.


Lesson Implementation Template

Download Lesson Implementation Template: Word Document or PDF File


Equity

In this experience model strategies for meeting the needs of diverse learners. As an example, compose groups with diversity in mind. Be aware that students' abilities in mathematics and science may vary widely.

Developers of the activities on the site assure the user that administration of the tasks took into account the diversity of learners - that is, between 500 and 1000 students with a variety of demographers (gender, ethnicity, socio-economic status, disability, and limited-English proficiency) were tested with these materials.


Resources

At the website you will find several files whose contents give useful directions to teachers and students, connections to the standards, and a detailed rubric. Examples of students' work are available, but do not keep their format when printed. There is no "printer friendly" option for printing the files on the site. You can print each file, however, margins on the paper and other formatting features will not agree with what you see on the screen. We recommend that when using the contents of this site you should use a projection of the material rather than provide hard copies for each participant.


References