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Grade 7 Mathematics Module 5, Topic B: Estimating Probabilities

  Classroom Resource Information  

Title:

 Grade 7 Mathematics Module 5, Topic B: Estimating Probabilities

URL:

 https://www.engageny.org/resource/grade-7-mathematics-module-5-topic-b-overview

Content Source:

 EngageNY
Type: Lesson/Unit Plan

Overview:

In Module 5, Topic B, students move to compare probabilities from simulations to computed probabilities that are based on theoretical models (7.SP.C.6, 7.SP.C.7). They calculate probabilities of compound events using lists, tables, tree diagrams, and simulations (7.SP.C.8). They learn to use probabilities to make decisions and to determine whether or not a given probability model is plausible (7.SP.C.7). The Mid-Module Assessment follows Topic B.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 7
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:
M.AAS.7.14 Describe the probability of events occurring as possible or impossible.
Mathematics
MA2019 (2019)
Grade: 7
15. Approximate the probability of an event using data generated by a simulation (experimental probability) and compare it to the theoretical probability.

a. Observe the relative frequency of an event over the long run, using simulation or technology, and use those results to predict approximate relative frequency.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Predict the approximate relative frequency of an event given the probability.
  • Compare the accuracy of estimated probabilities from different experiments to the actual probability.
  • Describe how a single event can be simulated using an experiment.
Teacher Vocabulary:
  • Experimental probability
  • Simulation
  • Theoretical probability
  • Relative frequency
Knowledge:
Students know:
  • relative frequencies for experimental probabilities become closer to the theoretical probabilities over a large number of trials.
  • Theoretical probability is the likelihood of an event happening based on all possible outcomes.
  • long-run relative frequencies allow one to approximate the probability of a chance event and vice versa.
Skills:
Students are able to:
  • approximate the probability of a chance event.
  • observe an event's long-run relative frequency.
Understanding:
Students understand that:
  • real-world outcomes can be simulated using probability models and tools.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.15.1: Define probability of chance, outcome, theoretical probability, experimental probability and event.
M.7.15.2: Recognize the difference between possible outcomes and likely outcomes.
M.7.15.3: Write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.
M.7.15.4: Recall how to simplify fraction to lowest terms.
M.7.15.5: Recognize equivalent fractions.
M.7.15.6: Define relative frequency.

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.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.15 Given a data set that represents a series of events, identify the event most likely to occur.
Mathematics
MA2019 (2019)
Grade: 7
16. Find probabilities of simple and compound events through experimentation or simulation and by analyzing the sample space, representing the probabilities as percents, decimals, or fractions.

a. Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams, and determine the probability of an event by finding the fraction of outcomes in the sample space for which the compound event occurred.

b. Design and use a simulation to generate frequencies for compound events.

c. Represent events described in everyday language in terms of outcomes in the sample space which composed the event.

Unpacked Content
Evidence Of Student Attainment:
Students:
  • Conduct probability experiments to quantify and interpret likeliness of an event occurring.
  • Design and use a simulation to generate frequencies for compound events
  • Analyze the results from a simulation of a compound event to estimate the probability of the compound event.
  • Represent probabilities as percents, decimals, and fractions.
Teacher Vocabulary:
  • Tree diagram
  • Compound probability
  • Simulation
  • Sample space
  • Event
Knowledge:
Students know:
  • how the sample space is used to find the probability of compound events.
  • A compound event consists of two or more simple events.
  • A sample space is a list of all possible outcomes of an experiment.
  • how to make an organized list.
  • how to create a tree diagram.
Skills:
Students are able to:
  • find probabilities of compound events using organized lists, tables, tree diagrams and simulations
  • 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 a simulation to generate frequencies for compound events.
  • Use a designed simulation to generate frequencies for compound events.
Understanding:
Students understand that:
  • the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
  • A compound event can be simulated using an experiment.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.7.16.1: Define simple events and compound events.
M.7.16.2: Discover when to add or multiply events to find probability of compound events.
M.7.16.3: Recall how to find the probability of simple events.
M.7.16.4: Demonstrate adding and multiplying fractions.
M.7.16.5: Recognize how to obtain a common denominator when adding fractions.
M.7.16.6: Recall how to add fractions with like denominators.
M.7.16.7: Define simulation, frequency, and compound events.
M.7.16.8: Recall how to find the probability of compound events.
M.7.16.9: Create a tree diagram including all possible outcomes.
M.7.16.10: Choose appropriate model to display outcomes (tree diagram, organized list, or table).
M.7.16.11: Identify the desired outcomes in model. M 7.16.12: Create and use a simulation to illustrate compound events.
M.7.16.13: Recall when to add or multiply events to find probability of compound events.
M.7.16.14: Recall how to find the probability of simple events.
M.7.16.15: Demonstrate adding and multiplying fractions.
M.7.16.16: Recognize how to obtain a common denominator when adding fractions.
M.7.16.17: Recall how to add fractions with like denominators.
M.7.16.18: Recall how to construct a table.

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.
Tags: chance, compound events, data, event, lists, model, probability, simulations, tables, tree diagrams
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Author: Hannah Bradley
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