ALEX Classroom Resource

  

Count Outcomes Using Tree Diagram

  Classroom Resource Information  

Title:

 Count Outcomes Using Tree Diagram

URL:

 https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-statistics/cc-7th-compound-events/v/tree-diagram-to-count-outcomes

Content Source:

 Other
Khan Academy
Type: Audio/Video

Overview:

Tree diagrams display all the possible outcomes of an event. Each branch in a tree diagram represents a possible outcome. Tree diagrams can be used to find the number of possible outcomes and calculate the probability of possible outcomes.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Algebra I with Probability
39. Compute the conditional probability of event A given event B, using two-way tables or tree diagrams.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Using two-way tables or tree diagrams, compute the probability of event A given event B.
Teacher Vocabulary:
  • Conditional probability
  • Independence
  • Probability
Knowledge:
Students know:
  • Methods to find probability using two-way tables or tree diagrams.
  • Techniques to find conditional probability.
Skills:
Students are able to:
  • Accurately determine the probability of events from a two-way table or tree diagram.
Understanding:
Students understand that:
  • The independence of two events is determined by the effect that one event has on the outcome of another event.
  • The occurrence of one event may or may not influence the likelihood that another event occurs.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
ALGI.39.1: Define likelihood, probability and event.
ALGI.39.2: Construct a graphic representation of all outcomes (probability model-tree diagram, organized list, table, etc.).
ALGI.39.3: Compare and contrast probability of chance and probability of observed frequency.
ALGI.39.4: Write the probability as a fraction, with likely outcomes as the numerator and possible outcomes as the denominator.

Prior Knowledge Skills:
  • Calculate the probability of a single event.
  • Calculate the number of outcomes by listing all possible outcomes.
Mathematics
MA2019 (2019)
Grade: 9-12
Applications of Finite Math
6. Use multiple representations and methods for counting objects and developing more efficient counting techniques.
Note: Representations and methods may include tree diagrams, lists, manipulatives, overcounting methods, recursive patterns, and explicit formulas.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Use tree diagrams or other systematic listing methods to determine the number of total possible outcomes in an application-based problem.
Teacher Vocabulary:
  • Tree diagram
  • Recursive pattern
  • Explicit formula
Knowledge:
Students know:
  • Tree diagrams can be used to systematically list all possibilities for a given set of constraints.
Skills:
Students are able to:
  • List all possible outcomes for a given set of constraints
Understanding:
Students understand that:
  • Tree diagrams and other systematic methods can be used to count objects but may not be the most efficient method when counting large quantities.
  • Recursive and explicit formulas can be developed from examining patterns in tree diagrams and systematic lists.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 9-12
Applications of Finite Math
7. Develop and use the Fundamental Counting Principle for counting independent and dependent events.

a. Use various counting models (including tree diagrams and lists) to identify the distinguishing factors of a context in which the Fundamental Counting Principle can be applied.

Example: Apply the Fundamental Counting Principle in a context that can be represented by a tree diagram in which there are the same number of branches from each node at each level of the tree.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Given a real-world context problem, determine if the the Fundamental Counting Principle can be applied, use various counting models to count using a variety of different context parameters.
Teacher Vocabulary:
  • Fundamental counting principle
  • Independent events
  • Dependent events
  • Tree diagram
  • Branches
  • Node
Knowledge:
Students know:
  • How to construct a tree diagram.
Skills:
Students are able to:
  • Count the number of events when given a variety of constraints/parameters when the Fundamental Counting Principle can be applied.
Understanding:
Students understand that:
  • The Fundamental Counting Principle can be applied in contexts where an ordered list of events occur and there are a ways for the first event to occur, b ways for the second event to occur so the number of ways of the ordered sequence of events occuring is axb.
Diverse Learning Needs:
Tags: Algebra I, counting, dependent, fundamental counting principle, independent, probability, tree diagram
License Type: Custom Permission Type
See Terms: https://www.khanacademy.org/about/tos
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments

There are practice problems that students can complete after viewing the video.

  This resource provided by:  
Author: Hannah Bradley
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