The teacher uses a table of values and a pattern to review a linear model with students.  Students come up with pattern and make conclusions.  The teacher uses the review to build on their understanding of linear functions to prepare students for exponential functions.  

The teacher makes the mathematics of the lesson explicit by using explanations, representations, and/or examples.

In this part of the lesson, the teacher makes the mathematics of the lesson explicit by using explanations, representations, and/or examples.  The students fold paper, create a table, and create a graph to visualize the pattern.  

Students using paper folding, a table, a graph, and their patterns to come up with a rule for the model.  The teacher pauses to look at student solutions and reasoning. 

In this part of the lesson, the teacher uses real life examples to help students understand exponential growth and the exponential growth function.  She defines exponential growth and the exponential growth function. 

Teacher does not dismiss student example, but she explores this with students to confirm a non-example of exponential growth. 

The teacher connects students’ informal language to precise mathematical language appropriate to their course.
The teacher uses terms like "decreasing exponentially" and "initial value."  She uses an example to explain what this means.  This was used to introduce her activity. 

Here the teacher creates a situation where students find their own data and create a exponential decay model.  Students look at patterns in a hands-on experiment and make conclusions about what they expect to happen.  The teacher closes the lesson by using group data to model an exponential decay function.