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

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

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?

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

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.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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?

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?

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

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?

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

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

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

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

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

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

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

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

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

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

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?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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

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

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

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

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

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

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

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

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

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.

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

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

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

How many centimetres of rope will I need to make another mat just like the one I have here?

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

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.

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

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Can you find a way of counting the spheres in these arrangements?

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

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?