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# A1-D-1-3

last edited by 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).

## 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.

## 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.

• 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