1. Darts anyone? A study in probability Sean Macduff ETEC 442 June 23, 2005

2. Learner 10 th grade co-ed math and science students10 th grade co-ed math and science students Students should have some understanding of chance and averagesStudents should have some understanding of chance and averages Expert dart throwers, not necessary.Expert dart throwers, not necessary. Normal Probability density function Probability density function

3. Objective The 10 th 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.

4. 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

5. 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.

6. Terminology Review 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

7. 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. Experiment

8. Experiment 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.

9. Lesson Closure Students will discuss why random acts will produce a bell shaped curve.. Discuss results with teacher. Cleanup.

10. Follow up activity Students will discuss other activities that can be explained by normal distribution. –Example, class grades, SAT test scores, population densities...

11. Assessment 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...

12. Resources http://occawlonline.pearsoned.com/bookbind/pubbooks/triola_awl/ch apter1/deluxe.htmlhttp://occawlonline.pearsoned.com/bookbind/pubbooks/triola_awl/ch apter1/deluxe.html HCPS II Educational Technology Standards HCPS II Content Standards MS Clip Art