Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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

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

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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?

Can you find out in which order the children are standing in this line?

My coat has three buttons. How many ways can you find to do up all the buttons?

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

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

How many different shapes can you make by putting four right- angled isosceles triangles together?

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

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

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

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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

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 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?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

Number problems at primary level that require careful consideration.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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?

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

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

This task follows on from Build it Up and takes the ideas into three dimensions!

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

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

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

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

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?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Can you find all the ways to get 15 at the top of this triangle of numbers?

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

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

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

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

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.