The Paper Box Problem is a 3-dimensional extension of the Chicken/Fence
Problem.
A rectangular piece of cardboard (40 cm x 50 cm) is used
to make a box without the lid in the following way: squares with the side
x are cut out of each corner. The rest is folded up and stuck together to
form a box. Find the value of x to get the maximal volume of the box.
The technology enables different approaches for the students. Through different
approaches in solving the same problem, and different visualizations,
the students can develop different concept images of the same concept and
build connection between them.
Detailed explanation of the aims ...
Different approaches - different solutions?
- Why is the graph from section 3 different from the graph from section
4?
- Are the results in section 2, 3 and 4 equal? If not, which are the
most accurate? How to improve the accuracy?
The students have to be encouraged to discuss the different approaches and
the solutions with the colleagues.