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?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Frank and Gabriel competed in a 200m race. Interpret the different units used for their times to work out who won.

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

Weekly Problem 41 - 2014

Three straight lines divide an equilateral triangle into seven regions. What is the side length of the original triangle?

How much are you likely to win from a raffle? How many loops will you make with some strings? Here, two guided examples can be found for you to work through.

This drawing shows the train track joining the Train Yard to all the stations labelled from A to S. Find a way for a train to call at all the stations and return to the Train Yard.

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

Use the clues about the shaded areas to help solve this sudoku

How far should the roof overhang to shade windows from the mid-day sun?

Look at the calculus behind the simple act of a car going over a step.

Can you build a distribution with the maximum theoretical spread?

In Classical times the Pythagorean philosophers believed that all things were made up from a specific number of tiny indivisible particles called ‘monads’. Each object contained. . . .

In this beautifully written-up investigation Abhay describes his discovery of a 'theory of cycles'.

Find these 4 numbers, given their mode, median and range.

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

This collection of activities for KS2 children focuses on ratio and proportion.

Cutting a rectangle from a corner to a point on the opposite side splits its area in the ratio 1:2. What is the ratio of a:b?

What is the ratio of the area of the hexagon to the area of the triangle?

An article for teachers which discusses the differences between ratio and proportion, and invites readers to contribute their own thoughts.

Match pairs of cards so that they have equivalent ratios.

Can you work out the ratio b:c given the ratios a:b and a:c?

How many adults would need to join this group of people to reverse this ratio?

Working on these problems will help your students develop a better understanding of ratio, proportion and rates of change.

Working on these problems will help you develop a better understanding of ratio, proportion and rates of change.

A collection of short problems on ratio, proportion and rates of change.

Weekly Problem 39 - 2012

For how many values of $n$ are both $n$ and $\frac{n+3}{n−1}$ integers?

Can you make a curve to match my friend's requirements?

Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

What fractions can you find between the square roots of 65 and 67?

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

A tetrahedron has two identical equilateral triangles faces, of side length 1 unit. The other two faces are right angled isosceles triangles. Find the exact volume of the tetrahedron.

Some graphs grow so quickly you can reach dizzy heights...

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...