Before this, ensure your students understand at least similar triangles and have seen some related rates questions before.
1) Bring students to a chemistry lab with different beakers, or bring different beakers into your class. **You will need a water tap**
2) Divide the students into groups of 3 or 4 and provide each group with one of each of the following beakers, shown in the picture below.
Hypothesis: Will the height change at a constant rate or will it change throughout, if we were fill these beakers up with water? Explain. If the rate of change of the height of the water changes, when will the rate be the largest, and when will it be lowest.
Procedure: Turn the tap on and record the time it takes to fill the beaker up to the last marking on the glass, using a constant stream of water. Record this three times and average your times. What does this represent?
Fill up both beakers, using this stream of water. Was your hypotheis correct? If not, what did you notice?
Calculations: If you were to fill up the cylindrical beaker with the stream of water how fast would the height change when it was half full? When it was entirely full?
If you were to fill up the conical beaker with the stream of water how fast would the height change when it was half full? When it was entirely full?
I have used this before with my students and watched how they had to determine not only WHAT to measure but HOW to measure it. Feel free to use, change, tweak as you see fit.
Here is video one student made:
**SOON TO BE UPDATED**
And his Prezi: