darts anyone? a study in probability sean macduff etec 442 june 23, 2005

Darts Darts anyone?anyone?A study in probabilityA study in probability

Sean Macduff

ETEC 442

June 23, 2005

Learner• 1010thth grade co-ed math grade co-ed math

and science studentsand science students

• Students should have Students should have some understanding some understanding of chance and of chance and averagesaverages

• Expert dart throwers, Expert dart throwers, not necessary.not necessary.

Probability density function

Objective

The 10th grade students will be able to conduct and graph experimental results by using darts to experimentally

gather data and analyzing data with knowledge of averages and with graphs with a 100% accuracy.

Standards• Math

• Data analysis, statistics and probability. Standards 2 & 3.

• Science• Domain 1. Scientific Inquiry and Safety.

• Educational Technology • (5) Technology as a tool for research

Lesson Introduction

•This lesson will use darts and a target board to obtain random data.

•A review of averages, and probability will be conducted.

•Data will be graphed and analyzed.

Terminology Terminology ReviewReview

• Average Any one of several measures designed to reveal the center of a collection of data

• Standard deviation Measure of variation equal to the square root of the variance

• Mean The sum of a set of values divided by the number of values

• Normal distribution Bell-shaped probability distribution described algebraically by a curve

• Groups of 2 will have 50 throws at a target board.

• Groups will record dart position and tally all darts thrown.

• Groups will use MS Excel to plot smooth line graph.

ExperimentExperiment

Experiment Experiment cont.cont.

•Students will compare their graph with a theoretical one.

•All groups in the class will combine data for a class count of 500 individual throws.

•Class data will also be graphed and compared to group data.

Lesson ClosureLesson Closure• Students will discuss why random acts will

produce a bell shaped curve..

• Discuss results with teacher.

• Cleanup.

Follow up activityFollow up activity

• Students will discuss other activities that can be explained by normal distribution.– Example, class grades, SAT test scores,

population densities . . .

AssessmentAssessment• Students will be tested on their knowledge

of averages, means, and normal distribution.

• Students will be asked to explain and analyze hypothetical data.– Example, test scores . . .

ResourcesResources• http://occawlonline.pearsoned.com/bookbind/pubbooks/triola_awl/ch

apter1/deluxe.html

• HCPS II Educational Technology Standards

• HCPS II Content Standards

• MS Clip Art