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

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

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

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?

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

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

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

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

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

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?

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

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?

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.

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

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

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

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?

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

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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?

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.

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

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

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

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

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?

Can you work out how to win this game of Nim? Does it matter if you go first or second?

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

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?

A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

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

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?

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

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

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?

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.

It starts quite simple but great opportunities for number discoveries and patterns!

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

What happens when you round these numbers to the nearest whole number?

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

Stop the Clock game for an adult and child. How can you make sure you always win this game?

These tasks give learners chance to generalise, which involves identifying an underlying structure.

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