What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Follow the diagrams to make this patchwork piece, based on an
octagon in a square.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
A huge wheel is rolling past your window. What do you see?
Which hexagons tessellate?
A design is repeated endlessly along a line - rather like a stream
of paper coming off a roll. Make a strip that matches itself after
rotation, or after reflection
When a strip has vertical symmetry there always seems to be a
second place where a mirror line could go. Perhaps you can find a
design that has only one mirror line across it. Or, if you thought
that. . . .
I noticed this about streamers that have rotation symmetry : if
there was one centre of rotation there always seems to be a second
centre that also worked. Can you find a design that has only. . . .
Draw three equal line segments in a unit circle to divide the
circle into four parts of equal area.
Make a footprint pattern using only reflections.
Nick Lord says "This problem encapsulates for me the best features
of the NRICH collection."
Isabelle, Henry and Will describe some journeys that could fit the shape of the paths drawn.
Here are some imaginative stories that fit the graphs. Perhaps you can make up a different one?
Look at this cunning detective work which helped to unravel the mystery.
Great reasoning from Alice who knows exactly when the speed is zero even if the motion doesn't stop in the way you might expect.
Jenny Murray describes the mathematical processes behind making patchwork in this article for students.
Creating designs with squares - using the REPEAT command in LOGO.
This requires some careful thought on angles
A Sudoku that uses transformations as supporting clues.
Toni Beardon has chosen this article introducing a rich area for
practical exploration and discovery in 3D geometry
Patterns that repeat in a line are strangely interesting. How many types are there and how do you tell one type from another?
Some simple ideas about graph theory with a discussion of a proof
of Euler's formula relating the numbers of vertces, edges and faces
of a graph.
A gallery of beautiful photos of cast ironwork friezes in Australia with a mathematical discussion of the classification of frieze patterns.