If you have only four weights, where could you place them in order to balance this equaliser?
Investigate the different distances of these car journeys and find out how long they take.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Here is a chance to play a 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?
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?
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?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
Choose a symbol to put into the number sentence.
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.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
This article for teachers suggests ideas for activities built around 10 and 2010.
Got It game for an adult and child. How can you play so that you know you will always win?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
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?
This is an adding game for two players.
How is it possible to predict the card?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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. . . .
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?
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?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
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?
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?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
There are nasty versions of this dice game but we'll start with the nice ones...
Can you explain how this card trick works?
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 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?
This challenge extends the Plants investigation so now four or more children are involved.
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
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?
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'.
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.