What two-digit numbers can you make with these two dice? What can't you make?

Can you find the chosen number from the grid using the clues?

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

This challenge is about finding the difference between numbers which have the same tens digit.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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?

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

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?

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

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

Can you work out some different ways to balance this equation?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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

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

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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.

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

In how many ways can you stack these rods, following the rules?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

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

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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.

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?

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!

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?