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 to have an ordered approach.

What could the half time scores have been in these Olympic hockey matches?

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

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?

How many possible necklaces can you find? And how do you know you've found them all?

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

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

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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?

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?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Can you make square numbers by adding two prime numbers together?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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?

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?

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?

This dice train has been made using specific rules. How many different trains can you make?

These practical challenges are all about making a 'tray' and covering it with paper.

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

How many different triangles can you make on a circular pegboard that has nine pegs?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

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.

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.