Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP
have equal areas. Prove X and Y divide the sides of PQRS in the
Can you make a tetrahedron whose faces all have the same perimeter?
A 1 metre cube has one face on the ground and one face against a
wall. A 4 metre ladder leans against the wall and just touches the
cube. How high is the top of the ladder above the ground?
This problem creates a context where students are challenged to
pick out detail from a large block of text, represent that data and
the relationships between the data as a set of equations, which
need solving and interpreting back into the practical context.
This kind of work can be hard and not always rewarding for
individuals not motivated just because it's a puzzle. It may be
that the problem achieves most to develop a problem solving culture
in the classroom if it is approached with plenty of discussion
between students and in the spirit of a group effort. Less
motivated students can still verify and critique the proposals of
Pair students to extract the relevant data and relationships
from the text. Check orally that all the group has all the needed
data and debate items that are not universally agreed upon.
Ask pairs to express these relationships as equations, again
pooling all and discussing elements of contention.
Set students to work looking for a solution, which is then
written up poster-size for display around the room.
Students peruse each others results and presentation of method,
before a whole group discussion of the routes followed and the
comparative efficiency of the methods deployed. Finally, ask
different students to explain how the algebraic results work as a
meaningful solution to the practical problem context.