Can you fill in the empty boxes in the grid with the right shape and colour?

I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

How many generations would link an evolutionist to a very distant ancestor?

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .

What is the same and what is different about these circle questions? What connections can you make?

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?

Sort these mathematical propositions into a series of 8 correct statements.

How would you massage the data in this Chi-squared test to both accept and reject the hypothesis?

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2

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.

Nicholas, Emily, Sam and children from Ysgol Aberdyfi all worked very systematically to solve this problem.

We had lots of impressive solutions to this problem. You were able to explain very clearly why odds and evens are so important.

The nice things about the solutions we received to this problem are that they revealed different insights and different levels of generalisation.

See how graphical methods can be used to solve this rates of change problem and how this simple congfiguration leads to an equation which needs a numerical solution.

Peter Hall was one of four NRICH Teacher Fellows who worked on embedding NRICH materials into their teaching. In this article, he writes about his experiences of working with students at Key Stage Three.

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.