ALEX Classroom Resource

  

Introduction to Functions and Equations for Functions

  Classroom Resource Information  

Title:

 Introduction to Functions and Equations for Functions

URL:

 https://aptv.pbslearningmedia.org/resource/our20-math-8523/introduction-to-functions-and-equations-for-functions/

Content Source:

 PBS
Type: Audio/Video

Overview:

In this video lesson, students learn the term function for a rule that produces a single output for a given input. This lesson introduces and connects the different ways in which we represent functions in mathematics: verbal descriptions, equations, tables, and graphs. Students transition from input-output diagrams and descriptions of rules to equations. The lesson also introduces the use of independent and dependent variables in the context of functions.

Grade 8, Episode 7: Unit 5, Lessons 2 & 3 | Illustrative Math

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 8
13. Determine whether a relation is a function, defining a function as a rule that assigns to each input (independent value) exactly one output (dependent value), and given a graph, table, mapping, or set of ordered pairs.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Define a function as a rule assigning each input exactly one output.
  • Identify functions when given a relation as graph, table of values, mapping, or set of ordered pairs.
Teacher Vocabulary:
  • Relation
  • Function
  • Input
  • Output
Knowledge:
Students know:
  • how to interpret a graph, table, mapping, and ordered pairs.
Skills:
Students are able to:
  • give an accurate definition of a function.
  • Analyze graphs, tables, mappings, and sets of ordered pairs to determine if a relation is a function.
Understanding:
Students understand that:
  • Functions assign every input one output, but they may see outputs repeat.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.8.13.1: Define function, ordered pairs, input, output.
M.8.13.2: Demonstrate how to plot points on a Cartesian plane using ordered pairs.
M.8.13.3: Recall how to complete input/output tables.
M.8.13.4: Recognize numeric patterns.
M.8.13.5: Given a function, create a rule.

Prior Knowledge Skills:
  • Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection.
  • Demonstrate an understanding of an extended coordinate plane.
  • Draw a four-quadrant coordinate plane.
  • Draw and extend vertical and horizontal number lines.
  • Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.
  • Recall how to graph points in all four quadrants of the coordinate plane.
Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.8.13 Determine whether a relation is a function given a graph or a table.

Mathematics
MA2019 (2019)
Grade: 8
Accelerated
18. Compare and contrast relations and functions represented by equations, graphs, or tables that show related values; determine whether a relation is a function. Identify that a function f is a special kind of relation defined by the equation y = f(x). [Algebra I with Probability, 16]
Unpacked Content
Evidence Of Student Attainment:
Students:
Given relations between two variables in graphical form, set of ordered pairs, tables, mappings, or equations,
  • Distinguish between those that are functions and non-functions.
  • Use key features to compare and contrast the relations.
  • Explain and justify the similarities and differences of the relations.
Teacher Vocabulary:
  • Function
  • Relation
  • vertical line test
Knowledge:
Students know:
  • In graphing functions the ordered pairs are (x,f(x)) and the graph is y = f(x).
  • Techniques for graphing functions.
  • Techniques to find key features of functions when presented in different ways.
  • Techniques to convert a function to a different form (algebraically, graphically, numerically in tables, or by verbal descriptions).
  • The vertical line test can be used to determine if a graph is a function.
  • A function is a special kind of relation.
Skills:
Students are able to:
  • Accurately determine which key features are most appropriate for comparing functions.
  • Manipulate functions algebraically to reveal key functions.
  • Convert a function to a different form (algebraically, graphically, numerically in tables, or by verbal descriptions) for the purpose of comparing it to another function.
Understanding:
Students understand that:
  • Functions can be written in different but equivalent ways (algebraically, graphically, numerically in tables, or by verbal descriptions).
  • Different representations of functions may aid in comparing key features of the functions.
Diverse Learning Needs:
Tags: dependent variable, function, independent variable
License Type: Custom Permission Type
See Terms: https://aptv.pbslearningmedia.org/help/terms-of-use/
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityVideo resources: includes closed captioning or subtitles
Comments

Additional activity and practice pages are provided for this video lesson.

  This resource provided by:  
Author: Kristy Lacks
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