I, like most others, always attempt to use students’ existing knowledge base on which to build and connect new concepts (or new perspectives on old concepts); simple motion problems are one such example. The concept in this entry is integration and it provides a new and very rich perspective on an “old” concept already familiar to students.

The following excerpt is taken from reflections of my 1st two weeks in calculus.

**Question:** What can we do when “**dv=(a)dt**” shows up in this way?

**Answer:** We can integrate.

**Question:** What does integration give us?

**Answer:** The area between the function and the x-axis.

**Question:** What does our function represent?

**Answer:** Acceleration.

**Question:** What does the area in question represent?

**Answer:** Velocity.

**Question:** Have you ever seen this before and, if so, where?

**Answer:** Yes, in Physics class.

As an extra activity, students could sketch slope fields for **dv/dt** and **ds/dt** to become more familiar with those. In addition, students would also benefit from drawing comparisons between integrating functions in 2-dimensions above (focus on area) and its 3-dimensional counterpart.

Thanks for reading.