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?

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?

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

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.

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

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

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

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

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

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?

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?

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

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

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?

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

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 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?

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

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

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

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

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

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?

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

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

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?

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

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

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

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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

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?

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

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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.

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

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

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

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?

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

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

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

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