This is an exercise I give my IB/Precalculus students. It is based on the classic mathematics question, "What is the maximum number of slices of pizza may be formed by a series of random cuts?"
It holds students hands enough that they generally see the formula is not as simple as 2n, and it also guides them through making a difference table to determine the equation as a quadratic.
I use this activity within cooperative groups, and I circulate to make sure they are getting the purpose of the questions.
The file includes spiral review problems.
This worksheet is intended to be written on directly.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.