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?
Straight lines are drawn from each corner of a square to the mid
points of the opposite sides. Express the area of the octagon that
is formed at the centre as a fraction of the area of the square.
Two cyclists, practising on a track, pass each other at the starting line and go at constant speeds... Can you find lap times that are such that the cyclists will meet exactly half way round the track.
Once someone says out loud where to look for the discrepancy the problem is over.
To avoid this, encourage students who are ready to develop a convincing argument to share and then to move on to the challenge of creating similar problem. When ready move to a whole group discussion emphsising the need for convincing arguments. The extesnion activity also gives scope to those who see what is happening quickly.
Try the problems Muggles Magic and Lying and Cheating.