Intro to Concept of Functions

Functions are perhaps the most prevalent and important topic covered in secondary math, aside from maybe 1 variable linear equations. The concept of a mathematical function is challenging for many students. This post provides details about a meaning making approach to introducing functions.

Overview

The introduction is presented on a Google Jamboard, to allow for movement in the pairing of inputs and outputs. It starts with analogies pairing of items using a gumball machine and a Coke machine and proceeds incrementally towards the various representations. The functions are contrasted with examples of relationships that are not functions.

Slides of the Jamboard

  • Slides1 and 2 present the gumball and Coke machines. Students can move the items to see how a quarter can result in 2 different color gumballs while the Coke button results in only 1 output.
  • In slides 3 and 4, the use of an hourly wage introduces input and output with quantities. Slide 4 shows two different pay amounts for the same number of hours worked. This taps into prior knowledge.
  • The sequencing progresses through
    • function machines
    • equations
    • tables
    • graphs
  • Each includes an example and a non-example.
  • The last slide provides a sorting activity.

Access to Jamboard

Here is the link. To access the Jamboard, you need to make a copy.

Matching Activity for Linear Function Representations

Here is a matching activity on a Google Slides file for various representations of a set of linear functions: verbal, symbolic (equation), graphical, and tabular (or data). The students use gallery view of the slides and sort them by function. Then they can change the background color with a different color for each function. This invokes their analytical skills to decipher key elements of the function and of each representation, for example they may identify the value of the y-intercept in the equation and find a graph with the same value.