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PA-D-2-2

Page history last edited by Tashe Harris 6 years, 2 months ago

PA.D.2.2 Determine how samples are chosen (random, limited, biased) to draw and support conclusions about generalizing a sample to a population.

In a Nutshell

Students need to understand that a sample must be a fair representation of its data population. Discuss the implications of biased or limited samples, compared to random samples, and how they can cause a probability to be an unfair representation of a population. Students need to be able to use probability to make conclusions and generalizations about a larger population.

Student Actions	Teacher Actions
Develop a Deep and Flexible Conceptual Understanding by looking at how a sample is selected, evaluate how well the sample represents the population it was selected from and determine if bias exists that skews the data. Develop Ability to Communicate Mathematically when using real world examples to explore and discuss different ways companies can use biased data samples to promote their products. (Example- “4 out of 5 dentists chose brand x toothpaste”) Develop Ability to Communicate Mathematically when discussing the implications of biased or limited samples, compared to random samples, when calculating probabilities. Develop Mathematical Reasoning by using experimental and theoretical probabilities to make predictions about populations (ex. If 1 out of 5 students voted to have pizza on Thursdays, how many students voted for pizza if there are 675 students in the school).	Implement tasks that promote reasoning and problem solving by providing students with several real life examples that use a small sample to discuss the pros and cons of using the data to make a generalization about the entire population. Promote meaningful mathematical discourse by reinforcingdifferent types of samples (random, limited, and biased) and have students describe situations where each type would be used for efficiency or necessity. Implement tasks that promote reasoning and problem solving by using technology or a whole class activity to study a cases/topics that used each type of sample collection (random, limited, and biased) and the implications that occur when making predictions from random, to limited, and biased.
Key Understandings	Misconceptions
Know what random, limited, and biased mean in relation to probability Determine if the representation of a data population is fair. Draw conclusions about the population based on a sampling.	Some students do not consider the population, that is being sampled, has any bearing on the overall fairness of the representation. Ex- Average vertical jump of the male population. If the Thunder basketball team were among the sample group, that is not a fair representation of the male population as a whole.