# Random Spectacular! - July 2012, All Stages

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

### Curve Spotting

##### Stage: 1 Challenge Level:

Can you spot circles, spirals and other types of curves in these photos?

### Doing and Undoing

##### Stage: 1 Challenge Level:

An investigation looking at doing and undoing mathematical operations focusing on doubling, halving, adding and subtracting.

### Ordering Cards

##### Stage: 1 and 2 Challenge Level:

This problem is designed to help children to learn, and to use, the two and three times tables.

### Cuisenaire Spirals

##### Stage: 2 Challenge Level:

Can you make arrange Cuisenaire rods so that they make a 'spiral' with right angles at the corners?

### Exploring Number Patterns You Make

##### Stage: 2 Challenge Level:

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

### Making Spirals

##### Stage: 2 Challenge Level:

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

### Constructing Triangles

##### Stage: 3 Challenge Level:

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

### Marbles in a Box

##### Stage: 3 Challenge Level:

How many winning lines can you make in a three-dimensional version of noughts and crosses?

### Warmsnug Double Glazing

##### Stage: 3 Challenge Level:

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

### 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?

### 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.