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

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?

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?

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

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

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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?

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?

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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.

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

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

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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?

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

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?

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

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?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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

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?

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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

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

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

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!

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.

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

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.

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

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

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

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

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?

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

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

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

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?