Content Standard(s):
Mathematics 14. Define and develop a probability model, including models that may or may not be uniform, where uniform models assign equal probability to all outcomes and non-uniform models involve events that are not equally likely.
a. Collect and use data to predict probabilities of events.
b. Compare probabilities from a model to observed frequencies, explaining possible sources of discrepancy.
Unpacked Content
Evidence Of Student Attainment:
Students:
Develop uniform (all outcomes have the same probability) and non-uniform (outcomes with different probabilities) probability models and use them to find probabilities of simple events.
Explain possible sources of discrepancy if the agreement between the probability model and observed frequencies is not good.
Estimate the probability of an event happening in an experiment.
Compare the accuracy of estimated probabilities from different experiments to the actual probability. Teacher Vocabulary:
Probability model Uniform model non-uniform model observed frequencies Knowledge:
Students know:
the probability of any single event can be expressed using terminology like impossible, unlikely, likely, or certain or as a number between 0 and 1, inclusive, with numbers closer to 1 indicating greater likelihood.
A probability model is a visual display of the sample space and each corresponding probability
probability models can be used to find the probability of events.
A uniform probability model has equally likely probabilities.
Sample space and related probabilities should be used to determine an appropriate probability model for a random circumstance. Skills:
Students are able to:
make predictions before conducting probability experiments, run trials of the experiment, and refine their conjectures as they run additional trials.
Collect data on the chance process that produces an event.
Use a developed probability model to find probabilities of events.
Compare probabilities from a model to observed frequencies
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. Understanding:
Students understand that:
long-run frequencies tend to approximate theoretical probability.
predictions are reasonable estimates and not exact measures. Diverse Learning Needs:
Essential Skills:
Learning Objectives: M.7.14.1: Define probability of chance, probability of events, outcome, and probability of observed frequency.
M.7.14.2: Compare and contrast probability of chance and probability of observed frequency.
M.7.14.3: Display all outcomes in a graphic representation (probability model-tree diagram, organized list, table, etc.).
M.7.14.4: Demonstrate how to write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
M.7.14.5: Recall how to simplify fractions to lowest terms.
M.7.14.6: Recognize equivalent fractions.
M.7.14.7: Recall how to create a table or graphic display of data.
M.7.14.8: Define probability of chance, outcome, and event.
M.7.14.9: List all possible outcomes using a graphic representation (probability model-tree diagram, organized list, table, etc.).
M.7.14.10: Using the model, count the frequency of the desired outcome.
M.7.14.11: Demonstrate how to write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
M.7.14.12: Recall how to simplify fractions to lowest terms.
M.7.14.13: Recognize equivalent fractions.
M.7.14.14: Recall how to create a table or graphic display of data.
M.7.14.15: Analyze collected data to predict probability of events.
M.7.14.16: Define probability of observed frequency, outcome, discrepancy and event.
M.7.14.17: List all actual outcomes using a graphic representation (probability model-tree diagram, organized list, table, etc.).
M.7.14.18: Using the model, count the frequency of the actual outcome.
M.7.14.19: Demonstrate how to write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
M.7.14.20: Recall how to simplify fractions in lowest terms.
M.7.14.21: Recognize equivalent fractions.
M.7.14.22: Recall how to create a table or graphic display of data.
Prior Knowledge Skills:
Recall addition and subtraction of fractions as joining and separating parts referring to the same whole.
Identify two fractions as equivalent (equal) if they are the same size or the same point on a number line.
Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
Generate equivalent fractions.
Recall how to read a graph or table.
Alabama Alternate Achievement Standards
AAS Standard:
Mathematics 30. Define and develop a probability model, including models that may or may not be uniform, where uniform models assign equal probability to all outcomes and non-uniform models involve events that are not equally likely.
a. Collect and use data to predict probabilities of events.
b. Compare probabilities from a model to observe frequencies, explaining possible sources of discrepancy. [Grade 7, 14]
Unpacked Content
Evidence Of Student Attainment:
Students:
Develop uniform (all outcomes have the same probability) and non-uniform (outcomes with different probabilities) probability models and use them to find probabilities of simple events.
Explain possible sources of discrepancy if the agreement between the probability model and observed frequencies is not good.
Estimate the probability of an event happening in an experiment.
Compare the accuracy of estimated probabilities from different experiments to the actual probability. Teacher Vocabulary:
Probability model Uniform model non-uniform model observed frequencies Knowledge:
Students know:
the probability of any single event can be expressed using terminology like impossible, unlikely, likely, or certain or as a number between 0 and 1, inclusive, with numbers closer to 1 indicating greater likelihood.
A probability model is a visual display of the sample space and each corresponding probability.
probability models can be used to find the probability of events.
A uniform probability model has equally likely probabilities.
Sample space and related probabilities should be used to determine an appropriate probability model for a random circumstance. Skills:
Students are able to:
make predictions before conducting probability experiments, run trials of the experiment, and refine their conjectures as they run additional trials.
Collect data on the chance process that produces an event.
Use a developed probability model to find probabilities of events.
Compare probabilities from a model to observed frequencies
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. Understanding:
Students understand that:
long-run frequencies tend to approximate theoretical probability.
predictions are reasonable estimates and not exact measures. Diverse Learning Needs:
