A Structured Class Lesson: To find Pick's
Theorem
The teacher gives out pinboards (or squared paper
will do) so that each group of children has access to a board or
boards, and some elastic bands.
Teacher: Make me a shape with area 4 squares.
I'm going to draw mine on the squared board.
Now I'll give you about five minutes to find as
many more shapes with area 4 as you can … Keep a record, though,
of E and I and we'll collect together our results.
Activity!! Time to chat to a few individuals who
might need a bit of help/encouragement.
Back at the front … and we fill in a table
with two columns already completed:
Teacher: Has anybody found a shape with 0 pins
inside? or Can anybody fill in the values of E for these I's?
The table is quickly filled in … any gaps
being searched for … comparison of results to lose any inconsistencies.
A discussion can develop here about what possibilities
are available for I and E.
Sometimes the children will automatically look
for patterns in the table … but if nothing is forth coming
…
Teacher: Anybody notice anything about these numbers?
Students: A's always 4; The E's go up in 2's;
I's in one's!; You always get 10 if you add double the I column
to the E column …
Teacher writes … E + 2I = 10.
Now over to them … See if you can find rules
for A = 5, 6 … etc … and save your results to the end
of the lesson …
More activity … more time to talk and help
… If people are interested in the number of possible I's and
E's at this stage … fine … it is an interesting problem.
It's now about 10 minutes before the end of the lesson…
See if you can find rules for:
a) triangular pinboards
b) hexagonal pinboards etc …
or … to practise linking 3 variables
in a different situation Faces, Vertices and Edges or Nodes, Arcs
and Regions to generate Euler's Law: V + F = E + 2 or N + R = A
+ 2.
