### Late Again

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

### Simple Train Journeys

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

### Train Routes

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

# How Many Pieces This Time?

## How Many Pieces This Time?

You might like to try How Many Pieces? before you have a look at this problem.

You can see how many loops of string were used to make these string patterns because the strings are different colours.

In the next pictures can you work out how many loops were used?

Can you describe how you know?

You might like to print off this sheet of the pictures if you would like to work on paper.

### Why do this problem?

This problem is a more challenging version of How Many Pieces? and can be approached in similar ways. If you tried How Many Pieces? visually with your class, you may like to introduce this problem in a more practical way and vice versa. The longer length of the pieces of string in this version make it slightly harder to solve.

Children may enjoy making up their own string patterns for a partner to work out the number of pieces used. It is quite a challenge to draw the patterns convincingly.

You might like to read the article Celtic Knotwork Patterns and share some of the ideas with your class, particularly the tips for drawing knots!

### Key questions

Can you can follow a piece of string just by looking?
Why don't you use a different coloured pencil to trace over each new loop of string?
Can you explain how you decided on the number of loops there are?

### Possible extension

Learners who found this easy might enjoy this more challenging problem.

### Possible support

Suggest staying with the simpler problem How Many Pieces?