This investigative case module was prepared as part of a BioQUEST faculty development workshop entitled PRISM Workshop: Implementing Investigative Case-Based Learning at Center for Science Education in June 2003. The cases, resources, and implementation strategies were developed by participants for use with their own students. We invite you to adopt and adapt the following materials.

The BioQUEST Curriculum Consortium is committed to the reform of undergraduate biology instruction through an emphasis on engaging students in realistic scientific practices. This approach is sometimes characterized as an inquiry driven approach and is captured in BioQUEST's three P's (problem-posing, problem-solving, and peer-persuasion). As part of this workshop groups of faculty were encouraged to initiate innovative curricular projects. We are sharing these works in progress in the hope that they will stimulate further exploration, collaboration and development. Please see the following links for additional information:

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Investigative Cases
   
The Case: How Did You Spend Your Summer Vacation?

How did you spend your summer vacation?

Scene1:

Ismael, Queequeg and Ahab are three high school buddies. They have rented a small sailing sloop for a two week whale poaching excursion. Unfortunately, on the fifth day of their odyssey they encounter a tropical storm and the boat sinks. As members of their championship swim team, they take the challenge to stroke their way to a small island which is conveniently located within sight of the mishap. They lie in the sane long enough to give dramatic effect, then walk to a point above the high tide mark and begin to assess their situation.

What do you know? Questions for characters? What do you need to know?





Scene 2:

After a quick exploration, the three adventurers determine that the island is unpopulated, very small, has only a few coconut palms, an artesian freshwater spring flowing from the one rocky outcrop in the center of the island. Ismael is vertically challenged, standing exactly one meter in height. Queequeg is exactly twice Ismael’s height and really should go out for the basketball team if they ever get back to the school. Ahab is the class president and begins to organize the group. “If we are going to survive this dilemma we need a shelter. Ismael, look around and report back to me in 30 minutes. It is a good thing your digital watch is still working.”

Scene 3:

Ismael returns in 30 minutes and takes them to an opening in the rocky outcrop. The width of the opening is wide enough to allow them to fit inside with room to spare, but there is no roof overhead. Ahab turns to Queequeg, “Queeq, you are the physics genius here. How can we cover this opening to keep us out of the sum and rain?”

Scene 4:

Queeq has made some measurements. “The opening is between 15 and 16 Ismael’s wide. We will need to chop down a tree that is tall enough to cover it without wasting any wood.” “Since there aren’t many trees on the island, we need to know the exact distance of the opening,” Ahab announced, “Ismael, go back to the opening and make the measurement using smaller increments. Also, we need to measure the height of the trees and I’m not sure how we can do that.” “Don’t worry, I have a simple plan,” replied Queeq.

Part 4a (small lab)—Students will be given a meter stick and asked to divide the meter stick into 100 subdivisions.

Part 4b (second lab)—After a group discussion about a possible plan introduce a lab exercise: 1. Students will be given five sticks of different lengths. They will go outside and hold the sticks vertically (using a string to suspend them) and measure the length of the shadow cast by the stick. 2. A graph of length of stick vs. length of shadow will be constructed. 3. Data will be shared between classes and the data plotted on one graph. 4. A line of best fit will be drawn for each data set. 5. A slope will be calculated for each data set. 6. An equation will be written using the slope-intercept form of a linear equation. 7. A name will be generated for the slope.

The tangent function will be introduced. An additional drawing will be made using a protractor and graph paper. Comparison will be made with a trig table to discover the relationship between angle and slope. Differences in class data will be discussed and hypotheses generated about a cause for these differences.

Scene 5:

The three castaways are sitting under their beautifully constructed shelter. Ismael’s watch is no longer working. Food and water have been plentiful, but they were getting homesick. As they watch the shadows of the trees on the white sandy beach, the boys begin to think of ways to insure they are discovered. Ismael remembers that the cruise ship his father owns sails near them in late December. With limited wood for a signal fire or a raft construction, they wonder how they can know when the ship will pass.

What have you learned? How can you extend this?



Part 5b: Activity with a sundial and the analemma. Extrapolate the data from the class data in the shadow lab. Introduce the photographs of the analemma. How could you construct a device to reproduce the analemma shape without a camera?

Part 5c: Use a protractor to measure the height of the flag pole. (reinforce tangents)

Case Analysis

How to find height of large objects.

How to make a calendar using the sun.

Option: Include a know / need to know chart like the one below:

What do you know?
What do you need to know?
   

Learning Goals

Goal(s)

Graphing skills - scaling axes, line of best fit, slope calculation, significance of slope, writing equations for relationships

Measurement - metric units, significant figures

Introduction to trig functions - specifically the tangent

Standards

QCC Physics 1.2.1, 1.3.2 etc.

 

Investigations and Activities

Laboratory exercises are included in the case narrative.

Subdividing a blank meter stick.

Using shadows to measure the height of unknown objects.

 

Resources

http://www.analemma.com

Students will usually obtain additional references or resources
to help answer or explore their questions.

Special Data Items

 

Student Products

A shadow analemma on the front lawn of the school. "Sun Calendar"

Assessment and Evaluation Plan

Students will record data and graph results in a bound quadrille ruled lab book. Calculations, analysis and conclusions will be written with the results.

 

Implementation

Course name:
General Physics
Likely sequence in syllabus:
Introductory activity for the first semester
Time during term:
August, first week of course
Duration:
one week
Setting:
classroom and front lawn of the school
Students in course:
20-25 students, mostly 9th graders (accelerated)
Collaborative elements:
Additional notes:
Students will be expected to have command of basic algebra skills

 

Credits

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