### Ladder and Cube

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?

### Doesn't Add Up

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

### From All Corners

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.

# Steady Free Fall

##### Stage: 4 Challenge Level:

The main problem-solving tasks for the student here are :
• To get a sense for motion under gravity.
• To make sense of the graph and to grasp the characteristic "vertical velocity"
• To identify and accurately describe the properties of the rail shape and the effect these have on the motion of the bead.
• And then to bring together interpretation of the graph and appreciation of rail shape to produce constant vertical velocity.
We hope that this challenge will provide a rich opportunity for students to develop their reasoning and communication skills as they work to produce a good commentary on features and effects.