This year was the first year I used the Crow and Pitcher simulation activity to introduce Linear Functions. And, LOVED IT! I have used it in Math 8 and Algebra 1. I have tinkered with it and available equipment to finally get it right (for my conditions anyway!). Its a hands on activity showing how rate of change is related to slope and slope-intercept form (y = mx +b) of an equation based around Aesop's fable of the Crow and Pitcher.
Firstly, students watched the fable Thirsty Crow clip as a hook, before rereading the text version (slide below showing what equipment we will be using to simulate the situation.
Students used the sheets and water filed beakers (or straight drinking glasses - my version of "take one!") and marbles to introduce investigate. We came together as a class to compare results and discuss conclusions. It was a nice was to introduce y-intercept in context, rate of change and review relevant domain and range in a limiting situation.
One tip I picked up form the Math Camp at Columbia, is whenever you have an activity its important to give students some responsibility to reporting out - otherwise whats the point or how can their reflect on their learning? In this case a poster showing the situation in multiple representations was a useful way to reflect on the activity.