Investigate the different distances of these car journeys and find out how long they take.

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

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

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

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

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.

This article for teachers suggests ideas for activities built around 10 and 2010.

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

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

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

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

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

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?

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

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

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

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?

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

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

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

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

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

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

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

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

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. . . .

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

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?

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

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?

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?

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?

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.

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.

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?

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

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.

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?

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

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?

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?

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?

This task follows on from Build it Up and takes the ideas into three dimensions!

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?

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

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.