In my Algebra class, I’ve made a big push this year to more often start with a context and then work our way to an equation, graph, or whatever more abstract representation of that context. But for this activity, I decided to start with the abstraction and have the students invent the context. Here’s the set up:

1.) Students are set up in groups of two or three. Each group starts with either a table of values or a function:

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2.) The groups are told to create a whiteboard with the following:

- a table
- a graph
- a function
- a context

**What I liked: **

The students are asked to create multiple representations for the same function. Sometimes I ask things like “make a graph from this table” or “write an equation from this graph” but stop short of having students create more than one new representation. It’s nice for them to make the connections between the different representations in an activity like this.

Writing the context was something new for most of my students and they were **confused** by it. This confusion led to **good questions** being asked and **good conversations** between students. One group that started with the function wanted it to represent the growth of a plant over time. But it’s got a negative slope, so that didn’t really make sense. It was nice that they had the graph already on their whiteboard to help visualize this.

**What I didn’t like: **

I have been struggling with getting everyone to participate in group activities like this. I think sometimes the students who don’t participate are thinking that they are just skipping something “extra” and therefore not missing anything important. But really they’re missing the most important part of the learning process.

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