### 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?

### Sixational

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Prove that all terms of the sequence are divisible by 6.

### Squaresearch

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

# Seven Squares

##### Stage: 3 and 4 Challenge Level:

How did Phoebe group the matchsticks that she drew?
How did the others, Alice and Luke, group their matchsticks?

In the follow-up activities draw them out for yourself and notice how YOUR drawings develop. Always begin with simple cases and try to PREDICT what will happen.

Look for patterns.
How can you describe the lines? Horizontal? Vertical?
Try to understand why the patterns develop in the ways that they do.