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A1-A-4-4

Page history last edited by Levi 6 years, 1 month ago

A1.A.4.4 Translate between a graph and a situation described qualitatively.


In a Nutshell  

Students will analyze qualitative graphs that are used to represent situations that do not necessarily have numerical values. Students will discover qualitative graphs represent the essential elements of a situation in a graphical form.

Student Actions

Teacher Actions

  • Students will develop accurate and appropriate procedural fluency as they use the information given in a real-world or a mathematical relationship involving two variables to create tables, equations, and graphs.

  • Students will develop a deep and flexible conceptual understanding by exploring how graphs show visual representations between the two given variable quantities as they both change.

  • Students will develop the ability to communicate mathematically by using both graphs and equations to describe solutions in the original context of the problems using the proper relationship of the two variables.
  • Use and connect mathematical representations by providing students various models including graphs to help the students discover the relationship of the two variable quantities.

  • Pose purposeful questions to direct students’ thinking toward finding relationships between the variables.

  • Implement tasks that promote reasoning and problem solving by expecting students to interpret the mathematical relationship in the original context of the problem.

     

Key Understandings

Misconceptions

  • The student will interpret key features of a function that models the relationship between two quantities when given in graphical or tabular form.
  • Students will sketch the graph of a function from a verbal description showing key features. Key features  may include intercepts; intervals where the function is increasing, decreasing, constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and periodicity.

 

Example: Describing a situation of a graph.

From zero to 15 seconds, a person is increasing his distance from the starting point and is at the maximum point of 100 ft. Then, from 15 to 35 seconds the person’s distance is decreasing and getting closer to the starting point where he remains at a constant distance of 20 ft. for 10 seconds. At 45 seconds into his journey, the person is moving for 5 seconds and is back at the original starting point. At 50 seconds the journey is over.

  • Students may misinterpret parts of the diagram or data given as important information of the problem.


  • Students may misinterpret the visual representation as the wrong behavior.

 

Example:

Students will see a line rise from left to right on a graph and call it increasing speed over time and the axes are labeled differently, e.g. increasing distance over time. Address that this depends on what each axis is labeled

 

 

 

 

 

OKMath Framework Introduction

Algebra 1 Introduction

 

 

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