Continuous vs. Discrete Data

Physical Science Middle School Module: Adrift

Step #1: Learn the Tools Understanding Ocean Currents and CODAR
Students visit the Control Room and background material what Coastal Ocean Radar (CODAR) is and how it works.

Step #2: Analyze Data Practice Analyzing CODAR Images
Students will understand how surface currents are mapped and how to analyze data contained on the maps.

Step #3: Pracitce Calculations Adding Vectors
Students will use both component and resultant vectors to solve a problem and understand the concept of vector addition

Step #4 and #5: Using Real-Time CODAR Data to Locate the Ship
Students will use real-time CODAR data for sea surface currents to determine the drift rate of a ship in the ocean and predict its eventual location.

Description:
In this lesson cluster, students will work with component and resultant vectors. They will learn that the motion of an object is a function of many different forces. Students will then graphically add vectors to determine the displacement of a boat adrift at sea. Through this task, the concepts of distance and displacement will be distinguished. Ultimately, students will use real-time CODAR data for sea surface currents to determine the drift rate of a ship in the ocean and predict its eventual location. Predictions will be compared in following days to the actual sea surface current data to assess the validity of the students' hypotheses.

Subject:
Middle School Physical Science or Physics

Assumptions of Prior Knowledge:
Students will have have previous knowledge that
- objects in motion have a direction and speed that can be changed;
- speed can be quantified using equations;
- the motion of objects can be represented with graphs;
- map locations can be determined using a system of coordinates in latitude and longitude.

Duration:
Three to four 45-50 minute sessions

Credits:
These lessons were created by Liesl Hotaling - CIESE at Stevens Institute of Technology, Daniel Griesbach - Homdel High School, Paul Ludgate – Upper Township Middle School, Janice McDonnell and Eric Simms – IMCS-Rutgers University. Edited by: Amy Pallant and Debra Kovacs - Turnstone Publishing. Scientific content reviewed by Michael Crowley, Dr. Scott Glenn, Dr. Josh Kohut, and Sage Lichtenwalner - IMCS-Rutgers University. Development supported with grant funds from the National Ocean Partnership Program.

Step #1: Learn the Tools-- Understanding Ocean Currents and CODAR
Step #1 is an introduction to the technology and techniques that scientists use to study the surface currents of the coastal ocean. In this activity, students will be introduced to the use of CODAR (Coastal Ocean Radar) by reading the Science Background material and completing the CODAR online tutorial located in the Control Room. Students can work individually or brainstorm in groups to answer the questions on the Adrift Activity Worksheet.

Step #2: Analyze Data -- Practice Analyzing CODAR Images

Objectives:
Students will
- Locate a vector on a map
- Compare a vector to a scale and determine its velocity
- Understand how a vector can be used to determine the traveling time of an object over a known distance

Materials:
For each group of 2-3 students
- Pen or pencil
- 1 ruler
- 1 copy of the “Analyzing CODAR” activity map
- 3 printed copies of the Adrift Activities Worksheet (continued from previous activity)
- 1 calculator (optional)

Classroom Implementation

Time required:
One 45-50 minute class session

Thematic Sequence:
This unit is best done following the “Gone Fishing” Unit (See Thematic Instructional Sequence). If students have not done so, suggest that they explore “What’s COOL?” and “COOL Cards” sections of the site either as homework or as a class. Students should utilize the sampling demonstration the benefits of continuous sampling. Background information within the site illustrates that traditional oceanographic sampling techniques allow scientists to only get ‘snapshots’ of what is taking place in the ocean, rather than a complete, continuous picture. The COOL Cards allow students to explore the collaborative nature among biologists, oceanographers, and modelers within the COOLroom. Students can also learn these concepts by doing the “Welcome to the COOL Classroom” activity found in the Teachers’ Guide, either as homework or as a class.

Lesson and Activities:
After students have completed their exploration of the CODAR background section and CODAR tutorial in the Control Room, divide the students into groups of 2-3. Have them begin Step #2 to calculate how long it will take for a wave to travel over a determined distance. Based on the length and color of the arrow students will calculate the speed at which the water is moving using the following formula: distance = rate x time. To determine the distance for a twenty-four hour day, convert cm/sec to mph, and multiply the mph product by 24. Students may use this conversion table located within the Control Room to convert from cm/sec to mm/h. (see www.thecoolroom.org/data/data_codar.htm).

Have the students record their answers on the Adrift Activity Worksheet. Students can use the “Speed Conversion” calculator to expedite the lesson, or they can calculate the answer themselves to practice using ratios, scales, and unit conversions. Once the groups are finished, allow the students to share and discuss their answers including explanations for their answers. See the Adrift Activity Worksheet Answer Key for the answers to the problems and questions in the activity. Keep in mind that the actual answer may vary slightly because of differences in actual measurements on the printed images because of individual printer settings.

