Investigating Slope
By Eduardo Narvaez
11th Grade Advanced Algebra Teacher
This week, juniors at Roberto Clemente Community Academy focused on finding and interpreting the change of rate in their Advanced Algebra & Trigonometry class. Throughout their math education, many of them have studied the change of rate of different scenarios (as interpreted by slope) but not many have had a hands on experiment with it outside of their science class.
Students where shown 3 different sized candles that were burning, and were asked to make predictions of how long each one would take to melt. Many students took guesses based on experience, some asked about the materials the candles were made of, and others jumped to grab a ruler and check a timer to see at what pace they were burning. This all led to interesting discussions and the students defending their choice and arguing against others.
Soon, students began asking for graph paper and were plotting their measurements. This led to a discussion of the rates of change and slope. While some students observe slope as just the measure of rise over run, our Clemente students were able to dissect it as a measurement of the change of something over time. They investigated how miscalculating slope can impact the integrity of roads being built and can mean the difference between a fun ride down a slide or an uncomfortably painful one.
Students were also asked to match descriptions of activities to different graphs that displayed different rates of changes and slope, such as the rate of which a sprinter might run a race compared to a long-distance runner.
In this introductory lesson to the study of linear and non-linear systems, slope is going to be at the heart of the subject. Now that students understand what the change of rate is and how it can be useful for making predictions, they are ready to continue their investigations as IB inquirers!