Posted October 15th, 2009 by Admin

Part 2: The Story of Pi

Introduction:

Students will design an experiment to test the importance of decimal places by rounding the value of pi. The collected data will be applied in a variety of circumstances to help students make a decision about the importance of decimal places.

Learning Outcomes:

Students will design and complete an experiment.
Students will use their data to answer questions.

Curriculum Alignment:

1.01 Identify and create questions and hypotheses that can be answered through scientific investigations.

1.02 Develop appropriate experimental procedures for:

Given questions.
Student generated questions.

1.04 Analyze variables in scientific investigations:

Identify dependent and independent.
Use of a control.
Manipulate.
Describe relationships between.
Define operationally.

1.05 Analyze evidence to:

Explain observations.
Make inferences and predictions.
Develop the relationship between evidence and explanation.

1.06 Use mathematics to gather, organize, and present quantitative data resulting from scientific investigations:

Measurement.

Analysis of data.
Graphing.
Prediction models.

1.08 Use oral and written language to:

Communicate findings.
Defend conclusions of scientific investigations.
Describe strengths and weaknesses of claims, arguments, and/or data

Classroom Time Required:

Approximately 5 class periods (~50 minutes each) will be needed, however, some things can be assigned as homework to decrease the time spent in class.

Materials Needed:

Pins/ string/ corkboard OR paper/ string/ pencil
Measuring tapes and rulers
Calculators with pi

Technology Resources:

Overhead Projector, if computer access is available students can research the elaboration assignment and type their response

Pre-activities/ Activities:

Engage

Class Discussion — Discuss these questions as a class or in small groups.
How important are decimal places?
When is it OK to round decimal places?
How might your grades be affected by rounding decimal places?
How might the Olympics change if timers had different numbers of decimal places?
How might a basketball game be affected if timers were only in full seconds?

Explore

Students will complete the guided inquiry lab — How important is a decimal place? (See Worksheet 1)
Students will be drawing a circle and measuring the circumference. Students can be given soft tape measures or hard rulers for this. If students have different tools or even different markings on their tools it can give them an opportunity to discuss why it was difficult or why everyone should have the same tools.
After students have answered the questions to the first piece, they will be designing an experiment to test the effect of rounding pi using the experimental design graphic organizer (See Worksheet 2). The students should then complete the experiment and write their result statement. Make sure the students make an organized data table and they keep this information. They will need to use this data to support themselves in the Explain and Elaborate sections.

See:

How important is a decimal place? Explore (paper/string method OR pin/corkboard method)
Experimental Design Graphic Organizer
Teacher Notes: How important is a decimal place?

Explain

Students should complete the questions that go with the lab. (See Worksheet 3) They will need their data from their experiment.

Elaborate

Students should complete the elaboration (See Worksheet 4). This is a good chance to practice writing and editing skills. You may need to explain editorials before writing. A student hint sheet is available (See Hints).
You can also work with your Language Arts teacher for this writing portion. Students can edit and revise their writing.
A second option is that the students draw a political cartoon that shows why we should or should not change pi. You can show students some examples of these cartoons from the paper or work with your social studies teacher.

Evaluate

Students will use their knowledge of pi and decimal places to answer questions about car speed. (See Worksheet 6 or 7(more details) ) You will need to complete a sample calculation (See worksheet 5) with the class before they complete this on their own.