## This post provides details for a discovery activity for intercepts. Students shop for tacos and burritos at Taco Bell. They are to find combinations of number of tacos and number of burritos. This will include no tacos or no burritos. The activity is provided on a Google Doc.

### Overview

Student prior knowledge is leveraged to provide a meaning making activity. The concept of intercepts is developed through 0 tacos or 0 burritos. Here are the steps for the activity.

• The students are tasked with spending the entire balance of the \$30 in gift cards on tacos and burritos.
• They are to find all the combinations that are possible.
• Students enter the combinations into a table found on a linked graph on Desmos. The image below shows the final product, upon completion.
• Then they are tasked to identify the two combinations that standout in the table.
• Finally, they unpack why these two combinations are unique in the graph.
• At that point, the teacher can present the “mathy” term, intercepts.

Below are images of a Google Doc with the activity. You have to make a copy to edit it. Here is the link to the Demos graph with blank table and labeled axes. It is included in the Google Doc.

## Graphing Calculator and Miami Vice

The TI-83 appeared only 6 years after Miami Vice but it and the upgrade versions are still suggested or even required in SOME* US colleges (see gallery of math syllabi below). This has implications for math classes in high schools, as seen in many teacher Facebook posts.

*In a previous iteration of this post I wrote “many” and wanted to clarify.

Teachers are faced with a dilemma, do they use Miami vice era technology because the higher institutes of learning may require it or do they avail themselves and their students of user-friendly and effective technology like Desmos, which is FREE!

I suggest using Desmos (or similar technology) to unpack topics and then assigning practice with the TI model of choice, with it used on the tests as well. This will mirror what students will likely see in college.

To make this situation even more disjointed, a commonly used math placement test for colleges does not allow either Desmos or a TI calculator.

Clockwise from top left: syllabi from CCSU (Connecticut), Gordon State, Texas A&M Commerce, THE Ohio State University, University of Kentucky, and University of Oregon.

## AWESOME Online Graphing Calculator

This can be a game changer for students with special needs who struggle with math. The Desmos graphic calculator allows students to interact with math equations through multiple representations. It is far superior to graphing calculators in terms of quality and ease of use and is free. The app for Smartphones is outstanding.

Here are features that make this calculator user-friendly and an outstanding instructional strategy.

• Students can click on dots and the ordered pair will appear (see top photo below).
• Students can change features of the equation and immediately see how the graph changes.
• Students can collect data and create a graph and convert the data into “mathy” representations like equations (see top photo below).