Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

A task which depends on members of the group noticing the needs of others and responding.

Can you solve this problem involving powers and quadratics?

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .

Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.

Surprising numerical patterns can be explained using algebra and diagrams...

The curve $y=x^2−6x+11$ is rotated through $180^\circ$ about the origin. What is the equation of the new curve?

A lune is the area left when part of a circle is cut off by another circle. Can you work out the area?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .

What's special about the area of quadrilaterals drawn in a square?

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

Four small numbers give the clue to the contents of the four surrounding cells.

Resources to accompany Charlie's workshop with teachers from overseas.

Weekly Problem 27 - 2014

Four congruent isosceles trapezia are placed in a square. What fraction of the square is shaded?

An activity causing pupils to seriously consider and create ways of quartering shapes.

Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.

See how 4 dimensional quaternions involve vectors in 3-space and how the quaternion function F(v) = nvn gives a simple algebraic method of working with reflections in planes in 3-space.

Find out how the quaternion function G(v) = qvq^-1 gives a simple algebraic method for working with rotations in 3-space.

Can you find the length of the third side of this triangle?

25 students are queuing in a straight line. How many are there between Julia and Jenny?

This resource explores the rich mathematics in activities for young children involing queues.

What is the quickest route across a ploughed field when your speed around the edge is greater?

32 x 38 = 30 x 40 + 2 x 8; 34 x 36 = 30 x 40 + 4 x 6; 56 x 54 = 50 x 60 + 6 x 4; 73 x 77 = 70 x 80 + 3 x 7 Verify and generalise if possible.

Can you work out how many quizzes have to be played before we have a winner?

Jack does a 20-question quiz. How many questions didn't he attempt?

This problem explores the biology behind Rudolph's glowing red nose.