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: 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 In Support of Academic Disciplines Critical Analysis Targeted Synthesis Awareness of Themselves as Learners Metacognition Transfer Reflection

Communication Skills Using Images, Symbols, Equations, Words, etc. 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 & Written Statements Routinely

Integrate Within Curriculum The Mathematical Studies Course Aims & 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 which follow conventions 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 & 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