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?

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.

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

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

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?

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

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?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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?

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

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

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

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?

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?

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.

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?

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

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?

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

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

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

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?

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

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?

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?

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?

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

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?

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

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 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.

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

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

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.

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?

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

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

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

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

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.

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

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