In this activity, students make connections between equations, tables, graphs, and verbal descriptions. They are given equations representing bank accounts and use that information to create tables, describe the situations, and use technology to graph the equations. If students also use technology to create the tables, they are using appropriate tools strategically (MP5).

The goal of this discussion is to focus on the connection between the equations, descriptions and graphs. Here are some questions for discussion:

• “What do all of the functions have in common?” (The vertical intercept is 500, and each bank account starts with $500.)
• “How does the money change each week? How do we see this change in the graph?"
• “How are and the same and different?” (They are the same because they are each linear, and each start with $500 and change by $40 per week. They are different because increases and decreases (or the rate of change is positive versus negative).)
• “How are and the same and different?” (They are the same because they are each exponential, and each start with $500. They are different because increases and decreases (or the growth factor is greater than 1 versus less than 1).)

Students continue to work with the functions from the previous activity but strategically modify them so that they represent new situations. Then students select a graph that represents the new situation and use technology to see if their new equation is correct (by seeing whether its graph matches the one they chose). Students reason abstractly and quantitatively (MP2) when making decisions about how to adjust equations to represent altered situations.

The goal of this discussion is to compare strategies and identify key features that connect different representations. Here are some questions for discussion:

• “What were some strategies you used for building new functions to represent new situations?” (I used a function that was similar to the situation I wanted to represent and then made the small changes necessary to represent the new situation.)
• “In exponential functions, what are the differences between an equation representing a situation that grows and an equation representing a situation that shrinks?” (An exponential function that grows has a growth factor that is greater than 1. One that shrinks has a growth factor between 0 and 1.)
• “Where can you see each rate of change and growth factor on the graph?” (The rate of change can be seen in the slope of the graph or by subtracting a -value from the next -value. The growth factor can be seen by dividing a -value by the previous -value.)