# Open-ended, release from curriculum - July 2011, Stage 3&4

This month we have chosen a selection of activities, both for use in the classroom and for working on during the holidays.

## Problems

### Sieve of Eratosthenes

##### Age 11 to 14 Challenge Level:

Follow this recipe for sieving numbers and see what interesting patterns emerge.

### Can They Be Equal?

##### Age 11 to 14 Challenge Level:

Can you find rectangles where the value of the area is the same as the value of the perimeter?

### Number Pyramids

##### Age 11 to 14 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

### More Number Pyramids

##### Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

### Generating Triples

##### Age 14 to 16 Challenge Level:

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

### Filling the Gaps

##### Age 14 to 16 Challenge Level:

Which numbers can we write as a sum of square numbers?

### The Best Square

##### Age 14 to 18 Challenge Level:

How would you judge a competition to draw a freehand square?