# February 2003, Stage 2&3

## Problems

##### Stage: 2 Challenge Level:

If you had 36 cubes, what different cuboids could you make?

### Three Cubed

##### Stage: 2 Challenge Level:

Can you make a 3x3 cube with these shapes made from small cubes?

### Cereal Packets

##### Stage: 2 Challenge Level:

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

### Construct-o-straws

##### Stage: 2 Challenge Level:

Make a cube out of straws and have a go at this practical challenge.

### Playground Snapshot

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

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?

### Cubes Within Cubes

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

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

### Pretty Prism Perspective

##### Stage: 3 Challenge Level:

Try making 3D patterns in two dimensions with LOGO

### Icosian Game

##### Stage: 3 Challenge Level:

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.

### Marbles in a Box

##### Stage: 3 Challenge Level:

How many winning lines can you make in a three-dimensional version of noughts and crosses?

### All in the Mind

##### Stage: 3 Challenge Level:

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. . . .

### Cutting a Cube

##### Stage: 3 Challenge Level:

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?

### Cubist Cuts

##### Stage: 3 Challenge Level:

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?

### Cubic Conundrum

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

Which of the following cubes can be made from these nets?

### Excel Technique: LOOKUP Functions

##### Stage: 3 and 4 Challenge Level:

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

### Excel Interactive Resource: Equivalent Fraction Bars

##### Stage: 3 and 4 Challenge Level:

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

### Excel Investigation: Happy Numbers

##### Stage: 3 and 4 Challenge Level:

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.