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

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?

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

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

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

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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

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

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

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

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

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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?

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?

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?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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

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

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

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?

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?

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

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

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

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?

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

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 ...?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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?

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.

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

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they 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?

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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

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

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?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?