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

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'.

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?

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

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

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

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?

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

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

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?

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

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

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

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.

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

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?

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

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.

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?

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

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

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?

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

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

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

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 can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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

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?

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

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?

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

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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

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

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.

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

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

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

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

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.

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

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?