Basically students measure the diameter of the orange, and draw four circles with the same diameter. Students then peel and flatten the orange peel and try to fit together the peel into as many circles as needed. Students will observe that the surface area of the orange is equal to the same amount as the area of the four circles that have the same diameter. This will help students to see how the two formulas are connected to each other! Plus they have the chance to get kinesthetic during class.
You can find this activity on the Math Solutions Webpage and searching for the activity "Orange You Glad...?" in the search bar. Happy teaching!
I agree that the ability to present math visually is very helpful for students and improves learning. I think that if math concepts can be visualized they are more easily understood with better retention. The importance of visuals might also be reflected in the discrepancy that students seem to find data management and measurement easier than number sense. A possible reason might be that data management uses charts, tables, graphs, circles and diagrams. Teachers traditionally tend to use more visual manipulatives when explaining data and probability, as we've seen with drawing red and blue marbles from a bag? It may be that in teaching number sense there is traditionally less tendency to use visuals (although they certainly exist), and more reliance on showing many examples usually on the board or overhead.
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