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?

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

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

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?

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

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

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.

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

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

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

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 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.

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

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?

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?

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?

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

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

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

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

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

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

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?

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?

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

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

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

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

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?

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

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

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

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

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

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

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

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

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.

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.

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?

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.