A circle touches the lines OA, OB and AB where OA and OB are
perpendicular. Show that the diameter of the circle is equal to the
perimeter of the triangle
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?
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
Ask the group to draw a variety of squares using paper with
dots, to calculate the area of each and to keep a record.
Ask the group to organise their record in a way they think
useful, and invite conjecture about the situation.
Ask the group to look at the way they decided to organise their
results and to decide what additional results might usefully be
Ask members of the group to share their thoughts.
Once the proposed additional work has been done again invite
conjecture about the situation: any comment, or things to try.
Suggest to the students that they look at the remainder when the
area values are divided by 4, leave some thinking time before again