Why do this problem?
This problem allows practice of conversions in a context which
might be more difficult than that usually available to the
students, made accessible by the card sorting process.
This problem works well as a group or individual activity.
Suggest the students try to work out which cards could appear at
each step, even if they are initially unsure of the entire
calculation. There are various ways that they can do this: either
directly by working out the conversion or by logically eliminating
cards which do not directly follow from the previous one. At each
stage, encourage clear explanation of reasoning.
Once the calculation is completed, read through it together
and be sure that it make sense.
- Are there any cards which definitely do not follow directly
from the first card?
- What physical quantities is the question referring to? Are you
unsure as to the meaning of any of the symbols?
You might naturally try
Mixed up Mixture
Can the students find the solution by trial and error (by
noting the direction of the ball, they could quickly work out the
final ordering)? Then, they can try to understand the final