Challenge Level

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?

Challenge Level

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Challenge Level

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?

Challenge Level

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Challenge Level

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?

Challenge Level

What is the best way to shunt these carriages so that each train can continue its journey?

Challenge Level

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?

Challenge Level

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

Challenge Level

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

Challenge Level

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?

Challenge Level

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Challenge Level

How many different triangles can you make on a circular pegboard that has nine pegs?

Challenge Level

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?

Challenge Level

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Challenge Level

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Challenge Level

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?

Challenge Level

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?

Challenge Level

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Challenge Level

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Challenge Level

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Challenge Level

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?

Challenge Level

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Challenge Level

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.

Challenge Level

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?

Challenge Level

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?

Challenge Level

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?

Challenge Level

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?

Challenge Level

Can you fit the tangram pieces into the outline of the house?

Challenge Level

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?

Challenge Level

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?

Challenge Level

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?

Challenge Level

Can you find ways of joining cubes together so that 28 faces are visible?

Challenge Level

Exploring and predicting folding, cutting and punching holes and making spirals.

Challenge Level

Can you fit the tangram pieces into the outline of the child walking home from school?

Challenge Level

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Challenge Level

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Challenge Level

Can you fit the tangram pieces into the outline of this teacup?

Challenge Level

Join pentagons together edge to edge. Will they form a ring?

Challenge Level

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?

Challenge Level

Can you fit the tangram pieces into the outline of the butterfly?

Challenge Level

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

Challenge Level

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.

Challenge Level

Can you fit the tangram pieces into the outline of the candle?

Challenge Level

Can you fit the tangram pieces into the outline of the telephone?

Challenge Level

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?

Challenge Level

Can you fit the tangram pieces into the outline of the sports car?

Challenge Level

Can you fit the tangram pieces into the outlines of the telescope and microscope?

Challenge Level

Can you fit the tangram pieces into the outline of Little Fung at the table?