MA.912.D.7.1Archived Standard

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Perform set operations such as union and intersection, complement, and cross product.

Remarks

Example: Let A={1,2,3} and B={2,4,5} be two sets in universe U={1,2,3,4,5,6}. Find the union of A and B and the complement of B. Find AXB.
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Discrete Mathematics
Idea: Level 1: Recall
Standard: Set Theory - Operate with sets, and use set theory to solve problems.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 1: Recall - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC , FR item(s)

  • Clarification :
    Students will perform set operations such as union and intersection, complement, and cross product.
  • Content Limits :

    Items may include set notation and symbols from set theory.

    Finite sets should contain no more than a total of 15 unordered elements and no more than 30 ordered elements.

    If an item follows a numerical pattern, data may be represented by infinite sets. Example: Natural numbers {1, 2, 3, 4 . . .}

    Notation for the complement of set A will be limited to A' and ~A.

  • Stimulus Attributes :

    Items may be set in either real-world or mathematical contexts.

    Graphics should be used for most of these items, as appropriate.

    Sets should list all elements in the stem (e.g., do not use natural numbers between 2 and 5.).

Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question: The set T represents several Taurine breeds of cattle.
          T = {Angus, Devon, Shorthorn, Texas Longhorn}
    The set Z represents several Zebu breeds of cattle.
          Z = {Boran, Nelore, Ponwar}
    What is the total number of elements in the set T × Z ?
  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question: Set D lists the ages of Dianna’s grandchildren.
         D = {2, 5, 6, 8, 10, 11}
    Set K lists the ages of Karen’s grandchildren.
         K = {2, 10, 18}
    Set P lists the ages of Patrick’s grandchildren.
         P = {10, 11, 14}

  • Difficulty: N/A
  • Type: FR: Fill-in Response

Related Access Points

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Video/Audio/Animation

MIT BLOSSOMS - Taking Walks, Delivering Mail: An Introduction to Graph Theory:

This learning video presents an introduction to graph theory through two fun, puzzle-like problems:"The Seven Bridges of Königsberg" and "The Chinese Postman Problem". Any high school student in a college-preparatory math class should be able to participate in this lesson. Materials needed include: pen and paper for the students; if possible, printed-out copies of the graphs and image that are used in the module; and a blackboard or equivalent. During this video lesson, students will learn graph theory by finding a route through a city/town/village without crossing the same path twice. They will also learn to determine the length of the shortest route that covers all the roads in a city/town/village. To achieve these two learning objectives, they will use nodes and arcs to create a graph and represent a real problem. This video lesson cannot be completed in one usual class period of approximately 55 minutes. It is suggested that the lesson be presented over two class sessions.

Type: Video/Audio/Animation

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