During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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.

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?

Number problems at primary level that require careful consideration.

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.

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

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.

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

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

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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

What could the half time scores have been in these Olympic hockey matches?

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

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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.?

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

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

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.

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

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

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

Can you replace the letters with numbers? Is there only one solution in each case?

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?

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

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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

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 happens when you round these three-digit numbers to the nearest 100?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

What happens when you round these numbers to the nearest whole number?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Have a go at balancing this equation. Can you find different ways of doing it?

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

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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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?

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 work out some different ways to balance this equation?

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?