### Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

### Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

### Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

# Home Time

## Home Time

Alice, Beccy, Craig, David, Ellie and Francis all go to the same school. Usually they catch the bus home, but today they are staying later for hockey club. Alice lives the closest to school, so they walk round there and her mum gives the others a lift home.

The map below shows how the children's houses are connected by road (it is not to scale!). To make things easier, just the first letter of each name has been used.

Alice's mum sets off from their house (A) with all the children. She needs to go to each house just once and then back home again. How many different routes are there?

In the end, she took a route like this:

The entire journey took $1\frac{1}{2}$ hours and she was travelling at an average speed of $30$ miles per hour.

The total distance from A to D is the same as the total distance from E to A, which is $19$ miles.

It took twice as long to get from B to D as it did from D to E.

A is twice as far from F as it is from B.

The distance between A and B is a third of the distance between C and E.

Using this information can you find out how long each road is on the route taken by Alice's mum?

### Why do this problem?

This problem requires a systematic approach and a good method of recording. The second part of the problem challenges children to calculate using distance and time.

### Key questions

How do you know you've got all the routes?
How will you record the routes?
Have you written the distances on the picture?
What is the calculation you need to do?
Knowing how long the journey took and the speed she travelled, how can you work out the total distance they went?
Using this and the second piece of information, how far is it between D and E?

### Possible extension

Learners could make up a simple map of their own and ask a friend some questions relating to it.

### Possible support

Having a copy (or copies) of the map will help children have a go at this problem.