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

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

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?

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?

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

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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

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

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

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.

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?

Can you find a way of counting the spheres in these arrangements?

Watch this animation. What do you see? Can you explain why this happens?

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

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

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?

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

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

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?

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?

Find out what a "fault-free" rectangle is and try to make some of your own.

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

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

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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?

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

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

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

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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.

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

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

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?

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

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

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?

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

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

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?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

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

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

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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

Here are two kinds of spirals for you to explore. What do you notice?

An investigation that gives you the opportunity to make and justify predictions.

This challenge encourages you to explore dividing a three-digit number by a single-digit number.