### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

### Sweets in a Box

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

# Sea Level

## Sea Level

Well, here's a pretty scene, the underwater creatures and the tall lighthouse joined by a seagull and a cloud in the sky.

There are black markings all the way up the lighthouse and on the support for the lighthouse going down to the sea bed. These markings are $1$ metre apart. I have left the numbering for you to do.

The sea level is of course "$0$" and then positive numbers going up and negative numbers going down to the sea bed.

If we think about the mouths of the creatures then we can see how much deeper they are from each other, or what distance they are apart.

For example the (mouth of) the fierce looking blue and white fish near the middle is $1$ metre deeper than the (mouth of) the golden yellow fish.

1. What number should be where the light shines from the lighthouse?
2. What number should be where the (head of the) seagull is?
3. What number should be where the (mouth of the) red crab, near the bottom, is?
4. How far is it down from the (head of the) seagull to the (mouth of the) yellow fish?
5. How far is it from the turtle, near the surface of the water, to the crab?
6. There's a little brown sea-horse to the right of the lighthouse support. How far from the surface is it?
7. How high above the sea level is the seagull flying?
8. How far is the seagull from the sea-horse?
9. How high is the pointed end of the cloud?

It would be interesting to know how you arrived at your answers.

How about thinking up some questions of your own? Please do send them in - we would like to see your creative juices at work!

### Why do this problem?

This problem is a good way to increase familiarity with negative numbers on a number line. In answering the questions, children begin to calculate with negative numbers in a context that will give them confidence rather one which they perceive as difficult.

### Possible approach

It would be a good idea to print out the picture so that children can put on the numbers and more easily use a ruler to see which objects are at a certain level. To make the link with calculation more explicit, you could have a go at writing number sentences for some of the questions as a class, then challenge the children to complete number sentences for the other questions. Pupils can then go on to invent questions of their own and, in particular, they could find alternative ways of asking the same question. For example:
What depth is the octopus?
What number will the octopus be at?
How far from the surface is the octopus?

### Key questions

Tell me about the depth of these fish.
How do you know? How are you working this out?

### Possible extension

You could invite children to make up as many questions as they can which have, for example, the answer $3$m. This allows them to be as creative as they like, and is a good way to assess their understanding.

### Possible support

Some children will benefit from having a go at the Swimming Pool problem before this one.