CLASSROOM FLOOR PLAN

Step #3: Practice Calculations-- Adding Vectors

Objectives:
Students will
- Add component vectors to determine the movement of an object over time
- Predict the eventual location of an object adrift for three days
- Construct a resultant vector based on multiple component vectors
- Compare the results of calculating the movement of an object using both component and resultant vectors

Materials:
For each group of 2-3 students
- Pen or pencil
- 1 ruler
- 1 copy of the “Adding Vectors” activity map
- 3 printed copies of the Adrift Activities Worksheet (continued from previous activities)
- 1 calculator (optional)

Classroom Implementation

Time Required:
One 45-minute class session

Lesson:
Students will participate in an imaginary scenario and calculate the movement of a drifting boat (the distance between a point of origin and an endpoint) over several days by determining the magnitude of forces and the scale represented by combining 3 component vectors. They will then predict the eventual location of the boat, and calculate the resultant vector graphically and numerically for comparison. Students should be able to determine the difference between the total distance traveled (the 3 component vectors added together) and the boat’s displacement (the resultant vector). Displacement is defined here as the direct distance between the point of origin and the end point.

Have the students record their answers on the Adrift Activity Worksheet. Students can use the “Speed Conversion” calculator to expedite the lesson, or they can calculate the answer themselves to practice ratios and conversions. Once the groups are finished, allow the students to share and discuss their answers including explanations for their answers. See the Adrift Activity Worksheet Answer Key for the answers to the problems and questions in the activity. Keep in mind that the actual answer may vary slighty because of differences in actual measurements on the printed images because of individual printer settings.

Steps #4 and #5: Using Real-Time CODAR Data to Predict Motion!

Objective:
Students in groups of 2-3 will
- Apply concepts learned using hypothetical data to real scientific data
- Calculate and predict the movement of an object in the ocean
- Predict the eventual location of that object in the ocean
Analyze and track real-time ocean surface current data

Materials:
For each group of 2-3 students
- Pen or pencil
- 1 ruler
- 1 printed copy of the real-time COADAR map for that day
- 3 printed copies of the Adrift Activities Worksheet (continued from previous activities)
- 1 calculator (optional)

Classroom Implementation

Time Required:
Two 45-50 minute sessions

The previous lessons introduced skills involving the use of scales and unit conversions to determine distances and speeds. This lesson requires students to apply these skills to solve a problem. You may want to offer students less direct assistance in performing these tasks than you provided in the previous lesson.

Prior to the lesson, preview the CODAR real-time data site (www.thecoolroom.org/boaters/boat_codar.htm) to ensure data is available and useable. Scroll down to the second graph on the page (the Brant Beach to Brigantine graph). If the site is functioning properly, there should be data for the current day – if not, note the date and be sure to point it out to the students. Select a clear and distinguishable vector for students to use in this activity. If possible, select a vector near the middle of the graph that points toward the shore. If all of the vectors point north, south or east, select one that has some distance between the vector and the edge of the graph (which will be the end point for measurements). It would be helpful to select a vector whose tail is as close as possible to a point where latitude and longitude lines cross. This will enable the students to find the vector with more ease. If preferred, you can selected several different vectors at the beginning of the activity, assigning different vectors to different groups of students. Groups can then compare their predictions at the end of the activity. This may also make it more entertaining to see which groups’ prediction is most closely matched by the data.

Once the groups have determined how much time it will take the boat to reach the end point, have them visit the real-time data page several times during this period to check their predictions. Ideally, the data is updated every hour, which provides plenty of opportunities for students to visit the site for updates. An interesting extension could be to have two different groups track the same prediction, but one more frequently than the other. For example, one group may check 3 times over the selected period, while the other may check 6-9 times. When the groups report their results the explanations/answers would likely be different, and should emphasize the advantage of continuous sampling over intermittent sampling.

Have the students record their answers to the questions and problems on the Adrift Activity Worksheet. Students can use the “Speed Conversion” calculator to expedite the lesson, or they can calculate the answer themselves to practice ratios and conversions. Once the groups are finished, allow the students to share and discuss their answers including explanations for their answers. See the Adrift Activity Worksheet Answer Key for the answers to the problems and questions in the activity. Keep in mind that the actual answer may vary slightly because of differences in actual measurements on the printed images because of individual printer settings.

Extension
In addition to checking the effect of wind speed and direction on the surface currents, another extension including near real-time data could be to ask students to check the current sea surface temperature images (www.thecoolroom.org/boaters/boat_sst.htm). Students can be given the additional information that the Coast Guard received a message that someone from the stranded ship is overboard without a survival suit. The Coast Guard needs to know the sea surface temperature to predict how long the person can survive before they begin to suffer from hypothermia. Using sea surface temperature images from the same day, students can determine the temperature of the water where the person went overboard, and make a prediction about whether the person overboard is heading towards warmer water (which slows the effects of hypothermia) or colder water (which has the opposite effect). The assumption would be that the person overboard is drifting in the same general direction as the ship. Students can the test their prediction by checking sea surface temperature images at the same time they are checking the future CODAR images.