Overview and Background: Unit: Pit and the Pendulum

Marcia Uhls : Cheney USD 268

Mathematics. : normal distribution, , standard deviation : Interactive Mathematics

Cheney : Grades 10 - 10 : Aug. - Jun.

Title:	Pit and the Pendulum
Topics:	Quadratic Equations, curve fitting
Time Frame:	6-8 weeks
Start Date:	-
Status:	Draft
Date Revised:

Other Designers:

Summary:
In Edgar Allen Poe's story, The Pit and the Pendulum, a prisoner is tied down while a pendulum with a sharp blade slowly descends. If the prisoner does not act, he will be killed by the pendulum. Students read an excerpt from the story and are presented with the problem of whether the prisoner would have enough time to escape. To resolve this question, they construct pendulums and conduct experiments. In the process, they are introduced to the concepts of normal distribution and standard deviation as tools for determining whether a change in one variable really does affect another. They use graphing calculators to learn about quadratic equations and to explore curve fitting. Finally, after deriving a theoretical answer to the pendulum problem, students actually build a thirty-foot pendulum to test their theory.

Print Materials Needed:
Interactive Mathematics text

Resources:

Resource Attachments:

Internet Resource Links:

Notes:

Stage 1: Identify Desired Results

State:	KS
Title:	Mathematics
Standard(s):	Standard 2- Algebra - Benchmark 4 - Models The student develops and uses models to represent and show mathematical relationships found in a variety of situations. Standard 4- Data - Benchmark 2 -Statistics The student generates, organizes, and interprets real number and other data in a variety of situations. Statistics

Understandings:
user	Collecting and analyzing data can help the decision making process. Precision of measurement is related to the need.

Essential Questions:
User	Why are variables important? What variables are important? How precise is precise enough when measuring? When is a normal distribution helpful? What is rare? When do you categorize something as a rare occurrence?

Knowledge and Skills:

S
Plan and perform controlled scientific experiments.
Work with the concept of period.
Recognize the phenomena of measurement variation.
Collect and analyze data.
Make area estimates to understand the normal distribution.
Work with symmetry and concavity in connection with the normal distribution and standard deviation.
Use standard deviation and the normal distribution in problem contexts.
Distinguish between standard deviation and sample standard deviation.
Calculate the mean and standard deviation of data, both by hand and with calculators.
using standard deviation to decide whether a variation in experiment results is significant.
Fit a function to data using a graphing calculator.
Make predictions based on curve fitting.

Stage 2: Determine Acceptable Evidence

Assessment Summary:
Students will analyze data to make a prediction about a circus performer's stunt.

Task/Prompt: Silly Circus

Type:Performance Task

Topics: Quadratic Equations, curve fitting

Summary:
Students will analyze data to make a prediction about a circus performer's stunt.

Print Materials Needed:

Resources:

Resource Attachments:

Internet Resource Links:
Link 1: http://
Link 2: http://
Link 3: http://
Link 4: http://
Link 5: http://

Notes:

Student Directions:
You are a data analyst for the Silly Circus. A circus performer wants to ride a bike up to a wall of fire and stop dramatically very close to the fire without burning. She wants to know when to apply the brakes. She does not want to try the experiment because she is afraid of fire. She just wants to predict at what point she should hit the brakes. However, she also realizes that no matter how hard she tries to make the conditions the same every time, there maybe some variation in the distance required to stop her bicycle. Devise a plan to collect and analyze data that will allow her to make this prediction, and describe how she might use the data. Consider the variables that are important, the problems she will encounter, normal distribution, and standard deviation.

Other assessment evidence to be collected:

Stage 3: Plan Learning Experiences and Instruction

Learning Activities:

1. Hook - What do you know about Edgar Allen Poe? What do you know about pendulums?
2. Discuss the story "Pit and the Pendulum."
3. Perform initial experiments with pendulums to determine how long the prisoner has to remove himself before the pendulum will kill him.
4. Pulse analysis, Penny Weight, Graphing summary, Pendulum conclusions
5. Students should revise their answers from the initial experiments after working with data analysis. How long does the prisoner have to free himself?
6. Make predictions from circus data analysis in the assessment.