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

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?

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

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?

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

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?

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

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

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

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

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

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

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

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.

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

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?

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?

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

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!

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?

Can you find all the ways to get 15 at the top of this triangle of numbers?

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?

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

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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.

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

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

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?

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.

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

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

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.

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

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.

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

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

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?

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

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

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

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

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

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.

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?

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.