Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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

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?

Find the sum of all three-digit numbers each of whose digits is odd.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

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?

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

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Surprise your friends with this magic square trick.

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Try out this number trick. What happens with different starting numbers? What do you notice?

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers. . . .

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

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

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Are these statements always true, sometimes true or never true?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Nim-7 game for an adult and child. Who will be the one to take the last counter?

This task encourages you to investigate the number of edging pieces and panes in different sized windows.