By Patricia Helmuth
On the new High School Equivalency Exams, high emphasis is placed on functions. Learn Zillion has a five video lesson set that can serve as a means to deepen your own understanding of functions and their graphs, and can also be used to introduce your students to functions. Each video is short, about five minutes, and they all feature concrete examples of functions in real life. By the end of the third video you will have been introduced to ordered pairs, graphing, the vertical line test, and a simple function: y = mx.

If you decide to use the videos in the classroom, pair them with an online function machine and the Guess My Rule worksheet, and you will be able to help your students to bridge from concrete examples of functions to abstract representations. What follows is an example of how you could use Video 1 along with a function machine.

(Note that if you don’t have internet access in your classroom, but do have a SMARTboard or a projector, you can download the videos as PowerPoint presentations to use in the classroom.)

Understand a function as a type of relation

Before showing the video, instruct students to watch for the definition of what a function is as they view the video. Pause the video when it defines a function so that students can write the definition in their math journals.

After the video, break students into groups and have each group brainstorm a real-life example of a function. Come back together and have each group talk about their idea. As each group presents, ask the rest of the class if they agree or disagree that the example is a function. If not, why not?

Now visit an online function machine. I particularly like Ambleweb Function Machine for its versatility. Set the function machine to multiply by a single digit number because this is the function that was represented in Video 1.

Ambleweb Function Machine

When I introduce the function machine to my students, I usually explain that a number will go into the machine, then something happens to the number while it is in the machine (waving my hands wildly in the air for emphasis) and then a new number, or sometimes even the same number will come out. I instruct students to keep track of what number goes into the machine and what number comes out of the machine on the Guess My Rule worksheet and I model how to do this on the board as we go along.

After inputting three or so consecutive numbers, I will input the next number and ask students to quietly write down what they think the output will be on their worksheet, along with a rule to describe what is happening inside the machine. Have students share and compare their theories. Some students may pick up on an explicit rule as shown below, while others may be more inclined to notice a recursive rule (the output goes up by 5 each time).

Input/Output Table example

As students become more proficient in identifying explicit rules, you might allow students to choose the numbers that go into the machine. This sometimes results in some wild and crazy numbers that make it more difficult to identify the rule, but definitely engages the students because they had a hand in creating the function. You can also challenge students to come up with a real-life example that the function could represent. For example, the table above could represent a situation where someone puts $5.00 each week into a savings account.

The function machine can be used in tandem with the remaining videos or it can stand alone as a fun way to “Guess My Rule”. For example, if you have a computer lab available you can pair students at computer stations where they work together to identify functions. Regardless of how you decide to use the function machine, choose a different rule each time, until students are proficient at guessing a one-step operation. Then, have students bridge to two-step operations and graphing. If you try these videos or the function machine in your class, let us know how it went!

Patricia Helmuth is an Adult Numeracy Consultant and Educator, who teaches for the Adult Program and SC BOCES in New York. She also works with the Hudson Valley RAEN Regional Staff Developers Network, as a Teacher Leader-Trainer, to provide support for Adult Education Instructors in CCSS mathematics instructional strategies. She recently became Co-Editor of the Math Practitioner, a newsletter published by ANN, The Adult Numeracy Network.

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