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 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?

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?

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?

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

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

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

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 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.

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

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

This challenge is about finding the difference between numbers which have the same tens digit.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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?

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?

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

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

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

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

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? Many opportunities to work in different ways.

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

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

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

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?

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

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

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

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

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

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

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

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?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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?

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

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?

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

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

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

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