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?

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

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

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

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

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

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

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

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.

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

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

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?

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?

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

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

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

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

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?

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?

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 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.

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

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?

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.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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?

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

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.

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

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

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

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

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?

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

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

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

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

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.

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

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

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

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

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

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