Treasure Hunt
Age 7 to 14
Challenge Level
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
Air Nets
Age 7 to 18
Challenge Level
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Hidden Squares
Age 11 to 14
Challenge Level
Can you find the squares hidden on these coordinate grids?
Diminishing Returns
Age 11 to 14
Challenge Level
How much of the square is coloured blue? How will the pattern continue?
Frogs
Age 11 to 14
Challenge Level
How many moves does it take to swap over some red and blue frogs? Do you have a method?
ACE, TWO, THREE...
Age 11 to 14
Challenge Level
Can you picture how to order the cards to reproduce Charlie's card trick for yourself?
Constructing Triangles
Age 11 to 14
Challenge Level
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Shear Magic
Age 11 to 14
Challenge Level
Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?
Seven Squares
Age 11 to 14
Challenge Level
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Quadrilaterals in a Square
Age 11 to 14
Challenge Level
What's special about the area of quadrilaterals drawn in a square?
Route to Infinity
Age 11 to 14
Challenge Level
Can you describe this route to infinity? Where will the arrows take you next?
The Farmers' Field Boundary
Age 11 to 14
Challenge Level
The farmers want to redraw their field boundary but keep the area the same. Can you advise them?
Rolling Around
Age 11 to 14
Challenge Level
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Square It
Age 11 to 16
Challenge Level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Diamond Collector
Age 11 to 16
Challenge Level
Collect as many diamonds as you can by drawing three straight lines.
Marbles in a Box
Age 11 to 16
Challenge Level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Nine Colours
Age 11 to 16
Challenge Level
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Steel Cables
Age 14 to 16
Challenge Level
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Painted Cube
Age 14 to 16
Challenge Level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Attractive Tablecloths
Age 14 to 16
Challenge Level
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
Pick's Theorem
Age 14 to 16
Challenge Level
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Building Tetrahedra
Age 14 to 16
Challenge Level
Can you make a tetrahedron whose faces all have the same perimeter?
Vector Journeys
Age 14 to 18
Challenge Level
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
Coordinated Crystals
Age 16 to 18
Challenge Level
Explore the lattice and vector structure of this crystal.
NRICH is part of the family of activities in the Millennium Mathematics Project.