# Exploring the Normal Distribution

```Exploring
the
Normal
Distribution
Rick Luttrell
James Price
South Iredell High School
This will show how to use the following assignment,
or one like it, to accomplish course aims and objectives
while incorporating all eight of the
Common Core Standards for Mathematical Practice:
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Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
IB DP ATLs
International Baccalaureate
Diploma Program
• Approaches to Teaching and Learning
• International Pilot to develop content appropriate for
high school students
• Methodologies for teachers to use
• Skills for students to develop
Thinking Skills
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Critical Analysis
Targeted Synthesis
Awareness of Themselves as Learners
Metacognition
Transfer
Reflection
Communication Skills
Using Images, Symbols, Equations, Words, etc.
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To Formulate Thought Clearly
To Present Ideas Thoroughly
To Use Various Text Types Appropriately
To Argue Convincingly
To Reach the Intended Audience Directly
To Aid Spoken &amp; Written Statements Routinely
Integrate Within Curriculum
The Mathematical Studies Course Aims &amp; Objectives
being met through this activity are for students to:
• enjoy mathematics and develop an appreciation of the elegance
and power of mathematics
• develop an understanding of the principles and nature of
mathematics
• communicate clearly and confidently in a variety of contexts
• develop logical, critical and creative thinking, and patience and
persistence in problem-solving
• employ and refine their powers of abstraction and generalization
• apply and transfer skills to alternative situations, to other areas
of knowledge and to future developments
• appreciate how developments in technology and mathematics
have influenced each other
Student Investigative Procedure:
• Students will formulate their own plans to individually
collect data.
• Students will have access to a variety of measuring tools and
will take measurements following provided guidelines.
• Student groups will review Internet materials on the use of
the Normal Distribution and will draft a consensus about
data meanings. (Information Literacy component)
• They will chart their work and interpret and characterize
their data.
Student Products
• tables of measurement data
• charted data sets (as a visual depiction)
• symbolic population descriptions via mathematical statements
• oral presentation outline where students put language
(including technical jargon) to complex mathematical processes in
order to explain significant findings and supported conclusions
(Literacy component)
Presentations &amp; Interactions
• Students will present their work to their classmates.
This requirement recognizes this is an area where students
typically struggle and attempts to address this weakness.
• Classmates will have an opportunity to respectfully
comment and question each presenter’s work.
It is hoped that this sort of constructive dialogue will benefit
all parties.
• Students will have to operate at the highest levels of
Bloom’s taxonomy to accomplish this task successfully.
Outcomes This exercise will be foundational to interpreting
future continuous function data sets.
• Students will be able to discuss and explain mathematical
process appropriately with correct visual aids and terms.
• Students will communicate clearly by themselves, in small
groups, and in front of the entire class. Delivery will be
both spoken and written, using both words and symbols.
• Students will correctly collect, chart, and interpret
measurement data using the Normal Distribution.
• Students will hone their Internet research skills to find and
extract useful, pertinent, and unbiased math information.
• Students will be more aware of how thinking and
communicating are important factors in mathematical work.
Samples of Student Work
Sample Height Measurement Data Table
Sample Data: Sorted into Intervals
Histogram of Sample Data
Sample Data: Histogram with
Normal Distribution Overlay
Sample Data: Student Presentation
Sample Data: Group Interaction
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