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

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

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

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

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?

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

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

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

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

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.

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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

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?

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.

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

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.

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 players. Practises subtraction or other maths operations knowledge.

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 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?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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?

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?

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

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

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

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?

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

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

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?

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

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

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?

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.

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

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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. . . .

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!

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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

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

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.