Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .

Draw a line (considered endless in both directions), put a point somewhere on each side of the line. Label these points A and B. Use a geometric construction to locate a point, P, on the line,. . . .

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

Find a connection between the shape of a special ellipse and an infinite string of nested square roots.

Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers.

Cong from St Peter's RC School shaded the hexagon grid which helped him look for solutions to this problem.

Curt produced a clear demonstration of the fundamental result he wanted to use to proof the proposed relationship.

Proof does have a place in Primary mathematics classrooms, we just need to be clear about what we mean by proof at this level.

This game is known as Pong hau k'i in China and Ou-moul-ko-no in Korea. Find a friend to play or try the interactive version online.

An iterative method for finding the value of the Golden Ratio with explanations of how this involves the ratios of Fibonacci numbers and continued fractions.

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.