### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Tea Cups

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

### Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

# Tiles in the Garden

## Tiles in the Garden

This is a view, from above, of my friend's garden. You see a black path and a square patch in the middle.

He wants to tile the square in the middle with tiles going straight across and down. He would also like to have the corner of a tile at each of the corners of the square.

Then it'll look like this;

So, we are off to help him. He has a good tile cutter to get the "part-tiles", so he'll be able to cut a tile into two or more pieces and use them all. But I said that we would fetch the tiles for him. How many do we need for the example above?

How many would we need for these two other garden square shapes that someone might like to have? How are you working it out?

### Why do this problem?

This activity is designed to create a challenge that pupils will not have been taught or leant how to do straight away. they therefore have to use their individual problem solving skills. When different approaches have been used by different groups or individuals then the discussion about different appraoches can take place.

### Possible approach

Explain that you're not expecting them to necessarily know straight away how to do it. Encourage them to devise a way, through problem solving to find the answers. The pupils may be ecouraged to validate their suggestions. Then a discussion can be had around the class as to the advantages and disadvantages of the different approaches.

### Key questions

Tell me about what you are doing?