Why do this problem?
The White Box interactivity
models the scientific process of deducing the structure of atoms and molecules. It is a motivating and intriguing context in which learners can make and test hypotheses.
Set up the White Box so that it is relatively small to start with and perhaps just one triangle is filled. Explain how it works, giving learners some background about the process they will be modelling. This first set-up could be a challenge for the whole group working together so that everyone gets a feel for the way the interactivity works.
Ideally, then, learners will work in pairs using the interactivity at a computer. You might give them some time to explore for themselves and then you could pose one or more of the following questions (most of which refer to multi-atom configurations):
- if an incoming ray A(in) produces B(out), does B(in) produce A(out)?
- if an input ray A emerges at B can you be certain of any atomic position(s)? If not, how many ways can you find of producing that effect?
- if an input ray appears to go straight through what other explanations might be possible?
- is it possible to have an arrangement which has two possible exit points for an input ray?
- is it possible for a ray to be affected by the same atom more than once? If so, what is the largest number of deflections you can generate?
- can a ray ever get trapped inside so that it never emerges at all?
- are there any arrangements of atoms where it is impossible to be certain of the arrangement?