In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

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

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?

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

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?

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

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?

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

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

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

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?

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

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?

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 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?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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?

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

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

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?

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

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

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

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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

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

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

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?

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?

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

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

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

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

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

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

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

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

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

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

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!

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

Number problems at primary level that require careful consideration.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?