### 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.

# Building with Longer Rods

## Building with Longer Rods

This activity has been particularly created for the most able.

When you have completed Building with Rods then go further with this challenge of using rods that are $3$ units long.

Same rules as before - so just to remind you; here are two solutions that fit the rule.

Here are two that don't fit the rule as the small cubes have to be lined up squarely, with no overlapping.

The challenge is to find all the possible ways of stacking the rods, keeping the blue rod on the bottom, the red rod in the middle and the green rod on top.

What do you think will happen if you try the same activity with rods that are $4$ long?

What do you think will happen if the rods are $5$ long?

### Why do this problem?

This activity is specially designed for the highest-attaining pupils that you ever come across. It acts as a further extension to Building with Rods and Three Sets of Cubes, Two Surfaces. It's an activity that is intended to give opportunities for pupils to explore a spatrial situation using their intuition and flair.  It also provides them with an opportunity to create a system for solving such problems.

### Possible approach

As this is designed for the highest attaining, it might be presented as on the website or in a one-to-one situation, encouraging discussion between adult and pupil. The pupils may need access to a computer program for drawing solutions.

### Key questions

Tell me about what you have found.
Can you describe the ways that you arrived at these shape arrangements?
How did you construct these on the computer?