What Is a Logarithm?

In this activity (download), students build an intuitive understanding of what a logarithmic expression is. They also "discover," or empirically observe, how the basic laws of logarithms work. There's a lot of filling in the blanks here. Like many of my activities, the goal here is to start a conversation, so that the students can contribute just as much to the introduction of a new topic as the teacher.

Where Should My $1500 Go?

Topics: Exponential Functions, Compound Interest, and e.

This lesson (download) takes a student through the process of deciding at which bank to deposit $1500 in a savings account. The banks and their terms for interest are entirely fanciful, but the main purpose of the lesson is to guide the student to this understanding: that compounding interest at shorter and shorter intervals always increases the benefit, but by an amount that becomes less and less; in other words, the benefit approaches a limit as "n" goes to infinity. The extension activity (download) shows the student that for a principal of 1 and an interest of 100%, the limit of the formula for compound interest (as "n" goes to infinity) is equal to e.