UNIT 2
Investigating Data & Probability
IN THIS UNIT STUDENTS WILL BE EXPECTED TO:
Learning Objective |
7.PAR.4.9 Use proportional relationships to solve multi-step ratio and percent problems presented in applicable situations.
7.PAR.4.10 Predict characteristics of a population by examining the characteristics of a representative sample. Recognize the potential limitations and scope of the sample to the population.
7.PAR.4.11 Analyze sampling methods and conclude that random sampling produces and supports valid inferences.
7.PAR.4.12 Use data from repeated random samples to evaluate how much a sample mean is expected to vary from a population mean. Simulate multiple samples of the same size.
7.PR.6.1 Represent the probability of a chance event as a number between 0 and 1 that expresses the likelihood of the event occurring. Describe that a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
7.PR.6.2 Approximate the probability of a chance event by collecting data on an event and observing its long-run relative frequency will approach the theoretical probability.
7.PR.6.3 Develop a probability model and use it to find probabilities of simple events. Compare experimental and theoretical probabilities of events. If the probabilities are not close, explain possible sources of the discrepancy.
7.PR.6.4 Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events.
7.PR.6.5 Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
7.PR.6.6 Use appropriate graphical displays and numerical summaries from data distributions with categorical or quantitative (numerical) variables as probability models to draw informal inferences about two samples or populations.
7.PAR.4.10 Predict characteristics of a population by examining the characteristics of a representative sample. Recognize the potential limitations and scope of the sample to the population.
7.PAR.4.11 Analyze sampling methods and conclude that random sampling produces and supports valid inferences.
7.PAR.4.12 Use data from repeated random samples to evaluate how much a sample mean is expected to vary from a population mean. Simulate multiple samples of the same size.
7.PR.6.1 Represent the probability of a chance event as a number between 0 and 1 that expresses the likelihood of the event occurring. Describe that a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
7.PR.6.2 Approximate the probability of a chance event by collecting data on an event and observing its long-run relative frequency will approach the theoretical probability.
7.PR.6.3 Develop a probability model and use it to find probabilities of simple events. Compare experimental and theoretical probabilities of events. If the probabilities are not close, explain possible sources of the discrepancy.
7.PR.6.4 Develop a uniform probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events.
7.PR.6.5 Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.
7.PR.6.6 Use appropriate graphical displays and numerical summaries from data distributions with categorical or quantitative (numerical) variables as probability models to draw informal inferences about two samples or populations.
Learning target
- I can apply proportional reasoning to solve multi-step ratio and percent problems, including simple interest, tax, markups, markdowns, gratuities and fees.
- I can recognize that generalizations about a population from a sample are valid only if the sample is representative of that population.
- I can generalize that random sampling tends to produce representative samples and support valid inferences.
- I can apply statistics to gain information about a population from a sample of the population.
- I can identify an appropriate sample size.
- I can generate multiple samples (or simulated samples) of the same size to determine the variation in estimates or predictions by comparing and contrasting the samples.
- I can explain why the numeric probability of an event must be between 0 and 1.
- I can explain the likeliness of an event occurring based on probability near 0, ½, and 1.
- I can explain why a greater likelihood occurs as the number of favorable outcomes approaches the total number of outcomes.
- I can determine relative frequency (experimental probability) is the number of times an outcome occurs divided by the total number of times the experiment is completed. I can determine the relationship between experimental and theoretical probabilities by using the law of large numbers. I can predict the relative frequency (experimental probability) of an event based on the (theoretical) probability.
- I can use models to determine the probability of events. I can recognize uniform (equally likely) probability. I can develop a uniform probability model and use it to determine the probability of each outcome/event.
- I can compare bar graphs to make inferences about categorical data from two samples.
- I can compare two numerical summaries and/or graphical displays to make inferences about two samples or populations.