Today my 8th graders were given a task.
They were asked to pick a perimeter measurement out of a hat (on index cards cut in half).
They had to draw out 3-4 rectangles with the given perimeter (for example 18). They then had to find the area of each of the rectangles they had drawn. Given this information they had just created they were asked the following question:
How do you find the dimensions (side lengths) that will give you a rectangle with the largest area? Explain....
Once I've demonstrated and answered questions I am mute. I will only point out that there are other members of their group as well as the information I got when I did the original demonstration on the board.
Overwhelmingly students who don't confuse the terms Perimeter and Area are doing well. I purposely avoided any perimeter with 4 as a factor as I didn't want the square result to be so obvious. Of approximately 20, 3-student groups, less than a quarter of them are figuring out that result. most of the remainder are noticing that if the numbers are consecutive that the result is the largest area.
Its a start....