What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
One Out One Under
Stage: 4 Challenge Level:
For the first part, try starting with only four cards and compare
the resulting final card with the final card when you start with
Notice anything ?
What might be a good number of cards to try next ?
When you are ready to look for a general result, be systematic and
list your results, for example : seven cards and the final card is
6, eight cards and the final card is . . . , nine cards . . . .,
ten cards . . .
Remember to collect results in the other direction away
from seven cards. Six cards and the final card was . .
If you've been careful you will see a clear pattern.
First describe the pattern. Then try to account for it.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.