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TJ: CA II.1 Average v. Instantaneous Speed

This activity went well in class. I found that some students could very easily move to the limit definition of both instantaneous speed and instantaneous rate of change whereas other students struggled with that. It might be helpful to get the students to write out a sequence of the average rates of change - both in their purely numerical form and then in their more symbolic form where it is f(2.8)-f(2.7)/(2.8-2.7) and then f(2.75)-f(2.7)/(2.75-2.7) to see what is happening and then move to limit form. I'm not sure whether that is best done as a whole class or whether students could do this by themselves? I found that students moved relatively easily from the speed situation to the glucose scenario. They struggle again in the next activity though when we change representations.