# Open-ended, release from curriculum - July 2011, All Stages

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

## Problems

### Numbers as Shapes

##### Age 5 to 7 Challenge Level:

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

### Inside Triangles

##### Age 5 to 7 Challenge Level:

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

### Tangram Tangle

##### Age 5 to 7 Challenge Level:

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

### Junior Frogs

##### Age 5 to 11 Challenge Level:

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

### Four Go

##### Age 7 to 11 Challenge Level:

This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?

### Sponge Sections

##### Age 7 to 11 Challenge Level:

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

### Escape from the Castle

##### Age 7 to 11 Challenge Level:

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

### 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?

### Weekly Challenge 44: Prime Counter

##### Age 16 to 18 Challenge Level:

A weekly challenge concerning prime numbers.

### Function Pyramids

##### Age 16 to 18 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

##### Age 16 to 18 Challenge Level:

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

### Mechanical Mindgames

##### Age 16 to 18 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

##### Age 16 to 18 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?

##### Age 16 to 18 Challenge Level:

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

### Phase Space

##### Age 16 to 18 Challenge Level:

Explore the issues surrounding the concept of Phase Space.