ALEX Classroom Resource

  

Thinkport | Probability and Tree Diagrams

  Classroom Resource Information  

Title:

 Thinkport | Probability and Tree Diagrams

URL:

 https://aptv.pbslearningmedia.org/resource/mmpt-math-ee-intsurvey2/probability-and-tree-diagrams/

Content Source:

 PBS
Type: Interactive/Game

Overview:

Use a tree diagram to find the probability that a set of triplets will be all girls in this interactive from MPT. In the accompanying classroom activity, students find the probability of various outcomes of compound events involving a set of dice, such as the probability of rolling doubles and the probability of rolling at least one “2.” They share solution strategies, including methods of representing sample spaces for these compound events. To get the most from the lesson, students should have experience developing and using uniform probability models. For a longer self-paced student tutorial using this media, see "Tree Diagrams" on Thinkport from Maryland Public Television.

Content Standard(s):
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.
Mathematics
MA2019 (2019)
Grade: 7
Accelerated
32. 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. [Grade 7, 16]
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.
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:
Tags: compound events, fraction, lists, probability, simple events, simulation, tables, tree diagram
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Author: Hannah Bradley
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