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

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

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

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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.

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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?

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 many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

This challenge extends the Plants investigation so now four or more children are involved.

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

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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

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

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?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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.?

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

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

In this matching game, you have to decide how long different events take.

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?

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?

The pages of my calendar have got mixed up. Can you sort them out?

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

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?