February 2003, Stage 3&4

Problems

problem icon

Playground Snapshot

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

problem icon

Pretty Prism Perspective

Stage: 3 Challenge Level: Challenge Level:1

Try making 3D patterns in two dimensions with LOGO

problem icon

Icosian Game

Stage: 3 Challenge Level: Challenge Level:1

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

problem icon

All in the Mind

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

problem icon

Cutting a Cube

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

problem icon

Cubist Cuts

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?

problem icon

Excel Technique: LOOKUP Functions

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Learn how to use lookup functions to create exciting interactive Excel spreadsheets.

problem icon

Excel Interactive Resource: Equivalent Fraction Bars

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

problem icon

Excel Investigation: Happy Numbers

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.

problem icon

Marbles in a Box

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

problem icon

In a Spin

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

problem icon

Plum Tree

Stage: 4 and 5 Challenge Level: Challenge Level:1

Label this plum tree graph to make it totally magic!

problem icon

Magic Caterpillars

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.