Monday, December 7, 2009
For Figures 1 and 2, the following is given:
AD + AC = BD + BC
Perimeter of triangle = 36
AC = 15
Show that the length of AD = 3.
In other words, demonstrate that the length of AD is independent of sides AB and BC.
Instead of imposing or suggesting my way of using this question to build an investigation, how would you do it?
If you're new to this blog, I have published dozens of examples of investigations which are intended to develop process, conceptual understanding, generalization and a different view of what mathematics is for our students. An investigation allows students to explore particular cases before attempting to generalize and abstract. Some might call this scaffolding. I see it as creating an experimental environment in the classroom, encouraging our students to become mathematical researchers! I know every argument against this approach but, remember, I'm suggesting that this type of activity only be used perhaps once a month...
The question above can be given as is to some groups of students but may not be appropriate in its present form for many others. The question can be reworded or changed completely.
What would you do?