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.

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?

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

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

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

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.

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

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

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.

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

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

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

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?

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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

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

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.

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?

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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?

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

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?

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

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?

Number problems at primary level that require careful consideration.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

Can you explain the strategy for winning this game with any target?

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

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!

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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?

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

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Choose any three by three square of dates on a calendar page...

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

An environment which simulates working with Cuisenaire rods.

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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