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

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 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?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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

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

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

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

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

An investigation that gives you the opportunity to make and justify predictions.

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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?

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

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?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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?

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

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

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

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

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

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?

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

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

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

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

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

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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?

On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?

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?

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

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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.

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?