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

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

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?

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

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 arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

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?

What happens when you add a three digit number to its reverse?

By selecting digits for an addition grid, what targets can you make?

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

Number problems at primary level that may require resilience.

Number problems at primary level that require careful consideration.

How many ways can you find to put in operation signs (+ - x ÷) to make 100?

In this article for primary teachers, Ems outlines how we can encourage learners to be flexible in their approach to calculation, and why this is crucial.

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

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?

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

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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?

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

Play this game to learn about adding and subtracting positive and negative numbers

Find the sum of all three-digit numbers each of whose digits is odd.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

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

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

This Sudoku requires you to do some working backwards before working forwards.

Can you find different ways of creating paths using these paving slabs?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

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

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?