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

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

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

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

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?

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?

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

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 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?

Benâ€™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?

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

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

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?

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

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

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

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?

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

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

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

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

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

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

This challenge asks you to imagine a snake coiling on itself.

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?

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

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

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

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

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

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?

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

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

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

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

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.

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?

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

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

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?

I added together some of my neighbours house numbers. Can you explain the patterns I noticed?

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

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

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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.

This activity involves rounding four-digit numbers to the nearest thousand.

What happens when you round these three-digit numbers to the nearest 100?