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

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.

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!

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?

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

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

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?

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?

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?

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

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

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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

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

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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

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

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?

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?

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?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

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?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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?

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.

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.

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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

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?

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?

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.

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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

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!

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

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

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?

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

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?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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.