15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

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

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

Got It game for an adult and child. How can you play so that you know you will always win?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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

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. . . .

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

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

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?

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

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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.

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?

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?

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

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

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

Surprise your friends with this magic square trick.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

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.

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?

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

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Find out about Magic Squares in this article written for students. Why are they magic?!

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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

Delight your friends with this cunning trick! Can you explain how it works?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Try out this number trick. What happens with different starting numbers? What do you notice?

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

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.

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

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

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?

You have 5 darts and your target score is 44. How many different ways could you score 44?

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

Find the next number in this pattern: 3, 7, 19, 55 ...

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

Number problems at primary level that may require resilience.