# Analysing Alternative Approaches - November 2011, Stage 3&4

This month, we invite you to consider a variety of ways of approaching the tasks, and encourage you to reflect on the merits of different routes to solutions.

## Problems

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

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

### Going Round in Circles

##### Stage: 3 Challenge Level:

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

### Odds, Evens and More Evens

##### Stage: 3 Challenge Level:

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

### What's it Worth?

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

There are lots of different methods to find out what the shapes are worth - how many can you find?

### Steel Cables

##### Stage: 4 Challenge Level:

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

### LCM Sudoku

##### Stage: 4 Challenge Level:

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

### Calculating with Cosines

##### Stage: 4 and 5 Challenge Level:

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

### A Long Time at the Till

##### Stage: 4 and 5 Challenge Level:

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

### A Rational Search

##### Stage: 4 and 5 Challenge Level:

Investigate constructible images which contain rational areas.