Starting Functions - Independent & Dependent Variables

The next unit in our Algebra One course is "Functions". This can be a pretty abstract concept. I struggle with finding ways to make the concepts accessible to students.

(here comes why/how learn mathematics ramble.....)

 I HATE having students just memorize. I want there to be some context that I can couch concepts in; having them relate it to real life or see how it connects to mathematics they already know. It's great to be able to justify everything students learn with a "when will I ever use this" example. But also teachers shouldn't get too wedded to doing that. Sometimes I teach a mathematical concept with a lot of enthusiasm because I love the beauty of it (I say things such as "now this is really cool") or because it provides some essential structure to a larger overall concept the students are already familiar with. I'm always reminding them that mathematics is a very large system/language that us humans are always in the process of discovering and defining. We are not "making it up" - it's out there, it defines the structure of the universe, it's the language of science, etc.... I try not to go off too much on this marveling ramble but I want students to see how immense and powerful mathematics is.So when they might think something they learn is silly and meaningless I want them to remember it is an important cog in something larger than they can imagine. (talk about abstract!). I know my enthusiasm about this goes over the heads of many students but you can see some grab onto it and a little twinkle come into their eyes. And these are usually kids who are quite smart but never saw the use of mathematics. It's really cool when I see that.

Okay back to functions... 

we start with something a bit abstract that can be related to real life ...Independent and Dependent Variables!

I actually start this concept right after their test in the previous unit. I'm a big fan of giving students some pre-assessment type thing after a summative assessment. One to keep them busy if they finish early and two to get them thinking about the new material (and dusting off what they already know). Our students learn all about independent and dependent variables in science class, so they are familiar with them. Now we just want them to transfer this knowledge into an algebra setting where we eventually connect it to domain & range. So they get this preassessment after their last test. 

We start the next class by discussing what they came up with. Students come up with some neat independent variable ideas for the dependent variable "your level of happiness". 

Then we summarize what we know in general about independent and dependent variables (seen on top  half of this ISN page - which I might try to flesh out and do as a full page, saving the "right side reflection" page for their homework that night (see mini poster idea at end of this blog). Link for top half defining foldable.   Thought for fleshing out...here is the document..... Relating this to algebra, sneak in a first mention of function notation....

Then students do and independent/dependent variable card sort in their ISN. (next year will do as a two page spread). See the first bit of it above and it continues on a second page:

Students could write function sentences for each IV-DV pair. For example "The number of people you will be able to serve is a function of the number of meals you prepare".

Here are some documents you might find useful..

IV DV cards for sorting

IV DV classroom practice WS

IV DV homework practice WS

But something I'm looking at for next year...

And this looks pretty cool to me, might want to try it for the first HW. Blogger Tom DeRosa calls it a project, but these little mini-posters are cool for a homework assignment.

Full details can be found at his blog post "I want to teach forever".