I have seen function machines throughout my teaching career but I have mostly dismissed them as a way of displaying a question and I didn’t really appreciate how they could be useful. It wasn’t until I came across the ICCAMS question below that I began to see how they could be useful in the classroom. I have used the question below with a variety of abilities and I always love hearing how the students respond to the question. Usually the lower attaining classes would say that both outputs would be the same and then try values to see this isn’t true. With higher attaining students there was a mix of students who thought it might be the same but felt it should be different and those who thought they weren’t equal but would try values and confirm that they weren’t.
What I liked most about the question was the absence of formal algebra but also that it gave students an opportunity to look at order of operations and how multiply and addition affected values when used sequentially. I also liked how students could reverse the machine and think about inverse operations.
Another thing I liked about the function machines was it gave students the opportunity to notice connection between expressions so I thought about a few of my own questions. In the first pair of machines, I hope that students will notice the outputs are equal and start to think about why this is the case. I like an image that I saw in the ICCAMS project handbook. I have used it as a model to create a similar image for the first set of function machines.