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A1-D-2-2

Page history last edited by Brenda Butz 6 years, 2 months ago

A1.D.2.2 Describe the concepts of intersections, unions, and complements using Venn diagrams to evaluate probabilities. Understand the relationships between these concepts and the words AND, OR, and NOT.


In a Nutshell 

Students will use a Venn diagram to display data to understand intersection is the elements in common, union is all the elements and the complement is the elements not in a specific sample.  Students will use these to evaluate the probability of an event.

Student Actions

Teacher Actions

  • Students explore data sets to develop mathematical reasoning as they discover how to distinguish between “OR” being a union and “AND” being an intersection of the data.

  • Students develop a Venn diagram to display data to calculate the probability with accurate and appropriate procedural fluency.

     

  • Pose purposeful questions for students to distinguish between intersection and union.
  • Use and connect mathematical representations between a Venn diagram and the calculation of the probability an event by using intersection, union or complement of the data as appropriate.

  • Encourage productive struggle as students explore and discuss the difference between intersection and union.

Key Understandings

Misconceptions

  • Venn diagrams are useful tools in organizing. Although disjoint (mutually exclusive events) can be seen using two non-overlapping circles, independence cannot be shown on a Venn diagram. 
  • Probability is a fraction of the sample space or simply the part over the whole.
  • If the probability of an event is p, then the probability of the complement of an event is 1 - p.
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  • The probability of the intersection of two independent events is the product of their probabilities.
  • The probability of the union of two events equals the sum of the probabilities of each individual event minus the probability of the intersection of the events.

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  • Students will interchange the use of the words "and" and "or" 

  • Students confuse when to add and multiply the probability. 

  • Students misinterpret the  complement as the element(s) that lie outside of the given set.  

  • Students do not understand the null set is empty. 

  • Student confuse the notations for union and intersection.

 

OKMath Framework Introduction

Algebra 1 Introduction

 

 

 

 

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