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

problem icon

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?

problem icon

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?

problem icon

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?

problem icon

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?

problem icon

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?

problem icon

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.

problem icon

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?

problem icon

Sieve of Eratosthenes

Age 11 to 14 Challenge Level:

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

problem icon

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?

problem icon

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?

problem icon

More Number Pyramids

Age 11 to 14 Challenge Level:

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

problem icon

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?

problem icon

Filling the Gaps

Age 14 to 16 Challenge Level:

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

problem icon

The Best Square

Age 14 to 18 Challenge Level:

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

problem icon

Weekly Challenge 44: Prime Counter

Age 16 to 18 Challenge Level:

A weekly challenge concerning prime numbers.

problem icon

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?

problem icon

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.

problem icon

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.

problem icon

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?

problem icon

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?

problem icon

Phase Space

Age 16 to 18 Challenge Level:

Explore the issues surrounding the concept of Phase Space.