What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?
What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
What is the best way to shunt these carriages so that each train can continue its journey?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
How many different triangles can you make on a circular pegboard that has nine pegs?
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
Have a go at this 3D extension to the Pebbles problem.
How will you go about finding all the jigsaw pieces that have one peg and one hole?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
How can you make an angle of 60 degrees by folding a sheet of paper twice?
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
Can you fit the tangram pieces into the outline of the house?
Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
Can you find ways of joining cubes together so that 28 faces are visible?
Exploring and predicting folding, cutting and punching holes and making spirals.
Can you fit the tangram pieces into the outline of the child walking home from school?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
Can you fit the tangram pieces into the outline of this teacup?
Join pentagons together edge to edge. Will they form a ring?
I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
Can you fit the tangram pieces into the outline of the butterfly?
On which of these shapes can you trace a path along all of its edges, without going over any edge twice?
An activity centred around observations of dots and how we visualise number arrangement patterns.
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
Can you fit the tangram pieces into the outline of the candle?
Can you fit the tangram pieces into the outline of the telephone?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
Can you fit the tangram pieces into the outline of the sports car?
Can you fit the tangram pieces into the outlines of the telescope and microscope?
Can you fit the tangram pieces into the outline of Little Fung at the table?