Because they launched into steps 2 and 3 with abundant understanding, those steps typically took experts less time. Experts use each successful problem solving experience as a chance to hone their skills and knowledge.If you’d like to become an expert problem solver, the last step is vital. What extensions or related problems could be solved in a similar way? The non-experts rushed into a plan, carried it out and quit.
The vertex can “slide” along this parallel without changing the height of the triangle, so all triangles created this way have the same area. This led to the idea of “slide the base” of a trapezoid.
If you create a trapezoid with bases of length 1 and 4 (and height 1), you can slide either base along its parallel line without changing the area.
You find reasonably quickly that area calculations just mean counting up squares and half squares.
You run out of easy figures pretty quickly, maybe after 5 or 6. One problem is that many of the figures are congruent – they are exact copies of each other after a rotation or reflection (or both).
Expert problem solvers spent a large amount of time not just checking their work but reflecting. They had no idea if their solution was correct and typically gave up if their plan failed. Expert problem solvers often find during step 3 that the plan they devised isn’t working.
However, they realize that they are back to step 1 and now understand more about the problem.
The you create a triangle with area 2 (base 2, height 1) and begin adding triangles to its base. Step 4: Refelction When I did this problem, I realized several things.
First, the “slide the vertex” triangle activity is important. Draw a line through the third vertex that’s parallel to the base.
For example, they might simplify the problem purposefully and work on the easier problem for a few minutes.
They might draw diagrams or create an organized list.