## Graphing linear functions may be the most important topic in Algebra 1. While proportional reasoning is a prelude to functions, this is the first formally identified function presented to them. The graphing leads to slope and intercepts, beyond the entry point for graphical representations to functions. This post presents an activity that can serve as the entry point for linear functions.

### Overview

The activity is presented on a Google Jamboard, which provides manipulatives. It begins with a relevant context for students, money and being paid for a job. This allows them to engage the function using money. Before using numbers, they engage the work context through images. They are presented the table and then graph representations of the function before getting into the equation. Here is a FB Reel showing the movement of the images.

### The Slides

There are 3 categories of slides. Here is a description of each.

- Table and graph clocks for hours and dollar bill for the money.
- They graph the whole hours first, then fractional hours (1/2 and 1/4) to see that there are points “squeezed in between each other. This leads to the idea of infinite number of points. In turn, this leads to the idea of the line are a visual means to present all the points. The points can be presented as solutions. Hence, the graph presents all the solutions for the function.

- Table and graph with numbers on sticky notes that can be moved from the table to ordered pairs to positions on the coordinate plane.
- The equation, with sticky notes to show numbers substituted in for the variables and then moved to ordered pairs with parentheses.

Here is a link to the Jamboard. You need to make a copy to access it.