# Number - September 2007, Stage 2&3

## Problems

### Venn Diagrams

##### Stage: 1 and 2 Challenge Level:

Use the interactivities to complete these Venn diagrams.

### Mobile Numbers

##### Stage: 1 and 2 Challenge Level:

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

### More Carroll Diagrams

##### Stage: 2 Challenge Level:

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

### Various Venns

##### Stage: 2 Challenge Level:

Use the interactivities to complete these Venn diagrams.

### Alien Counting

##### Stage: 2 Challenge Level:

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

### Factors and Multiples Puzzle

##### Stage: 3 Challenge Level:

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

### The Cantor Set

##### Stage: 3 Challenge Level:

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?

### How Long Is the Cantor Set?

##### Stage: 3 Challenge Level:

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?