Sunday, August 11, 2024, 11:04 PM
Site: Learnbps
Course: BPSS (MAT) Mathematics Standards (S-MAT)

# Statistics and Probability

## Narrative for the (SP) Statistics and Probability

The standards within the Statistics and Probability domain require students to (1) use random sampling to draw inferences about a population, (2) draw informal comparative inferences about two populations, and (3) investigate chance processes and develop, use, and evaluate probability models.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-07.SP.01

Domain (SP) Statistics and Probability
Cluster: Use random sampling to draw inferences about a population

MAT-07.SP.01 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.

## Vocabulary:

Sample, Population, Validity, Generalization, Random Sample, and Representative Sample.

Rubric - Resources

#### MAT-07.SP.02

Domain (SP) Statistics and Probability
Cluster: Use random sampling to draw inferences about a population

MAT-07.SP.02 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.

## Student Learning Targets:

• I can draw inferences about a population based on data generated by a random sample.
• I can generate multiple samples from the same population and analyze the estimates or predictions based on the variation of each sample.

### Vocabulary:

Population, Sample, and Random Sample.

Rubric - Resources

#### MAT-07.SP.03

Domain (SP) Statistics and Probability
Cluster: TOPIC

MAT-07.SP.03 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.

## Student Learning Targets:

• I can find the difference in the mean or the median of two different data sets.
• I can demonstrate how two data sets that are very different can have similar variabilities.
• I can draw inferences about the data sets by making a comparison of these differences relative to the mean absolute deviation or interquartile range of a set of data.

### Vocabulary:

Measures of Center (Measures of central tendencies)

Variability

mean

median

mode

mean absolute deviation

interquartile range.

Rubric - Resources

#### MAT-07.SP.04

Domain (SP) Statistics and Probability
Cluster: Draw informal comparative inferences about two populations

MAT-07.SP.04 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.

## Student Learning Targets:

• I can apply central measures t draw conclusions.
• I  draw conclusions from different population samples.
• I can make inferences about two populations.

# Proficiency Scale

### Vocabulary:

Measures of Variability

Measures of Center

Mean

Median

Absolute Deviation

Interquartile Range

Population

Random Sample

Rubric - Resources

#### MAT-07.SP.05

Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

MAT-07.SP.05 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 ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

## Student Learning Targets:

• I can define probabilite as a ratio that compares favorable outcomes to all possible outcomes.
• I can recognize and explain that probabilities are expressed as a number between 0 to 1.
• I can interpret a probability near 0 as unlikely to occur and a probability near 1 as likely to occur.
• I can interpret a probability near 1/2, as being equally able to occur as to not occur

#### Vocabulary:

Likely

unlikely

Rubric - Resources

#### MAT-07.SP.06

Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

MAT-07.SP.06 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.

## Student Learning Targets:

• I can collect data on a chance process to approximate its probability.
• I can use probability to predict the number of times a particular event will occur given a specific number of trials.
• I can use variability to explain why the experimental probability will not always exactly equal the theoretical probability.

### Vocabulary

Theoretical Probability

Experimental Probability

Relative Frequency

Rubric - Resources

#### MAT-07.SP.07

 7th Grade MAT Targeted StandardsDomain (SP) Statistics and ProbabilityCluster: Investigate chance processes and develop, use, and evaluate probability models MAT-07.SP.07 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. b. Develop a possibly model (which may not be uniform) by observing frequencies in data generated from a chance process.

## Student Learning Targets:

### Reasoning Targets

• I can explain the difference between theoretical and experimental probability of an event

### Skills Domain (Performance) Targets

• I can find experimental probability of an event
• I can find theoretical probability of an event

## Resources

### Vocabulary

• probability
• theoretical probability
• experimental probability
• outcome
• event

#### MAT-07.SP.07.a

 7th Grade MAT Targeted StandardsDomain (SP) Statistics and ProbabilityCluster: Investigate chance processes and develop, use, and evaluate probability models 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. MAT-07.SP.07.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.

## Student Learning Targets:

• I can find the theoretical probability.
• I can find the number of favorable outcomes.
• I can find the number of possible outcomes.
• I can use a proportion to solve for the total number of outcomes or favorable number of outcomes.
• I can use theoretical probabilities to solve real-world problems.

### Vocabulary

• List
• Event
• Outcomes
• Event
• Tree diagram

#### MAT-07.SP.07.b

 7th Grade MAT Targeted StandardsDomain (SP) Statistics and ProbabilityCluster: Investigate chance processes and develop, use, and evaluate probability models 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. MAT-07.SP.07.b Develop a possibly 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?

## Student Learning Targets:

• I can find experimental probability.

### Vocabulary

• List

#### MAT-07.SP.08

Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

MAT-07.SP.08 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

• a. 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.
• b. 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 with compose the event.
• c. Design and use a simulation to generate frequencies for compound events.

## Student Learning Targets:

• I can find the theoretical Probability
• I can find the experimental Probability
• I can determine the relationship between experimental and theoretical probability
• I can predict the experimental probability of an event based on the theoretical probability
• I can determine the likelihood of an event occurring based on the probability
• I can use organized lists tree diagrams, tables, simulations, and mathematical computations to determine the probability of compound events.

### Vocabulary

Compound events

sample space

tree diagram

outcomes

favorable outcomes

simulation

### Proficiency Scale

Rubric - Resources

Theoretical Probability

Marble Probability

Compound Probability using a sample space

Compound Probability using a tree diagram

Dependent Events

Big Ideas Math: Probability is found in Chapter 9 of the Big Ideas math book

#### MAT-07.SP.08a

Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

MAT-07.SP.08a 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.

## Student Learning Targets:

• I can
• I can

• I can
• I can

• I can
• I can

### Product Targets

• I can
• I can
Rubric - Resources

#### MAT-07.SP.08b

Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

MAT-07.SP.08b 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 with compose the event.

## Student Learning Targets:

• I can
• I can

• I can
• I can

• I can
• I can

### Product Targets

• I can
• I can
Rubric - Resources

#### MAT-07.SP.08c

Domain (SP) Statistics and Probability
Cluster: Investigate chance processes and develop, use, and evaluate probability models

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

MAT-07.SP.08c 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?

## Student Learning Targets:

• I can
• I can

• I can
• I can

• I can
• I can

### Product Targets

• I can
• I can
Rubric - Resources