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This unit examines how probability and statistics act as tools for prediction of events in our every day surroundings. Students will investigate the concept of prediction first from a probabilistic point followed by a statistical framework. The lessons can be made adaptable for 7th-12 grade students. The level of difficulty can be modified, depending on the students' mathematical background and skills. The following is a description of the goals for the three sections in this unit as it is applied to 8th grade students.

PART I: Theoretical vs. Experimental Probabilities and Their Uses

• Develop an appreciation for the uses of probability and how it applies to our every day encounters.
• Achieve a deeper understanding of experimental and theoretical probabilities and the relationship between them.
• Analyze how game theory (using Backgammon) is effected by probability thus recognizing the difference between luck and chance.
• Develop a conceptual as well as a written understanding of the possible outcomes in a situation.
• Recognize and discuss situations that are seen as experimental versus those that are theoretical.
• Understand the law of large numbers-experimental probabilities are better estimates of theoretical probabilities when they are based on a larger number of trials.
• Understand that probabilities are useful for predicting what will happen over the long run.
• Understand and use probabilities to make informed decisions.
  • Realize that theoretical probabilities and experimental probabilities can be interchanged among one another to either provide proof for an outcome or to develop an outcome or possible theory.

PART II: Surveys Seen as Probabilities

• Understand that experimental probability is not only used in games of chance (from the lottery, to gambling, to game boards) but also in research and surveys that are carried out in a broad range of areas of study.
• Draw the connection between performing surveys and polls and their uses for predicting future outcomes.
• Relate experimental probability and its uses to conducting surveys and compiling results which can be recognized as experimental probabilities.
• Engage in data investigation to include collecting data and representing data utilizing a variety of methods (i.e. circle graphs, histograms, frequency tables), posing questions and interpreting results.
• Describe survey results using ratios, fractions or percents.
• Reflect on survey results and the significance of the topic chosen.
• Understand how chosen samples, varying environments, and biases can influence survey results and develop strategies to eliminate such factors.
• Compare predictions to actual survey results.
• Analyze and critique opinion polls, research articles and consumer reports and draw conclusive arguments based on reported results.

PART III: Correlations

• Determine the strength and nature of a relationship amongst 2 variables and provide a justification for the argument.
• Explore how scatter plots become tools for predicting and describing the strength and nature of relationships.
• Understand the meaning of correlation and how it applies to real life contexts.
• Understand the relevance of a "best fit" line as well the purpose for developing an equation of a line.
• Predict from graphs using the "best fit line" and the equation of the line.
• Use real life data to interpret the meaning of slope and y-intercept.
• Make inferences and convincing arguments that are based on data analysis and graphical interpretations.

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