Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

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

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

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

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

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

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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

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

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?

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.

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.

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

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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.

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

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

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

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

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.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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?

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

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

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.

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.

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

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

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

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

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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 put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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

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

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?

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

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?

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?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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?