# Open-ended, release from curriculum - July 2011, Stage 4&5

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

## Problems

### More Number Pyramids

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

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

### Generating Triples

##### Stage: 4 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

##### Stage: 4 Challenge Level:

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

### The Best Square

##### Stage: 4 and 5 Challenge Level:

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

### Weekly Challenge 44: Prime Counter

##### Stage: 5 Challenge Level:

A weekly challenge concerning prime numbers.

### Function Pyramids

##### Stage: 5 Challenge Level:

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

### Weekly Challenge 41: Happy Birthday

##### Stage: 5 Challenge Level:

A weekly challenge concerning the interpretation of an algorithm to determine the day on which you were born.

### Mechanical Mindgames

##### Stage: 5 Challenge Level:

A selection of intriguing questions to consider on mechanics, particularly surrounding the ideas concerning impulse and momentum.

### Weekly Challenge 43: A Close Match

##### Stage: 5 Challenge Level:

Can you massage the parameters of these curves to make them match as closely as possible?

### Weekly Challenge 42: What's My Equation?

##### Stage: 5 Challenge Level:

Can you find the differential equations giving rise to these famous solutions?

### Phase Space

##### Stage: 5 Challenge Level:

Explore the issues surrounding the concept of Phase Space.