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30 problems, 2 games, 13 articles, 4 general resources, 2 interactive environments, 40 Lists, 40 from Stage 1, 40 from Stage 2, 17 from Stage 3, 14 from Stage 4, 7 from Stage 5

Can you make arrange Cuisenaire rods so that they make a 'spiral' with right angles at the corners?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

An environment which simulates working with Cuisenaire rods.

Can you find all the different ways of lining up these Cuisenaire rods?

An environment which simulates working with Cuisenaire rods.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Using only the red and white rods, how many different ways are there to make up the other colours of rod?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Using only the red and white rods, how many different ways are there to make up the other colours of rod?

Train game for an adult and child. Who will be the first to make the train?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

A challenging activity focusing on finding all possible ways of stacking rods.

How many different lengths is it possible to measure with a set of three rods?

Pick two rods of different colours. Given an unlimited supply of rods of each of the two colours, how can we work out what fraction the shorter rod is of the longer one?

Three rods of different lengths form three sides of an enclosure with right angles between them. What arrangement maximises the area

In how many ways can you stack these rods, following the rules?

The lower primary tasks in this collection all focus on adding and subtracting.

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

A belt of thin wire, length L, binds together two cylindrical welding rods, whose radii are R and r, by passing all the way around them both. Find L in terms of R and r.

Here are some challenges that you can work on and then see if you can convince someone that your solutions are right! Have a go!

In these activities, you can practise your skills with adding and taking away. You can also solve problems about what happens when we add or take away different numbers!

Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)

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.

Find out what a "fault-free" rectangle is and try to make some of your own.

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

Details of the activities shared with teachers participating in this series of six half days at Wroxham School.

Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?

You and your friends are probably quite good at imagining things and seeing things in lots of different ways. Here you'll put that to use in doing some maths challenges.

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

These KS2 tasks focus on finding patterns and investigating sequences in a systematic way.

Four rods of equal length are hinged at their endpoints to form a rhombus. The diagonals meet at X. One edge is fixed, the opposite edge is allowed to move in the plane. Describe the locus of. . . .

There's more room to manoeuvre than you might initially imagine!

Bernard Bagnall describes how to get more out of some favourite NRICH investigations.

We have four rods of equal lengths hinged at their endpoints to form a rhombus ABCD. Keeping AB fixed we allow CD to take all possible positions in the plane. What is the locus (or path) of the point. . . .

General-purpose interactives for use in primary schools

What happens when you split an object or a few objects into different piles? Try these activities to find out!

This brief article, written for upper primary students and their teachers, explains what the Young Mathematicians' Award is and links to all the related resources on NRICH.

Make a cube out of straws and have a go at this practical challenge.