In today's lesson, students work with the previous lesson's task and create a poster to show two representations of linear growth and two representations for exponential growth. A new task in this assignment is for students to identify what the "change" is or be able to find the rate of change (for linear functions) and the change factor (for exponential functions).
I start today's class by reminding students of the patterns we looked at in the last lesson. I ask them to share out what makes a pattern a linear function and what makes a pattern an exponential function. I then ask them to take out the work they've done on Sorting Out the Change.
I explain that in today's class they'll be working in pairs to create posters. Each poster should be divided into two columns, one column for linear functions and one column for exponential functions. Students will choose two of each functions and represent them in as many ways as they can: with a graph, table, recursive and explicit equations, and a context. We read through Where's My Change? together and I let students know that in today's work they'll also be finding the rate of change and and change factor.
Students will spend most of the today's class working on their posters. If they have trouble getting started, I might suggest the take a look at Question 1 for a good example of a linear function. Students seem to like Question 12 to represent an exponential function (it lends itself well to a nice drawing).
Many students will base the change factor only on the out column. I remind them that while this might work for sequences, it won't work always work for functions. I try to use the language of the change in the out column in comparison to or over the intervals in the In column.
We end today's class with students sharing out their work. We start by looking at one group's work on linear functions. I ask students to demonstrate how they found the rate of change. Then we look at other posters to see similar functions and identify the rates of change there. I also ask students where they can see their rates of change in each of the representations. For example, I ask where they see the change of increasing by 3 over intervals of 4 in the graph of the same function.
We continue this same line of questioning for exponential functions, with different groups sharing out their work.
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