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

Stage: 1 Challenge Level:

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

Inside Triangles

Stage: 1 Challenge Level:

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

Tangram Tangle

Stage: 1 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

Stage: 1 and 2 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

Stage: 2 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

Stage: 2 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

Stage: 2 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

Stage: 3 Challenge Level:

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

Can They Be Equal?

Stage: 3 Challenge Level:

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Number Pyramids

Stage: 3 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

More Number Pyramids

Stage: 3 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.