Learning Targets/Success Criteria: Math 700
Module 5: Statistics and Probability
Priority Standards:
7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
7.SP.A.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. 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.SP.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.
b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Overarching Skills:
Population
Sample
Random sample
Predictions
survey
Data distribution
Variabilities
Measures of center
Measures of variability
Chance events
Collecting data
Frequency
Mean absolute deviation
Understand/Be able to do:
Topic:
Days: 1, 2, 3
Chance Probability
Eureka Lessons: 1, 2, 3, 4 & 5
Walt:
We are learning to find unit rate and reduce ratios
Success Criteria:
Topic:
Day: 4
Tree Diagrams
Eureka Lesson: 6
Walt:
We are learning to use tree diagrams to represent a sample space and to calculate probabilities
Success Criteria:
Topic:
Day: 7
Compound Events
Eureka Lesson: 7
Walt:
We are learning to calculate probability of compound events
Success Criteria:
Topic:
Days: 8, 9, & 10
Experimental/Estimated Probability
Eureka Lessons: 8, 9, 10 & 11
Walt:
We are learning to estimate the probability of an event.
Success Criteria:
Topic:
Day: 11
Applying Probability
Eureka Lesson: 12
Walt:
We are learning to apply probability to make informed decisions
Success Criteria:
Topic:
Days: 14, 15, & 16
Random Sampling
Eureka Lessons: 13, 14, 15, 16 & 17
Walt:
We are learning to differentiate between population and sampling.
Success Criteria:
Topic:
Day: 17
Sample Size
Eureka Lesson: 18
Walt:
We are learning to use sampling variability and the effect of sample size
Success Criteria:
Topic:
Days: 20 & 21
Estimating a Population
Eureka Lessons: 19, 20, & 21
Walt:
We are learning to understand variability when estimating a population proportion
Success Criteria:
Topic:
Day: 22
Comparing two Populations
Eureka Lessons: 22 & 23
Walt:
We are learning to use sample data to compare the means of two or more populations
Success Criteria:
Module 5: Statistics and Probability
Priority Standards:
7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
7.SP.A.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.
7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. 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.SP.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.
b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
- Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
- Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
- Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
Overarching Skills:
Population
Sample
Random sample
Predictions
survey
Data distribution
Variabilities
Measures of center
Measures of variability
Chance events
Collecting data
Frequency
Mean absolute deviation
Understand/Be able to do:
- Information can be gained from examining samples.
- Sampling needs to be representative of the entire population.
- Draw inferences about population.
- That probability is the likelihood of an event occurring.
Topic:
Days: 1, 2, 3
Chance Probability
Eureka Lessons: 1, 2, 3, 4 & 5
Walt:
We are learning to find unit rate and reduce ratios
Success Criteria:
- I can recognize that a probability is a number between 0 and 1 that represents the likelihood that an event will occur.
- I can interpret a probability as the proportion of the time that an event occurs when a chance experiment is repeated many times.
- I can estimate probabilities by collecting data on an outcome of a chance experiment.
- I can use given data to estimate probabilities.
- I can determine the possible outcomes for simple chance experiments.
- I can determine the sample space for the experiment, given a description of a simple chance experiment, students.
- I can determine for which outcomes in the sample space the event will occur, given a description of a chance experiment and an event.
- I can distinguish between chance experiments with equally likely outcomes and chance experiments for which the outcomes are not equally likely.
- I can calculate probabilities of events for chance experiments that have equally likely outcomes.
- I can calculate probabilities for chance experiments that do not have equally likely outcomes.
Topic:
Day: 4
Tree Diagrams
Eureka Lesson: 6
Walt:
We are learning to use tree diagrams to represent a sample space and to calculate probabilities
Success Criteria:
- I can use tree diagrams to organize and represent the outcomes in the sample space, given a description of a chance experiment that can be thought of as being performed in two or more stages.
Topic:
Day: 7
Compound Events
Eureka Lesson: 7
Walt:
We are learning to calculate probability of compound events
Success Criteria:
- I can calculate probabilities of compound events.
Topic:
Days: 8, 9, & 10
Experimental/Estimated Probability
Eureka Lessons: 8, 9, 10 & 11
Walt:
We are learning to estimate the probability of an event.
Success Criteria:
- I can describe what they expect to see when they observe many outcomes of the experiment, given theoretical probabilities based on a chance experiment.
- I can distinguish between theoretical probabilities and estimated/experimental probabilities.
- I can calculate an estimate of probabilities based on observing outcomes of a chance experiment.
- I can compare estimated probabilities to those predicted by a probability model.
- I understand simulation as a method for estimating probabilities that can be used for problems in which it is difficult to collect data by experimentation or by developing theoretical probability models.
- I can perform simulations to estimate probabilities.
- I can use various devices to perform simulations (e.g., coin, number cube, cards).
- I can use colored disks and a random number table in simulations.
- I can compare estimated probabilities from simulations to theoretical probabilities.
Topic:
Day: 11
Applying Probability
Eureka Lesson: 12
Walt:
We are learning to apply probability to make informed decisions
Success Criteria:
- I can calculate and use estimated probabilities to judge whether a given probability model is plausible.
- I can calculate and use estimated probabilities to make informed decisions.
Topic:
Days: 14, 15, & 16
Random Sampling
Eureka Lessons: 13, 14, 15, 16 & 17
Walt:
We are learning to differentiate between population and sampling.
Success Criteria:
- I can differentiate between a population and a sample.
- I can differentiate between a population characteristic and a sample statistic.
- I can investigate statistical questions that involve generalizing from a sample to a larger population.
- I recognize that how a sample is selected is important if the goal is to generalize from the sample to a larger population.
- I know random selection from a population tends to produce samples that are representative of the population.
- I can select a random sample from a population.
- I understand sampling variability.
- I can select a random sample from a population.
- I can design a plan for selecting a random sample from that population, given a description of a population.
- I can use data, from a random sample, to estimate a population mean.
- I can define the term sampling variability in the context of estimating a population mean.
Topic:
Day: 17
Sample Size
Eureka Lesson: 18
Walt:
We are learning to use sampling variability and the effect of sample size
Success Criteria:
- I can use data from a random sample to estimate a population mean.
- I realize that increasing the sample size decreases the sampling variability of the sample mean.
Topic:
Days: 20 & 21
Estimating a Population
Eureka Lessons: 19, 20, & 21
Walt:
We are learning to understand variability when estimating a population proportion
Success Criteria:
- I can explain the term sampling variability in the context of estimating a population proportion.
- I realize that changing the sample size changes the sampling variability.
- I can use data from a random sample to estimate a population proportion.
- I understand what a meaningful difference between two sample means is. (one that is greater than would have been expected due to just sampling variability)
Topic:
Day: 22
Comparing two Populations
Eureka Lessons: 22 & 23
Walt:
We are learning to use sample data to compare the means of two or more populations
Success Criteria:
- I can express the difference in sample means as a multiple of a measure of variability.
- I can explain how sample means
- I can evaluate data and infer the effect of sampling variability and decide how two population means differ.
- I can infer differences in population means based on data from random samples.
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