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?

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?

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

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

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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?

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

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

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

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

This article suggests some ways of making sense of calculations involving positive and negative numbers.

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.

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

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

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

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

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?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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

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?

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

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

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

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

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

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.

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.

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

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!

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

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?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

An environment which simulates working with Cuisenaire rods.

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?

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.

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.

You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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?

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

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