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.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

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

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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?

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

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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

This Sudoku, based on differences. Using the one clue number can you find the solution?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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 pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Try out the lottery that is played in a far-away land. What is the chance of winning?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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

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

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Investigate the different ways you could split up these rooms so that you have double the number.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

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

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?

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.