# Random Spectacular! - July 2012, Stage 4&5

This month we've chosen some old favourites as well as some new ideas. They're just right to round off the school year, and can be used in the classroom or at home during the holidays.

## Problems

### Witch's Hat

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

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

### Marbles in a Box

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

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

### Making Moiré Patterns

##### Stage: 3, 4 and 5 Challenge Level:

Moiré patterns are intriguing interference patterns. Create your own beautiful examples using LOGO!

### Kite in a Square

##### Stage: 4 Challenge Level:

Can you make sense of the three methods to work out the area of the kite in the square?

### Simply Graphs

##### Stage: 5 Challenge Level:

Look for the common features in these graphs. Which graphs belong together?

### Hyperbolic Thinking

##### Stage: 5 Challenge Level:

Explore the properties of these two fascinating functions using trigonometry as a guide.

### Fundamental Particles Collection

##### Stage: 5 Challenge Level:

A collection of problems related to the mathematics of fundamental physics.

### Interpolating Polynomials

##### Stage: 5 Challenge Level:

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.