I had expected Will to have some trouble with this task, which I simply handed to her, or to at least have to do some experimenting while she worked out the most efficient way to complete it, but as soon as I gave her the graph paper with the large, irregular polygons that I'd drawn on each page, and told her that she needed to find the total area of each shape, she was off! Within minutes she handed these back to me, and here's what I saw:
What Willow immediately noticed is that to find the area of these irregular polygons, you must first decompose them into rectangles. Find the area of each rectangle by multiplying the length by the width, then add all the areas together to find the total area.
Since Will had been fussing about not seeing the point of the order of operations, I also had her write down the final equation that one would use to solve this problem. She could then see that 1) you couldn't get the correct answer without using the order of operations, and 2) there is no more efficient way to record this equation without relying on the order of operations. Mwa-ha-ha!
She still hates the order of operations, mind you. But now she uses it!