I just finished a quick review of this. It was so helpful for understanding the concept or surface area.
Reply
Mark Betnel
3/18/2014 01:00:50 am
I'm not familiar with the middle school context, but in high school and college math and physics, many of the students will have no idea how to compute volume or surface area, and most will have no physical intuition about what it means, even if they have memorized L*W*H or L*W -- which especially shows up if you they need to find areas or volume of non-rectangular objects.
So my fix is to have them draw rectangles and rectangular prisms with small squares or cubes along the sides, so they can manually count up the number of components, then help them see that multiplying is a shortcut, and then help them start to visualize complex objects as built up from layers of simpler ones.
On a deeper level, decomposing a complex object (or task) into simple components is a key problem solving strategy in any field. For example, any conceptual understanding of calculus really depends on it.