How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Number problems at primary level that require careful consideration.

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

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

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

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

Here is a chance to play a version of the classic Countdown Game.

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

If you have only four weights, where could you place them in order to balance this equaliser?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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 problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

A game for 2 players. Practises subtraction or other maths operations knowledge.

Investigate what happens when you add house numbers along a street in different ways.

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

There are nasty versions of this dice game but we'll start with the nice ones...

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

This challenge extends the Plants investigation so now four or more children are involved.

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

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

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

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.