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?

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.

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?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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?

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

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

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

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

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?

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

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

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

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

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 find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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?

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

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 challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

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?

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?

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?

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.

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

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.

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.

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.

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 problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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?

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?

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

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

Find out about Magic Squares in this article written for students. Why are they magic?!

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?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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?

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.

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!