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

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?

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?

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

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

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?

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?

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

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

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?

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

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

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

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?

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

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

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

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?

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

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.

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

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

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?

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

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?

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

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

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

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

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

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?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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?

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

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

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?

Can all unit fractions be written as the sum of two unit fractions?

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

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

How many centimetres of rope will I need to make another mat just like the one I have here?

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.

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .

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?