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A1-D-1-3

Page history last edited by Tashe Harris 6 years, 5 months ago

A1.D.1.3 Interpret graphs as being discrete or continuous.


In a Nutshell 

Students will learn that  a discrete graph is one in which the data can only take on certain values, for example, integers and a continuous graph is one in which data can take on any value within a specified interval (which may be infinite).

Student Actions

Teacher Actions

  • Students will Develop Mathematical Reasoning to determine whether the ordered pairs of the graph should be connected, making it continuous.

  • Students will Develop a Deep and Flexible Conceptual Understanding of discrete being only a finite set of points and continuous is an infinite set of points.

  • Students will  interpret a real world application into a graph  and Make Conjectures, Model, and Generalize whether is it discrete or continuous and vice versa.

  • Students will Communicate Mathematically while justifying their reasoning for a graph being discrete or continuous.

     

 

  • Pose purposeful questions for students to distinguish between discrete and continuous graphs and real world applications.

  • Facilitate meaningful mathematical discourse to encourage and expert students to make connections between the real world application and the graph.

  • Elicit and use evidence of student thinking to direct students to justify their interpretations of solutions.

  • Encourage productive struggle as students explore and discuss the data to distinguish the difference between discrete and continuous graphs.

     

Key Understandings

Misconceptions

  • The graph of a discrete function, only separate, distinct points are plotted, and only these points have meaning to the original problem.
  • A discrete graph is a series of unconnected points (a scatter plot).
  • The graph of a continuous function is drawn without lifting the pencil from the paper.
  • A continuous graph allows the x-values to be ANY points in the interval, including fractions, decimals, and irrational values.

 

Image result for discrete vs continuous graphs

  • Students may confuse the words discrete and continuous as these are new vocabulary words for this grade level.   
  • When a graph is continuous on just an interval (section of the Real Numbers), students may consider it to be discrete instead of continuous on the interval.
  • When given a real world example, students may have difficulty determining whether the graph is discrete or continuous.

  • Students do not recognize that in a discrete graph, each x,y pair is a distinct point while in a continuous graph,the points are connected.

 

 

OKMath Framework Introduction

Algebra 1 Introduction

 

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