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

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

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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

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?

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

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

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

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?

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

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

This activity investigates how you might make squares and pentominoes from Polydron.

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

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.

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

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?

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

An investigation that gives you the opportunity to make and justify predictions.

Find out what a "fault-free" rectangle is and try to make some of your own.

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?

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

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

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?

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

An activity making various patterns with 2 x 1 rectangular tiles.

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

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

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

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?

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?

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Four small numbers give the clue to the contents of the four surrounding cells.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Number problems at primary level that require careful consideration.

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

A Sudoku that uses transformations as supporting clues.

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.