My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Can you draw a square in which the perimeter is numerically equal to the area?

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

These practical challenges are all about making a 'tray' and covering it with paper.

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Can you use the information to find out which cards I have used?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

How many ways can you find of tiling the square patio, using square tiles of different sizes?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

Investigate the different ways you could split up these rooms so that you have double the number.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Try out the lottery that is played in a far-away land. What is the chance of winning?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.