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PA-A-1-1

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

PA.A.1.1 Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable.


In a Nutshell

Students will take sets of data and discuss the different relationships between data, discovering which relations have properties of a function. Understanding that a function has data that shows each input value has a unique output value and that the output value is dependent on the independent input value.

Student Actions

Teacher Actions

  • Develop A Productive Mathematical Disposition when identifying independent and dependent relationships in real life.

  • Develop a Deep and Flexible Conceptual Understanding as you explore the meaning of the vertical line test as a way to graphically check for functions. By doing this, the discovery is made that in order for the graph to represent a function, for every input there is only one possible output. If this is not the case, then the graph fails the vertical line test and is not a function.

  • Develop Mathematical Reasoning by discussing how the input (independent variable/ x) changes the output (dependent variable / y). Work with a partner to make predictions and develop patterns based on the relationship between the input and output.

     

  • Pose purposeful questions that enable students to create lists of independent relationships in real life and dependent relationships in real life to understand the meaning that those terms have in functions.
  • Implement meaningful tasks that promote reason and understanding of graphs used to represent functions. Use the vertical line test to allow student to derive the idea that functions have only one possible output for every input.

  • Pose purposeful questions that ask for students to describe the input and output helping them to make connections between independence and dependence.

  • Use and Connect the students’ understanding of functions to real-world situations.  Provide activities that allow students to identify both the independent and dependent variables in various situations. (Ex.  Orange trees that receive the most water produce the most fruit.  What is the independent and dependent events?)

Key Understandings

Misconceptions

  • Changing the input changes the output in a specific way;

  • Identify independent and dependent variables in real-life situations;

  • Understand that there is a relationship between input(independent variable) and output(dependent variable).

  • Understand that in order for a relationship to be a function, for every input there is only one possible output.

  • In order for a graph to show a functional relationship, it must pass the vertical line test. 


  • A proportional relationship between two variables can always be modeled by a linear function, but not all linear functions represent proportional relationships.
  • When looking at a table of linear data where the x values are not increasing by a constant amount, students sometimes think the relationship is not linear because they think y is not changing by a constant amount, even though the rate of change is constant.  

 

    x    

    y    

    0

    3

   1

    6

   3

   12

   4

   15

   7

   24

 

Even though the input values (x-values) are not constant, the rate of change (change in y/change in x) is a constant value of 3. 

OKMath Framework Introduction

Pre-Algebra Introduction

 

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